Polar code construction method, device and equipment based on parallel polarization of underwater acoustic channel

Abstract

The present invention provides a polarization code construction method, apparatus, and device based on parallel polarization of underwater acoustic channels. The method comprises: transmitting a first OFDM signal containing a polarization code encoding sequence at a transmitting end to a receiving end via an OFDM underwater acoustic communication system; performing polarization processing on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and performing reliability analysis on the polarization sub-channels to obtain a polarization code construction result; combining characteristic information of the polarization code construction result to determine whether the sequence to be transmitted meets the call conditions of the polarization code construction result; if so, selecting a target polarization sub-channel according to the polarization code construction result to transmit the sequence to be transmitted from the transmitting end to the receiving end; if not, repeating the process to obtain a new polarization code construction result. The present invention can significantly reduce the communication bit error rate to ensure reliable data transmission, and can also effectively improve the high complexity of polarization code construction caused by the need for repeated measurements in existing technologies.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic positioning and underwater acoustic communication, and in particular to a polarization code construction method, device and equipment based on parallel polarization of an underwater acoustic channel. Background Art

[0002] With the rapid development of communications technology, polar codes, as a new channel coding technique, have attracted widespread attention due to their theoretical ability to reach the Shannon limit. The core concept of polar codes is to leverage the channel polarization phenomenon to transform a set of independent channels into a set of polarized channels, where some channels approach perfection and others approach complete noise. In practical applications, the construction of polar codes must be tailored to specific channel conditions to ensure reliable data transmission.

[0003] In existing technologies, polar code construction methods are typically based on channel estimation and polarization transformation. Specifically, the channel must first be measured to obtain channel state information. Polarization transformation is then performed based on this information to generate the corresponding polar code. However, due to the complexity and variability of channel conditions, existing polar code construction methods suffer from high communication bit error rates in practical applications, failing to guarantee reliable data transmission. Furthermore, to adapt to different communication scenarios, channel measurement and polar code construction must be repeated in different scenarios. This complicates the polar code construction process, increasing the difficulty and cost of system implementation. Summary of the Invention

[0004] In view of this, the object of the present invention is to provide a polar code construction method, apparatus, and device based on parallel polarization of an underwater acoustic channel. These methods can significantly reduce the communication bit error rate to ensure reliable data transmission. They can also effectively improve the high complexity of polar code construction caused by the need for repeated measurements in the existing technology.

[0005] In a first aspect, the present invention provides a polar code construction method based on parallel polarization of an underwater acoustic channel, which is applied to an OFDM underwater acoustic communication system. The OFDM underwater acoustic communication system includes a transmitter, an OFDM parallel underwater acoustic channel, and a receiver. The method includes:

[0006] Step 1: At the transmitting end, a current sample transmission sequence is encoded to obtain a polar code sequence, and a first OFDM signal containing the polar code sequence is sent to the receiving end via an OFDM underwater acoustic communication system.

[0007] Step 2: Polarization processing is performed on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and reliability analysis is performed on the polarization sub-channels based on the first OFDM signal sent by the transmitter and the first OFDM signal received by the receiver to obtain a polar code construction result;

[0008] Step 3: For any sequence to be transmitted at the transmitter, the characteristic information of the polar code construction result is combined to determine whether the sequence to be transmitted meets the call conditions of the polar code construction result. The characteristic information is used to describe the timeliness and reliability distribution of the polar code construction result.

[0009] In step 4, if the result of step 3 is yes, a target polarization subchannel is selected based on the polarization code construction result, and the sequence to be transmitted is sent from the transmitter to the receiver. If the result of step 3 is no, steps 1 and 2 are repeated to obtain a new polarization code construction result. Based on the new polarization code construction result, the sequence to be transmitted is sent from the transmitter to the receiver through the target polarization subchannel.

[0010] In one embodiment, the calling conditions include:

[0011] The transmission time of the sequence to be transmitted is within the valid time of the polar code construction result;

[0012] The relative speed between the transmitter and receiver at the time of transmission matches the relative speed scenario of the polar code construction result;

[0013] The code length of the sequence to be transmitted matches the code length scenario of the polar code construction result.

[0014] In one embodiment, timeliness is used to describe the validity period of a polar code construction result, and the reliability distribution law is used to describe relative speed scenarios and code length scenarios matched by the polar code construction result. The relative speed scenario includes multiple motion speeds associated with the polar code construction result, and the code length scenario includes multiple code lengths associated with the polar code construction result.

[0015] Combined with the characteristic information of the polar code construction result, it is determined whether the sequence to be transmitted meets the calling conditions of the polar code construction result, including:

[0016] If the transmission time of the sequence to be transmitted is within the valid time of the polar code construction result; the relative motion speed between the transmitting end and the receiving end at the transmission time is consistent with any of the multiple relative motion speeds associated with the polar code construction result; and the code length of the sequence to be transmitted is consistent with any of the multiple code lengths associated with the polar code construction result, then it is determined that the sequence to be transmitted meets the calling conditions of the polar code construction result.

[0017] In one embodiment, performing reliability analysis on a polar subchannel based on a first OFDM signal sent by a transmitting end and a first OFDM signal received by a receiving end to obtain a polar code construction result includes:

[0018] After performing BPSK modulation on the first OFDM signal received at the receiving end, recursively decoding the signal using a serial cancellation decoder based on the factor graph and the path metric is performed to determine a log-likelihood value corresponding to the polarization subchannel, thereby determining a log-likelihood ratio corresponding to the polarization subchannel;

[0019] The Bhattacharyya parameter estimate corresponding to the polarimetric subchannel is determined based on the log-likelihood ratio. The Bhattacharyya parameter estimate is negatively correlated with the reliability of the polarimetric subchannel.

[0020] Multiple target polarimetric subchannels are selected in ascending order of Bhattacharyya parameter estimates to obtain a polar code construction result. The target polarimetric subchannel is used to transmit information bits, and the remaining polarimetric subchannels are used to transmit frozen bits.

[0021] In one embodiment, recursive decoding is performed based on a path metric using a serial cancellation decoder according to a factor graph to determine a log-likelihood value corresponding to a polarization subchannel, including:

[0022] The log-likelihood value corresponding to the polarization sub-channel is determined according to the following formula:

[0023] ;

[0024] in, is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the bit decision value.

[0025] In one embodiment, determining a Bhattacharyya parameter estimate corresponding to a polarimetric subchannel based on a log-likelihood ratio includes:

[0026] If the log-likelihood ratio corresponding to the polarization channel is greater than or equal to 1, the square root of the reciprocal of the log-likelihood ratio is taken as the index value corresponding to the polarization channel. Alternatively, if the log-likelihood ratio corresponding to the polarization channel is less than 1, the square root of the log-likelihood ratio is taken as the index value corresponding to the polarization channel.

[0027] The expected value of the indicator is obtained by statistically analyzing all the indicator values, and the expected value of the indicator is used as the estimated value of the Bhattacharyya parameter corresponding to the polarization sub-channel.

[0028] In one embodiment, the method further comprises:

[0029] Performing an encoding operation on the current sample transmission sequence at the transmitting end to obtain a polarization code sequence, and sending a second OFDM signal containing the polarization code sequence to the receiving end via the OFDM underwater acoustic communication system;

[0030] Polarization processing is performed on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels;

[0031] Determining, by using a channel transfer probability function and its statistical characteristics, channel transfer probability values ​​corresponding to subcarriers included in the OFDM parallel underwater acoustic channel based on the second OFDM signal sent by the transmitter and the second OFDM signal received by the receiver, and determining a channel transfer probability value corresponding to the polarization subchannel based on the channel transfer probability values ​​corresponding to the subcarriers;

[0032] Based on the channel transition probability values ​​corresponding to the subcarriers and the polarization subchannels, the channel capacity and Bhattacharyya parameter corresponding to the subcarriers and the channel capacity and Bhattacharyya parameter corresponding to the polarization subchannels are determined respectively, which are used to determine the reliability distribution law corresponding to the polarization subchannels.

[0033] In a second aspect, the present invention further provides a polar code construction device based on parallel polarization of an underwater acoustic channel, which is applied to an OFDM underwater acoustic communication system. The OFDM underwater acoustic communication system includes a transmitter, an OFDM parallel underwater acoustic channel, and a receiver. The device includes:

[0034] A first signal transmission module is configured to perform an encoding operation on the current sample transmission sequence at the transmitting end to obtain a polarization code sequence, and transmit a first OFDM signal including the polarization code sequence to a receiving end via the OFDM underwater acoustic communication system;

[0035] a polarization code construction module, configured to perform polarization processing on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and perform reliability analysis on the polarization sub-channels based on the first OFDM signal sent by the transmitter and the first OFDM signal received by the receiver to obtain a polarization code construction result;

[0036] A call judgment module is used to determine whether any sequence to be transmitted at the transmitter meets the call conditions for the polar code construction result based on the characteristic information of the polar code construction result. The characteristic information is used to describe the timeliness and reliability distribution of the polar code construction result.

[0037] The second signal transmission module is configured to, if the judgment result of calling the judgment module is yes, select a target polarization sub-channel according to the polarization code construction result, and send the sequence to be transmitted from the transmitting end to the receiving end. If the judgment result of calling the judgment module is no, repeatedly execute the first signal transmission module to the polarization code construction module to obtain a new polarization code construction result, and send the sequence to be transmitted from the transmitting end to the receiving end through the target polarization sub-channel according to the new polarization code construction result.

[0038] In a third aspect, the present invention further provides an electronic device including a processor and a memory, wherein the memory stores computer-executable instructions executable by the processor, and the processor executes the computer-executable instructions to implement any of the polarization code construction methods based on parallel polarization of an underwater acoustic channel provided in the first aspect.

[0039] In a fourth aspect, the present invention further provides a computer-readable storage medium storing computer-executable instructions. When the computer-executable instructions are called and executed by a processor, the computer-executable instructions cause the processor to implement any one of the polarization code construction methods based on parallel polarization of an underwater acoustic channel provided in the first aspect.

[0040] The present invention provides a polarization code construction method, device and equipment based on parallel polarization of underwater acoustic channels, which are applied to an OFDM underwater acoustic communication system. The OFDM underwater acoustic communication system includes a transmitter, an OFDM parallel underwater acoustic channel and a receiver, including: step 1, encoding the current sample transmission sequence at the transmitter to obtain a polarization code sequence, and sending the first OFDM signal containing the polarization code sequence to the receiver via the OFDM underwater acoustic communication system; step 2, polarization processing the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and polarization processing the polarization sub-channels based on the first OFDM signal sent by the transmitter and the first OFDM signal received by the receiver. Reliability analysis obtains a polar code construction result. Step 3: For any sequence to be transmitted at the transmitter, the characteristic information of the polar code construction result is combined to determine whether the sequence to be transmitted meets the call conditions of the polar code construction result. The characteristic information is used to describe the timeliness and reliability distribution of the polar code construction result. Step 4: If the result of step 3 is yes, a target polarization sub-channel is selected based on the polar code construction result to send the sequence to be transmitted from the transmitter to the receiver. If the result of step 3 is no, steps 1 and 2 are repeated to obtain a new polar code construction result. Based on the new polarization code construction result, the sequence to be transmitted is sent from the transmitter to the receiver via the target polarization sub-channel. The above method uses the first OFDM signal sent by the transmitting end and the first OFDM signal received by the receiving end to perform reliability analysis on the polarization sub-channel obtained by the OFDM parallel underwater acoustic channel plan. Combined with characteristic information such as the timeliness and reliability distribution pattern of the polarization code construction result, it is determined whether the polarization code construction result can be called. If the conditions are met, the transmission of the to-be-transmitted sequence can be directly implemented according to the polarization code construction result. The present invention can significantly reduce the communication bit error rate to ensure reliable data transmission, and can also effectively improve the high complexity of polarization code construction caused by the need for repeated measurements in the prior art.

[0041] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or understood by practicing the present invention. The purposes and other advantages of the present invention are realized and obtained by the structures particularly pointed out in the description, claims and drawings.

[0042] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 A schematic diagram of a flow chart of a polar code construction method based on parallel polarization of an underwater acoustic channel provided by an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of an OFDM parallel underwater acoustic channel model provided by an embodiment of the present invention;

[0046] Figure 3 A schematic diagram of the processing process of a transmitting end of a polar code encoded OFDM underwater acoustic communication system provided by an embodiment of the present invention;

[0047] Figure 4 A schematic diagram of the processing process of a receiving end of a polar code encoded OFDM underwater acoustic communication system provided by an embodiment of the present invention;

[0048] Figure 5 A schematic diagram of a single-step conversion process of parallel channels provided by an embodiment of the present invention;

[0049] Figure 6 A schematic diagram of parallel channel polarization provided by an embodiment of the present invention;

[0050] Figure 7 A schematic diagram of a channel situation provided by an embodiment of the present invention;

[0051] Figure 8 A schematic diagram of a channel scattering function under different relative motion speeds provided by an embodiment of the present invention;

[0052] Figure 9 The system performance in different time periods when the relative motion speed is 0.029 m / s is provided in an embodiment of the present invention;

[0053] Figure 10 The system performance in different time periods when the relative motion speed is 0.29 m / s is provided in an embodiment of the present invention;

[0054] Figure 11 The system performance in different time periods when the relative motion speed is 1.45 m / s is provided in an embodiment of the present invention;

[0055] Figure 12The present invention provides an embodiment of the present invention for providing polarization results and reliability distribution of OFDM subchannels at different motion speeds;

[0056] Figure 13 The embodiment of the present invention provides a channel polarization result and reliability distribution at different speeds when N=256;

[0057] Figure 14 Polarization results and reliability distribution of OFDM subchannels with different code lengths provided by an embodiment of the present invention;

[0058] Figure 15 A schematic diagram of channel parameters when the relative motion speed is 2.9 m / s provided in an embodiment of the present invention;

[0059] Figure 16 A schematic diagram of polarization results and reliability distribution of polarized channels at different times provided by an embodiment of the present invention;

[0060] Figure 17 A schematic diagram of channel characteristics provided by an embodiment of the present invention;

[0061] Figure 18 Polarization results and reliability distribution of OFDM subchannels with different code lengths provided by an embodiment of the present invention;

[0062] Figure 19 A schematic diagram of an embodiment of the present invention showing a method for predicting a polarization construction result with a code length of 1024 using a code construction result with a code length of 512 and a code rate of 0.5;

[0063] Figure 20 A schematic structural diagram of a polar code construction device based on parallel polarization of an underwater acoustic channel provided by an embodiment of the present invention;

[0064] Figure 21 A schematic structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0066] Polar codes, with their high reliability, practical linear coding complexity, flexible code length and rate adjustment, and theoretically unique ability to reach the Shannon limit, have revitalized the field of channel coding. Their research has expanded across numerous channel types and application areas, and has been incorporated into the 5G standard. Currently, research on polar codes in OFDM (Orthogonal Frequency Division Multiplexing) underwater acoustic communications focuses primarily on code construction, multi-user communication, and joint coded modulation. Because existing polar code construction methods are mostly channel-specific, the Bhattacharyya (BA) bound method and the Monte Carlo (MC) method are commonly used to construct polar codes in OFDM underwater acoustic channels. However, the former does not guarantee strict bounds, while the latter requires numerous Monte Carlo simulation iterations. Subsequent research has employed the Gaussian approximation (GA) method for polar code construction. However, due to the need for decision feedback equalization (DFE) and hybrid automatic repeat request (HARQ) mechanisms, implementation is relatively complex. Furthermore, a polar code construction method based on MCGA was proposed for OFDM UWA channels. In terms of joint coding modulation, simulations and lake tests verified the performance of polar code-modulated bit-interleaved coded modulation (BICM) and polar code modulation combined with multilevel coded modulation (MLCM) underwater acoustic communication systems under different mapping rules. In terms of multi-user coded communication, polar codes were used to create a nested code structure and divide it into multiple subsets for dual-user OFDM UWC, which was verified through simulations and water tank experiments. However, no research has yet theoretically verified the polarization of OFDM underwater acoustic parallel channels and its relationship to the underwater acoustic channel.

[0067] For finite code lengths, the construction and encoding of polarization codes depends on the reliability of the polarization channel after incomplete channel polarization. The original polarization theory for polarization codes, unlike OFDM underwater acoustic channel polarization, is designed for serial, identical channel replicas in a binary input discrete memoryless channel (BDMC). Polarization theory for OFDM parallel underwater acoustic channels has yet to be established. Furthermore, the parameters and state of the underwater acoustic channel also influence the polarization results. Considering the spatiotemporal variations in underwater acoustic channel parameters and statistical characteristics in different communication scenarios, existing polarization code construction methods require a large number of real-time, repeated measurements of channel polarization, which complicates the polarization code construction process and increases the difficulty and cost of system implementation. Therefore, it is necessary to further clarify the time-frequency variations of channel polarization and the relationship between channel parameter variations. To simplify the code construction process and avoid repeated evaluations of polarization sub-channel reliability, it is essential to study channel polarization phenomena and the variations in polarization sub-channel reliability. However, to date, no research has specifically addressed this issue.

[0068] Based on the underwater acoustic channel model and the statistical characteristics of OFDM parallel channels, the embodiments of the present invention extend the original channel polarization theory to the OFDM parallel underwater acoustic channel communication scenario, establish an OFDM parallel underwater acoustic channel polarization model, and based on this polarization channel theoretical model, through simulation and lake tests, obtain the reliability distribution of the polarization subchannel after incomplete polarization transformation of the time-varying OFDM parallel underwater acoustic communication channel. The reliability and time-frequency variation of the channel polarization under different code lengths, frequencies, and channel parameters are also studied. A practical polarization code construction method is established, providing a reference for the simplified design of polarization code construction. Based on this phenomenon, a practical and simple polarization code construction scheme is proposed. Simulation and lake test verification show that the reliability of the OFDM underwater acoustic polarimetric subchannel exhibits polarization characteristics, which is consistent with the theoretical model of the present invention. The reliability of the polarimetric subchannel is affected by time-varying parameters such as multipath and Doppler in the underwater acoustic channel and is time-sensitive. Using the polar code construction method and channel coding proposed in the present invention within the effective period can effectively ensure reliable data transmission. The reliability of the polarimetric subchannel under Doppler can be applied to channel communications under large Doppler without repeated measurements. At the same time, when the same channel frequency band is divided into different code lengths, the channel reliability distribution is consistent, eliminating the need to repeatedly measure the polarimetric subchannel reliability for different code lengths, further simplifying the polarimetric code construction.

[0069] Channel polarization is the foundation and prerequisite for the application of polarization channel coding. The construction and coding of polarization codes are both based on channel polarization phenomena. OFDM technology, a representative multi-carrier modulation technique and a type of frequency-division multiplexing (FDM), achieves reasonable spectral efficiency and supports high data rates by dividing the available bandwidth into multiple narrower frequency bands and transmitting signals simultaneously on multiple orthogonal subcarriers. It effectively reduces inter-symbol interference (ISI) and enables robust communication in multipath channels. It can perform equalization in the frequency domain, eliminating the need for complex time-domain equalizers at the receiver, making it an effective alternative to wideband single-carrier communication systems. The integration of high-performance, low-power digital signal processors, along with advances in acoustic channel modeling and communication theory, has enabled the emergence of several OFDM-based commercial and scientific underwater applications.

[0070] Based on this, the present invention implements a method, device, and equipment for constructing polarization codes based on parallel polarization of underwater acoustic channels, which can significantly reduce the communication bit error rate to ensure reliable data transmission. It can also effectively improve the problem of high complexity in polarization code construction caused by the need for repeated measurements in the existing technology.

[0071] To facilitate understanding of this embodiment, a polar code construction method based on parallel polarization of an underwater acoustic channel disclosed in an embodiment of the present invention is first described in detail. The method is applied to an OFDM underwater acoustic communication system. The OFDM underwater acoustic communication system includes a transmitter, an OFDM parallel underwater acoustic channel, and a receiver. Figure 1 The flowchart of a polar code construction method based on parallel polarization of an underwater acoustic channel is shown. The method mainly includes the following steps 1 to 4:

[0072] Step 1: At the transmitting end, a coding operation is performed on the current sample transmission sequence to obtain a polarization code sequence, and a first OFDM signal including the polarization code sequence is sent to the receiving end via an OFDM underwater acoustic communication system.

[0073] In one example, after encoding, BPSK (Binary Phase Shift Keying) mapping, OFDM modulation and other processing are performed on the current sample transmission sequence at the transmitting end, a first OFDM signal containing a polarization code coding sequence is obtained, which is transmitted into the OFDM underwater acoustic communication system, and the OFDM underwater acoustic communication system sends it to the receiving end, which will receive the first OFDM signal. It should be noted that due to the presence of signal gain and noise in the OFDM underwater acoustic communication system, the first OFDM signal sent by the transmitting end is not completely consistent with the first OFDM signal received by the receiving end.

[0074] Step 2: Polarization processing is performed on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and reliability analysis is performed on the polarization sub-channels based on the first OFDM signal sent by the transmitter and the first OFDM signal received by the receiver to obtain a polarization code construction result.

[0075] In one example, an OFDM underwater acoustic communication system includes multiple parallel subcarriers, which are combined and decomposed to produce multiple polarimetric subchannels. A serial cancellation decoder performs recursive decoding based on a factor graph and path metrics to determine the log-likelihood ratios corresponding to the polarimetric subchannels. This log-likelihood ratios are used to estimate the Bhattacharyya parameters for the polarimetric subchannels. The Bhattacharyya parameter estimates are then used to evaluate the reliability of the polarimetric subchannels, resulting in the polar code construction. The target polarimetric subchannel is used to transmit information bits, while the remaining polarimetric subchannels are used to transmit frozen bits.

[0076] Step 3: For any sequence to be transmitted at the transmitting end, the characteristic information of the polar code construction result is combined to determine whether the sequence to be transmitted meets the calling conditions of the polar code construction result.

[0077] The characteristic information is used to describe the timeliness and reliability distribution of the polar code construction result. The timeliness describes the effective period of the polar code construction result, and the reliability distribution describes the relative speed and code length scenarios that the polar code construction result matches. The call conditions include: the transmission time of the sequence to be transmitted is within the effective period of the polar code construction result; the relative motion speed between the transmitter and receiver at the transmission time matches the relative speed scenario of the polar code construction result, which includes multiple relative motion speeds associated with the polar code construction result; and the code length of the sequence to be transmitted matches the code length scenario of the polar code construction result, which includes multiple code lengths associated with the polar code construction result.

[0078] In step 4, if the result of step 3 is yes, a target polarization subchannel is selected based on the polarization code construction result, and the sequence to be transmitted is sent from the transmitter to the receiver. If the result of step 3 is no, steps 1 and 2 are repeated to obtain a new polarization code construction result. Based on the new polarization code construction result, the sequence to be transmitted is sent from the transmitter to the receiver through the target polarization subchannel.

[0079] The polar code construction method based on parallel polarization of an underwater acoustic channel provided in an embodiment of the present invention uses a first OFDM signal sent by a transmitter and a first OFDM signal received by a receiver to perform reliability analysis on the polarization sub-channels obtained from the OFDM parallel underwater acoustic channel plan. The method then determines whether the polar code construction result can be used, combining characteristic information such as the timeliness and reliability distribution of the polar code construction result. If the conditions are met, the sequence to be transmitted can be directly transmitted according to the polar code construction result. This embodiment of the present invention can significantly reduce the communication bit error rate, ensuring reliable data transmission, and effectively improve the high complexity of polar code construction caused by the need for repeated measurements in the prior art.

[0080] Before executing steps 1 to 4 above, it is necessary to establish a theoretical model for the characteristic information of the polar code subchannel and verify the polarization theory. This includes:

[0081] (1) At the transmitting end, the current sample transmission sequence is encoded to obtain a polarization code sequence, and the second OFDM signal containing the polarization code sequence is sent to the receiving end via the OFDM underwater acoustic communication system.

[0082] (2) Polarization processing is performed on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels.

[0083] (3) Through the channel transfer probability function and its statistical characteristics, based on the second OFDM signal sent by the transmitter and the second OFDM signal received by the receiver, the channel transfer probability value corresponding to the subcarrier contained in the OFDM parallel underwater acoustic channel is determined, and the channel transfer probability value corresponding to the polarization subchannel is determined based on the channel transfer probability value corresponding to the subcarrier.

[0084] (4) Based on the channel transfer probability values ​​corresponding to the subcarriers and the channel transfer probability values ​​corresponding to the polarization subchannels, the channel capacity and Bhattacharyya parameters corresponding to the subcarriers and the channel capacity and Bhattacharyya parameters corresponding to the polarization subchannels are determined respectively to determine the reliability distribution law corresponding to the polarization subchannels.

[0085] To facilitate understanding of (1) to (4), the embodiments of the present invention explain the principles involved in the above processes.

[0086] In one example, in the OFDM parallel underwater acoustic channel: transmitted to the receiving end via the OFDM parallel underwater acoustic channel, see Figure 2 The schematic diagram of an OFDM parallel underwater acoustic channel model is shown in FIG. The OFDM parallel underwater acoustic channel can be regarded as multiple parallel channels located on each subcarrier, that is, , on each orthogonal sub-channel, 、 、 and Respectively represent symbol interval The transmitted signal, received signal, channel gain and noise on each subcarrier are determined, and each parallel channel has a different and independent channel transfer probability function.

[0087] In one example, at the transmitter: see Figure 3 The figure shows a processing diagram of the transmitter of a polar code encoded OFDM underwater acoustic communication system. After binary input, it will undergo polar code encoding, BPSK modulation, S / P (serial / parallel conversion), subcarrier allocation, pilot insertion, IFFT (inverse fast Fourier transform), P / S (parallel / serial conversion), adding CP (cyclic prefix), adding synchronization guard interval, etc., and then the second OFDM signal will be sent to the OFDM parallel underwater acoustic channel.

[0088] For example, consider the OFDM parallel underwater acoustic channel containing subcarriers, the data sequence after BPSK modulation is expressed as ,Through the inverse discrete Fourier transform (IDFT), the sequence samples of the time domain OFDM signal can be defined as:

[0089] Formula 1: ;

[0090] in, represents the imaginary part, The meaning is the subcarrier number index value.

[0091] After adding a cyclic prefix, pulse shaping and digital-to-analog conversion (DAC) to the sequence samples of the time-domain OFDM signal, a second OFDM signal containing a polar code sequence is transmitted through the OFDM parallel underwater acoustic channel.

[0092] In one example, at the receiving end: see Figure 4 The figure shows a schematic diagram of the processing process of the receiving end of a polar code encoded OFDM underwater acoustic communication system. After the OFDM parallel underwater acoustic channel sends the signal to the receiving end, the receiving end removes the CP, S / P, FFT (Fast Fourier Transform), channel estimation and equalization, P / S, BPSK demodulation, polar code decoding and other processes.

[0093] Assume that the channel impulse response of the multipath fading OFDM parallel underwater acoustic channel is modeled as Finite Impulse Response (FIR) filter with strip taps , , the frequency domain channel impulse response can be expressed as:

[0094] Formula 2: :

[0095] Assuming that the maximum delay spread of the channel is less than the length of the cyclic prefix, and ignoring inter-symbol interference (ISI) and inter-subcarrier interference (ICI), at the receiving end, after analog-to-digital conversion (A / D), removal of the cyclic prefix, and discrete Fourier transform (DFT), the second OFDM signal received by the receiving end can be expressed as:

[0096] Formula 3: ;

[0097] Among them, assuming has zero mean and variance The second received OFDM signal can be expressed in matrix vector form as follows:

[0098] Formula 4: ;

[0099] in, is included item The Fourier matrix of is the conjugate transpose, 、 and They are 、 and The signal vector matrix. is a circulant matrix, expressed as:

[0100] Formula 5: ;

[0101] Notice is a unitary matrix, is a circulant matrix, so the channel frequency domain response is a diagonal matrix, which can be expressed as:

[0102] Formula 6: ;

[0103] The diagonal elements can be expressed as:

[0104] Formula 7, ;

[0105] in for The envelope of , ,in 、 、 is the intermediate parameter, for The phase of , .

[0106] In one example, the channel transfer probability function is derived as follows:

[0107] In the time domain, it can be assumed that the channel The probability density function of the signal envelope (fading amplitude) at the strip tap can be modeled as a Rayleigh random variable:

[0108] Formula 8: ;

[0109] No. The tap power is , assuming the phase is uniformly distributed over , at this time The joint probability density function of the envelope and phase of the tap channel can be expressed as:

[0110] Formula 9: ;

[0111] In the frequency domain, the frequency domain channel response envelope can be expressed as the linear sum of several taps of the underwater acoustic channel:

[0112] Formula 10: ;

[0113] joint 、 、 and The statistical characteristics of the frequency domain channel response are studied, namely:

[0114] Formula 11: ;

[0115] in is the Jacobean matrix transform. The subcarrier channel frequency response follows the Rayleigh distribution, and its envelope probability density function can be expressed as:

[0116] Formula 12: :

[0117] The variance is For convenience of representation, let Figure 2 in , , , , then the channel transfer probability function can be expressed as Considering the case of known channel side information (KSI), for the underwater acoustic channel on any subcarrier, assuming BPSK modulation is used, the channel transition probability obeys the following formula:

[0118] Formula 13: , ;

[0119] in, The meaning of is the noise variance.

[0120] In one example, the channel capacity and Bhattacharyya parameters are derived as follows:

[0121] based on and Independence, conditional probability rule and total probability law, from the envelope probability density function of the OFDM subcarrier channel frequency response, it can be seen that the channel gain distribution can be obtained by formula 12 Satisfy the Rayleigh distribution, let , the ergodic channel capacity is:

[0122] Formula 14:

[0123] ;

[0124] At the same time, the channel Bhattacharyya parameter can be expressed as:

[0125] Formula 15: .

[0126] In one example, similar to the channel polarization theory of a single channel, the parallel channel polarization is mathematically modeled and analyzed. For example, given two original parallel channels with independent and different channel transfer probability functions and , after generating the matrix operation, two parallel channel polarization conversion , and obtain the composite channel , and then decomposed into two polarization sub-channels and ,in , is the bit-inverse matrix, Represents the matrix Conduct Kronecker product operations, where .like Figure 5 A schematic diagram of a parallel channel single-step transformation process shown in FIG. .

[0127] Continue with Figure 5 For example, the channel transfer probability values ​​corresponding to the subcarriers are determined using the above formula 13, and then the channel transfer probability values ​​corresponding to the polarization subchannels are determined. and ,satisfy:

[0128] Formula 16: ;

[0129] Formula 17: .

[0130] Use the above formula 14 to calculate the polarization sub-channel The channel capacity satisfies:

[0131] Formula 18: ;

[0132] Formula 19: ;

[0133] Formula 20: ;

[0134] The sum of the channel capacities remains unchanged before and after the channel polarization transformation, and the absolute value of the difference between the two polarization sub-channel capacities and the average capacity increases. and The location does not affect and The value of . Using the above 15, we can calculate the polarization channel Among them, the Bhattacharyya parameters satisfy:

[0135] Formula 21: ;

[0136] Formula 22: .

[0137] In one example, the following polarization is performed on multiple parallel channels based on the single-step channel transformation property. OFDM subcarrier channels are composed of parallel channels. All parallel channels have the same properties and are independent of each other. The transfer probability functions of each parallel channel are different. In this embodiment of the present invention, each subchannel is used only once. The code length is OFDM signal Place them on each subcarrier in sequence , , see Figure 6 The schematic diagram of a parallel channel polarization is shown, and the matrix is ​​generated Operation to obtain composite channel , , , and decomposed into polarization sub-channels , its channel transfer probability function is:

[0138] Formula 23: ;

[0139] in, .when , for any value ,satisfy The number of channels accounts for the total number of channels The proportion tends to ,satisfy The number of polarization channels accounts for the total number of polarization channels The proportion tends to Based on the polarization theory of the OFDM parallel underwater acoustic channel, the reliability distribution of the polarization sub-channel and its time-frequency variation are analyzed at the receiving end.

[0140] Based on the reliability distribution of the polarization sub-channel and its video variation pattern, the embodiment of the present invention provides a specific implementation of a polarization code construction method based on parallel polarization of an underwater acoustic channel.

[0141] In step 1, at the transmitter, the current sample transmission sequence is encoded to obtain a polar code sequence, and a first OFDM signal including the polar code sequence is transmitted to the receiver via the OFDM underwater acoustic communication system. For details, please refer to the aforementioned embodiment, and this embodiment of the present invention will not be further described.

[0142] Step 2: Polarization processing is performed on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and reliability analysis is performed on the polarization sub-channels based on the first OFDM signal sent by the transmitter and the first OFDM signal received by the receiver to obtain a polarization code construction result.

[0143] In one example, the process of performing polarization processing on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels can be referred to the aforementioned embodiment, and will not be described in detail in the embodiment of the present invention.

[0144] In one example, a process of performing reliability analysis on a polar subchannel to obtain a polar code construction result based on a first OFDM signal sent by a transmitting end and a first OFDM signal received by a receiving end is as follows:

[0145] (1) After BPSK modulation is performed on the first OFDM signal received at the receiving end, a serial cancellation decoder is used to perform recursive decoding based on the path metric according to the factor graph to determine the log-likelihood value corresponding to the polarization subchannel, thereby determining the log-likelihood ratio corresponding to the polarization subchannel.

[0146] Accurate channel estimation helps to more accurately quantify the reliability of the polarization bit subchannel. In the specific implementation, since the first OFDM signal in step 1 is known at the transmitter and receiver, it can be used as a reference sequence for least squares (LS) channel estimation. Through accurate channel estimation and noise measurement, real-time channel state information (CSI) is obtained. and noise variance After BPSK demodulation, the polar code decoder is initialized by calculating the log-likelihood ratio (LLR) according to the following formula, which is in the form of LLRV :

[0147] Formula 24: ;

[0148] in, is the transfer probability of the underwater acoustic channel, and the serial cancellation (SC) decoder is used to perform recursive decoding based on the path metric according to the factor graph. Let the depth in the factor graph be Node Group Nodes in The log-likelihood value (LLR) of , the log-likelihood ratio of each polarization channel is calculated using the recursive method according to the following formula: :

[0149] Formula 25:

[0150] ;

[0151] in, is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the bit decision value.

[0152] Formula 26: ;

[0153] in, Represents the formula 25 , Represents the formula 25 .

[0154] (2) The Bhattacharyya parameter estimate corresponding to the polarimetric subchannel is determined based on the log-likelihood ratio. The Bhattacharyya parameter estimate is negatively correlated with the reliability of the polarimetric subchannel.

[0155] In one example, if the log-likelihood ratio corresponding to the polarization subchannel is greater than or equal to 1, the square root of the reciprocal of the log-likelihood ratio is taken as the index value corresponding to the polarization subchannel. Alternatively, if the log-likelihood ratio corresponding to the polarization subchannel is less than 1, the square root of the log-likelihood ratio is taken as the index value corresponding to the polarization subchannel. Statistics are then taken of all index values ​​to obtain an expected index value, which is used as the Bhattacharyya parameter estimate corresponding to the polarization subchannel.

[0156] Specifically: Substitute it into the following formula to calculate the index value :

[0157] Formula 27:

[0158] Repeat steps 1 to 2 multiple times to obtain the index value. Expected value , as the Bhattacharyya parameter of the polariton channel The estimated value of is used to characterize the reliability of each polarization subchannel. The smaller the value, the more reliable the polarization subchannel.

[0159] Changes in channel parameters cause changes in the polarimetric channel reliability distribution. Therefore, steps 1 and 2 are repeated to observe the impact of underwater acoustic channel parameters, such as Doppler and time variations caused by the relative motion between the transmitter and receiver, channel multipath and delay, and the frequency domain partitioning of the underwater acoustic channel using different code lengths. This results in the time-frequency distribution of polarimetric channel reliability.

[0160] (3) Filter out multiple target polarimetric subchannels in descending order of Bhattacharyya parameter estimates to obtain polarimetric code construction results. The target polarimetric subchannel is used to transmit information bits, and the remaining polarimetric subchannels are used to transmit frozen bits. In one example, based on the polarimetric channel reliability results and code rate requirements, ,choose A bit channel with higher reliability (i.e., the target polarimetric subchannel) to transmit information bits, while allocating the frozen bits to other bit channels (i.e., the remaining polarimetric subchannels) At this point, the polarization code construction of OFDM underwater acoustic communication is completed.

[0161] In step 3, for any sequence to be transmitted at the transmitter, the characteristic information of the polar code construction result is combined to determine whether the sequence to be transmitted meets the calling conditions of the polar code construction result. The characteristic information is used to describe the timeliness and reliability distribution of the polar code construction result.

[0162] In one example, if the transmission time of the sequence to be transmitted falls within the valid time of the polar code construction result; the motion speeds of the transmitting end and the receiving end at the transmission time are consistent with any of the multiple relative motion speeds associated with the polar code construction result; and the code length of the sequence to be transmitted is consistent with any of the multiple code lengths associated with the polar code construction result, then it is determined that the sequence to be transmitted meets the calling conditions of the polar code construction result.

[0163] In practical applications, according to the timeliness and frequency distribution of the polarization code construction results, (1) within the valid time of the polarization code construction results, long-term communication is carried out according to the initial polarization code construction results to avoid the polarization code construction process before each communication. After the valid time exceeds, the polarization sub-channel reliability estimation and polarization code construction are performed again according to steps S1 to S4; (2) according to the reliability distribution law of the transmitter and receiver at different movement speeds, the polarization code construction results at one speed can be applied to different speed scenarios to avoid repeated polarization code construction work; (3) if the communication bandwidth is determined, the underwater acoustic channel bandwidth is divided into different frequency points and bands under different code lengths. According to the reliability distribution of the polarization sub-channel under different code lengths, the reliability distribution of each frequency band under one code length can be used to obtain the reliability results under other code lengths, providing a reference for the construction of polarization codes with other code lengths to avoid repeated polarization code construction work.

[0164] If the above call conditions are met, the sequence to be transmitted can be directly sent from the transmitter to the receiver through the target polarization subchannel, avoiding repeated polar code construction. Otherwise, steps 1 and 2 need to be repeated.

[0165] In one embodiment, the time-varying underwater acoustic channel between a moving sound source and a receiver is simulated by Bellhop. Figure 7 、 Figure 8 The communication scenario is given in the figure. The transmitter and receiver are set to be 1.5 km apart. The transmitter transducer is placed 15 m underwater. The receiver is placed 15 m underwater. The transmitter moves at a specified speed. (m / s) moves towards the receiving end and continues to move until the specified time ends. The channel is sampled at intervals of one CP-OFDM symbol time (about 53.4 ms) to obtain the channel impulse response, channel frequency domain response, scattering function and dual-frequency function of each OFDM symbol during the continuous movement. Figure 7 and Figure 8 As shown, Figure 7 A schematic diagram of a channel situation. Figure 7 (a) is the communication environment, (b) is the channel impulse response, and (c) is the frequency response. Figure 8 is a schematic diagram of the channel scattering function under different relative motion speeds. Figure 8(a) is the case where the moving speed is 0.0029 m / s, (b) is the case where the moving speed is 0.0290 m / s, (c) is the case where the moving speed is 0.2900 m / s, and (d) is the case where the moving speed is 1.450 m / s.

[0166] Set the transmitter movement speed (m / s) is 0.0029 m / s, 0.0145 m / s, 0.029 m / s, 0.145 m / s, 0.29 m / s, 1.45 m / s, corresponding to the Doppler shift (Hz) is approximately 0.0234 Hz, 0.117 Hz, 0.234 Hz, 1.17 Hz, 2.34 Hz, 11.7 Hz, and the corresponding normalized Doppler factor 1×10 -3 , 5×10 -3 , 1×10 -2 , 5×10 -2 , 0.1, 0.5. The parameters of the OFDM underwater acoustic communication system are shown in Table 1.

[0167] Table 1. OFDM system parameters

[0168]

[0169] The transmitter was operated continuously for 90 seconds. During the first 30 seconds, 500 OFDM symbols were transmitted. The channel polarization results and the reliability of the polarimetric subchannel were analyzed. During the next 60 seconds, 1000 OFDM communication signals were transmitted. These signals were encoded based on the reliability of each polarimetric subchannel, and the performance of the polarimetrically encoded OFDM channel was observed.

[0170] The timeliness of the polarization results is as follows:

[0171] When the transmitter moves at a speed of 0.029 m / s, the channel coherence bandwidth is about 500 Hz, the Doppler shift is 0.3 Hz, the ICI is negligible, and the Doppler spread is 0.45 Hz. Therefore, the channel coherence time is 2.22 s, and the channel can still be regarded as a slowly time-varying channel. The frequency shift range of each subcarrier is 0~0.1 Hz, which accounts for about 4.31×10 -3 Since the channel coherence time is short at this speed, the system performance under different time periods under this channel condition is simulated and the timeliness of the polariton channel reliability parameters is analyzed. The results are as follows: Figure 9The system performance at different time periods with a relative motion speed of 0.029 m / s is shown in the figure. The system performance at each time period from 0 to 60 s is similar with an interval of 15 s. Without channel Doppler estimation and compensation, and without channel coding error correction, the communication bit error rate can reach 10 when the signal-to-noise ratio is 4 dB. -2 In this case, after adopting polar code channel coding, the system bit error rate is further reduced, and can reach 10 when the signal-to-noise ratio is 4~5 dB. -4 Magnitude.

[0172] When the transmitter moves at a speed of 0.29 m / s, the Doppler shift is 2.6 Hz, the Doppler spread is 4.6 Hz, and the channel coherence time is 0.2174 s. The frequency shift of each subcarrier is different, ranging from 0 to 0.74 Hz, which is 0 to 3.16×10 of the bandwidth of each subcarrier. -2 The increase in Doppler causes the channel coherence time in this scenario to be less than the duration of a CP-OFDM symbol, and the channel exhibits fast time-varying behavior. Observe the system performance in different time periods under this channel condition and analyze the timeliness of the polariton channel reliability parameters, such as Figure 10 The system performance at different time periods, at a relative velocity of 0.29 m / s, is shown. The system performance remains similar across all time periods within 60 seconds. As the signal-to-noise ratio increases from 0 to 10 dB, the system bit error rate (BER) without channel coding decreases from 0.1329 to 0.057, while the BER with polar coding decreases from 0.09 to 10⁻⁵. The polarimetric channel reliability parameter ensures effective error correction with polarimetric channel coding over the 60-second communication period. Furthermore, the BER without channel coding gradually increases over time, with the coded system achieving a performance gain of approximately 1 dB between 0 and 15 seconds compared to the 15 to 60-second period.

[0173] When the transmitter moves at a speed of 1.45 m / s, the channel coherence bandwidth is approximately 500 Hz, and the channel frequency domain response varies little over time. At this time, the Doppler shift is 12 Hz, the Doppler spread is 23 Hz, and the coherence time is 0.043 s. The frequency shift of each subcarrier ranges from -3.9 to 3.86 Hz, which is approximately 0 to 0.16 of the bandwidth of each subcarrier. The frequency spread of each subcarrier is approximately 0.02 Hz. The system performance under these channel conditions is observed in different time periods, and the timeliness of the polarization subchannel reliability parameters is analyzed, as shown in Figure 2. Figure 11The figure shows the system performance in different time periods at a relative motion speed of 1.45 m / s. Without channel coding, the system bit error rate (BER) alternates between high and low every 15 seconds, following the temporal variation of the channel frequency domain response. The BERs for the 15-30 s and 45-60 s periods are similar, both approximately 0.02-0.03 higher than those for the 0-15 s and 30-45 s periods. With the application of polar code channel coding, the performance for the 15-30 s and 45-60 s periods is similar, while the 0-15 s period exhibits a performance gain of approximately 0.3-1 dB compared to the 30-45 s period. This indicates that the timeliness of the polarimetric channel reliability parameter is shortened. The decoded BER for all time periods is consistent with a 6 dB BER, reaching a BER on the order of 10-3.

[0174] The impact of channel parameters on polarization results:

[0175] Observe the channel polarization results at different motion speeds. According to the code rate of 0.5, the polarization sub-channel with a small Bhattacharyya parameter is selected as the information sub-channel, and the polarization sub-channel with a large Bhattacharyya parameter is selected as the frozen sub-channel, as shown in Figure 12 The polarization results and reliability distribution of OFDM subchannels at different motion speeds are shown, fd / F=1×10 -2 At speeds of 0.0029 m / s and 0.029 m / s, the reliability distribution of the channel polarization differs by only 7 bits. When the speed increases to 0.29 m / s, the difference in reliability distribution increases to 16 bits compared to 0.0029 m / s, and to 14 bits compared to 0.029 m / s.

[0176] like Figure 13 The figure shows the channel polarization results and reliability distribution at different speeds when N = 256. Due to the limited code length, the Bhattacharyya parameter for each polarimetric channel exhibits an incomplete two-tier differentiation trend. The smaller the Bhattacharyya parameter, the higher the reliability of the polarimetric channel. It can be seen that when the normalized Doppler is less than 0.5, the reliability values ​​of each polarimetric channel are similar and overlap. Therefore, in practical applications, the reliability of polarimetric channels under low Doppler can be applied to communication channels under high Doppler without repeated measurements.

[0177] Polarization results and distribution at different frequencies with different code lengths: Observe the reliability distribution of polarization sub-channels with different code lengths in the OFDM underwater acoustic communication frequency band. The code length is set to N = 128, 256, 512, and 1024. The 8-16 kHz underwater acoustic channel bandwidth is divided into different frequency points and bands with different code lengths. Figure 14 The polarization results and reliability distribution of OFDM subchannels with different code lengths are shown as follows, fd / F=1×10 -2The reliability distribution across frequency bands is consistent for different code lengths. This phenomenon is beneficial for practical applications. Based on the reliability of each frequency band, it can provide a reference for constructing polar codes with various code lengths.

[0178] Time-efficiency and time-frequency distribution of polarization results: The transmitter's velocity v (m / s) increases to 2.900 m / s. The Doppler is 23.4 Hz, and the corresponding normalized Doppler shift fd / F is 1. Figure 15 、 Figure 16 The channel scattering function and the dual-frequency function are given, where see Figure 15 The diagram shows a channel parameter diagram when the relative motion speed is 2.9 m / s. Figure 15 (a) is the channel scattering function, (b) is the channel dual-frequency function, and see Figure 16 The diagram shows the polarization results and reliability distribution of polarization channels at different times. Figure 16 (a) shows a relative motion speed of 2.9 m / s, and (b) shows a relative motion speed of 1.45 m / s.

[0179] To test polarization phenomena and the temporal variation of parameters under high-speed motion, 1,000 OFDM symbol blocks were acquired over 60 seconds. These symbols were then used to estimate the reliability parameters of the polarimetric subchannel. The polarimetric results obtained at different times were observed. Information bit indices and frozen bit indices were assigned based on the reliability parameters of the polarimetric subchannel at a code rate of 0.5.

[0180] When the relative speed is 2.9 m / s, Figure 16 As shown in (a) of Figure 1, compared with the polarization results of 1s~15s, there are 2, 6 and 5 bit index differences in 16s~30s, 31s~45s and 46s~60s respectively. When the relative motion speed is 1.45 m / s, as shown in Figure 16 As shown in (b) of the figure, compared to the polarization results from 1s to 15s, the results from 16s to 30s, 31s to 45s, and 46s to 60s differ by 2, 5, and 4 bit indices, respectively. These results demonstrate that the polarization phenomenon and its distribution remain stable within 60s of high-speed motion, maintaining timeliness.

[0181] Lake test results: The test site was located at Qiandao Lake (Xin'anjiang Test Site) in Hangzhou, China. During the test, the transmitting transducer was suspended from a dock, while the receiver was suspended from a surface vessel. During the communications test, the surface vessel with the receiving transducer was docked at two locations, designated P1 (29°33′5″N118°57′16″E) and P2 (29°33′20″N118°57′49″E), 749 meters and 1718 meters from the transmitter (29°33′38″N118°58′08″E), respectively. Both the transmitter and receiver were placed in water approximately 10 to 15 meters deep, at a temperature of approximately 16°C and a sound velocity of approximately 1470 m / s. The transducer had a center frequency of 12 kHz and a bandwidth of 8 kHz. The transmitted sound source level was 175 dB re. 1 µPa. The receiving sensitivity is -185 dB re. 1V / µPa and the sampling rate is 128 kHz.

[0182] See also Figure 17 A schematic diagram of channel characteristics, Figure 17 (a) is the channel impulse response, showing that the channel has a simple multipath structure and the maximum delay is less than 5 ms. Figure 17 (b) in Figure 3 shows that the channel exhibits frequency selective fading with a coherence bandwidth of approximately 200 Hz. Figure 17 As can be seen from (c) in the figure, the multipath structure and number of multipaths in the channel remain stable within 25 s. Figure 17 In (d), due to the ship's drift on the sea surface, the maximum Doppler shift in the channel is approximately 0.62 Hz, the Doppler spread is approximately 0.1 Hz, and the channel coherence time is approximately 10 s. Channel time variation can be considered as a slow time variation relative to the period of the transmitted signal.

[0183] For the construction of polar codes, considering the above-mentioned channel time-varying characteristics and the simulation results of the number of Monte Carlo iterations, five transmission signals were collected, each containing 100 blocks of OFDM signals. The collected signal durations were approximately 2.67 s, 5.335 s, 10.67 s, and 21.34 s, and the polar code lengths were 128, 256, 512, and 1024, respectively. The reliability distribution of the polarization subchannel with different code lengths was observed. The code lengths were set to N = 128, 256, 512, and 1024. Figure 18 The polarization results and reliability distributions for OFDM subchannels with different code lengths are shown. Consistent with the simulation results, the reliability distributions for different code lengths are stable across the entire frequency band. This phenomenon is beneficial for practical applications. Based on the reliability of each frequency band in the channel, it can provide a reference for constructing polar codes with various code lengths.

[0184] Taking the polarization result of code length 512 as an example, the polarization result of code length 1024 is predicted based on the polarization structure under the 512 code length, and compared with the polarization result of the actual 1024 code length. When the code length is 512, the center frequencies of 512 subcarriers and their corresponding polarization subchannel reliabilities are known. When the code length is 1024, assuming that the code rate requirement is 0.5, it is necessary to select 512 subchannels with high reliability from the 1024 OFDM subcarriers. On the one hand, the OFDM subcarrier frequencies used in overlapping code lengths of 512 and 1024 are considered, and the frequencies and adjacent frequencies corresponding to the information bit indexes of code length 512 are used as the information bit indexes of 1024. On the other hand, the information bit indexes of code length 512 are expanded by 2 times, and the adjacent positions are filled to generate an information bit index of 1024. According to the above selection, 537 position indexes can be obtained. As Figure 19 The figure shows a schematic diagram of predicting the polar code construction result for a code length of 1024 using the code construction result for a code length of 512 and a code rate of 0.5. When compared with the position index of the actual code length of 1024, 482 of the 537 position indices are identical. This phenomenon facilitates practical applications. When the polar code construction structure of a certain code length and frequency distribution is known, polar codes of other code lengths can be constructed without measurement.

[0185] According to the polar code construction scheme, under this channel condition, the timeliness of the polar code construction is observed. The detailed results are shown in Table 2 below. When communication is carried out according to the polar code construction results, the communication bit error rate within 4 minutes can still be maintained at 10 under the condition of time-varying channels. -4 This ensures reliable data transmission, eliminates the need to repeatedly measure the reliability of the polarization subchannel during this period, and simplifies the polarization code encoding step.

[0186] Table 2. Performance BER of OFDM UWC system in different time periods after polar code construction

[0187]

[0188] In summary, the present invention describes the polarization phenomenon and reliability variation of time-varying parallel channels in OFDM underwater acoustic communication after incomplete channel polarization transformation, and proposes a simplified polarization code construction method. Through simulations of time-varying underwater acoustic channels in real communication environments and lake tests, the reliability of OFDM underwater acoustic polarimetric channels exhibits a polarization characteristic, consistent with the theoretical model of the present invention. Polarimetric channel reliability is affected by time-varying parameters such as underwater acoustic channel multipath and Doppler, and is time-sensitive. Using the polarimetric code construction method and channel coding proposed in the present invention within the effective time period, communication bit error rates can reach the order of 10⁻4, effectively ensuring reliable data transmission. Furthermore, the reliability of polarimetric channels under Doppler can be applied to communication channels under large Doppler without repeated measurements. Furthermore, the channel reliability distribution is consistent when the same channel frequency band is divided by different code lengths, eliminating the need for repeated polarimetric channel reliability measurements for different code lengths. This further simplifies polarimetric code construction, providing a reference for the practical design of subsequent polarimetric code-encoded OFDM underwater acoustic communication mechanisms.

[0189] On the basis of the above embodiments, an embodiment of the present invention provides a polar code construction device based on parallel polarization of an underwater acoustic channel. The device is applied to an OFDM underwater acoustic communication system. The OFDM underwater acoustic communication system includes a transmitter, an OFDM parallel underwater acoustic channel, and a receiver. Figure 20 The figure shows a schematic diagram of a polar code construction device based on parallel polarization of an underwater acoustic channel. The device mainly includes the following parts:

[0190] A first signal transmission module 2002 is configured to perform an encoding operation on the current sample transmission sequence at the transmitting end to obtain a polar code encoding sequence, and transmit a first OFDM signal including the polar code encoding sequence to a receiving end via the OFDM underwater acoustic communication system;

[0191] A polarization code construction module 2004 is configured to perform polarization processing on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and perform reliability analysis on the polarization sub-channels based on the first OFDM signal sent by the transmitter and the first OFDM signal received by the receiver to obtain a polarization code construction result.

[0192] The call determination module 2006 is configured to determine, for any sequence to be transmitted at the transmitting end, whether the sequence to be transmitted meets the call conditions for the polar code construction result, based on the characteristic information of the polar code construction result. The characteristic information is used to describe the timeliness and reliability distribution of the polar code construction result.

[0193] The second signal transmission module 2008 is configured to, if the judgment result of calling the judgment module 2006 is yes, select a target polarization sub-channel according to the polarization code construction result, and send the sequence to be transmitted from the transmitting end to the receiving end. If the judgment result of calling the judgment module is no, repeatedly execute the first signal transmission module 2002 to the polarization code construction module 2004 to obtain a new polarization code construction result, and send the sequence to be transmitted from the transmitting end to the receiving end through the target polarization sub-channel according to the new polarization code construction result.

[0194] The polar code construction method based on parallel polarization of an underwater acoustic channel provided in an embodiment of the present invention uses a first OFDM signal sent by a transmitter and a first OFDM signal received by a receiver to perform reliability analysis on the polarization sub-channels obtained from the OFDM parallel underwater acoustic channel plan. The method then determines whether the polar code construction result can be used, combining characteristic information such as the timeliness and reliability distribution of the polar code construction result. If the conditions are met, the sequence to be transmitted can be directly transmitted according to the polar code construction result. This embodiment of the present invention can significantly reduce the communication bit error rate, ensuring reliable data transmission, and effectively improve the high complexity of polar code construction caused by the need for repeated measurements in the prior art.

[0195] In one embodiment, the calling conditions include:

[0196] The transmission time of the sequence to be transmitted is within the valid time of the polar code construction result;

[0197] The relative speed between the transmitter and receiver at the time of transmission matches the relative speed scenario of the polar code construction result;

[0198] The code length of the sequence to be transmitted matches the code length scenario of the polar code construction result.

[0199] In one embodiment, timeliness is used to describe the validity period of a polar code construction result, and a reliability distribution law is used to describe relative speed scenarios and code length scenarios matched by the polar code construction result. The relative speed scenario includes multiple relative motion speeds associated with the polar code construction result, and the code length scenario includes multiple code lengths associated with the polar code construction result. The calling judgment module 2006 is specifically configured to:

[0200] If the transmission time of the sequence to be transmitted is within the valid time of the polar code construction result; the relative motion speed between the transmitting end and the receiving end at the transmission time is consistent with any of the multiple relative motion speeds associated with the polar code construction result; and the code length of the sequence to be transmitted is consistent with any of the multiple code lengths associated with the polar code construction result, then it is determined that the sequence to be transmitted meets the calling conditions of the polar code construction result.

[0201] In one implementation, the polar code construction module 2004 is specifically configured to:

[0202] After performing BPSK modulation on the first OFDM signal received at the receiving end, recursively decoding the signal using a serial cancellation decoder based on the factor graph and the path metric is performed to determine a log-likelihood value corresponding to the polarization subchannel, thereby determining a log-likelihood ratio corresponding to the polarization subchannel;

[0203] The Bhattacharyya parameter estimate corresponding to the polarimetric subchannel is determined based on the log-likelihood ratio. The Bhattacharyya parameter estimate is negatively correlated with the reliability of the polarimetric subchannel.

[0204] Multiple target polarimetric subchannels are selected in ascending order of Bhattacharyya parameter estimates to obtain a polar code construction result. The target polarimetric subchannel is used to transmit information bits, and the remaining polarimetric subchannels are used to transmit frozen bits.

[0205] In one implementation, the polar code construction module 2004 is specifically configured to:

[0206] The log-likelihood value corresponding to the polarization subchannel is determined according to the following formula:

[0207] ;

[0208] in, is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the bit decision value.

[0209] In one implementation, the polar code construction module 2004 is specifically configured to:

[0210] If the log-likelihood ratio corresponding to the polarization channel is greater than or equal to 1, the square root of the reciprocal of the log-likelihood ratio is taken as the index value corresponding to the polarization channel. Alternatively, if the log-likelihood ratio corresponding to the polarization channel is less than 1, the square root of the log-likelihood ratio is taken as the index value corresponding to the polarization channel.

[0211] The expected value of the indicator is obtained by statistically analyzing all the indicator values, and the expected value of the indicator is used as the estimated value of the Bhattacharyya parameter corresponding to the polarization sub-channel.

[0212] In one embodiment, the system further includes a reliability verification module for:

[0213] Performing an encoding operation on the current sample transmission sequence at the transmitting end to obtain a polarization code sequence, and sending a second OFDM signal containing the polarization code sequence to the receiving end via the OFDM underwater acoustic communication system;

[0214] Polarization processing is performed on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels;

[0215] Determining, by using a channel transfer probability function and its statistical characteristics, channel transfer probability values ​​corresponding to subcarriers included in the OFDM parallel underwater acoustic channel based on the second OFDM signal sent by the transmitter and the second OFDM signal received by the receiver, and determining a channel transfer probability value corresponding to the polarization subchannel based on the channel transfer probability values ​​corresponding to the subcarriers;

[0216] Based on the channel transition probability values ​​corresponding to the subcarriers and the polarization subchannels, the channel capacity and Bhattacharyya parameter corresponding to the subcarriers and the channel capacity and Bhattacharyya parameter corresponding to the polarization subchannels are determined respectively, which are used to determine the reliability distribution law corresponding to the polarization subchannels.

[0217] The device provided in the embodiment of the present invention has the same implementation principle and technical effects as those in the aforementioned method embodiment. For the sake of brief description, for matters not mentioned in the device embodiment, reference can be made to the corresponding content in the aforementioned method embodiment.

[0218] An embodiment of the present invention provides an electronic device. Specifically, the electronic device includes a processor and a storage device. The storage device stores a computer program, and when the computer program is executed by the processor, it executes the method described in any one of the above-mentioned embodiments.

[0219] Figure 21 This is a structural diagram of an electronic device provided in an embodiment of the present invention. The electronic device 100 includes: a processor 210, a memory 211, a bus 212 and a communication interface 213. The processor 210, the communication interface 213 and the memory 211 are connected via the bus 212; the processor 210 is used to execute an executable module stored in the memory 211, such as a computer program.

[0220] Memory 211 may include high-speed random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage. Communication between the system network element and at least one other network element is achieved through at least one communication interface 213 (which may be wired or wireless), and may utilize the Internet, a wide area network, a local area network, a metropolitan area network, or the like.

[0221] The bus 212 may be an ISA bus, a PCI bus, or an EISA bus. The bus may be divided into an address bus, a data bus, a control bus, and the like. For ease of representation, Figure 21 Only one bidirectional arrow is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0222] Among them, the memory 211 is used to store programs, and the processor 210 executes the program after receiving the execution instruction. The method executed by the device for flow process definition disclosed in any embodiment of the above-mentioned embodiment of the present invention can be applied to the processor 210 or implemented by the processor 210.

[0223] The processor 210 may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method can be completed by hardware integrated logic circuits in the processor 210 or by software instructions. The processor 210 may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or any conventional processor. The steps of the method disclosed in conjunction with the embodiments of the present invention can be directly implemented and executed by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium well-known in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, etc. The storage medium is located in memory 211, and processor 210 reads information in memory 211 and, in conjunction with its hardware, completes the steps of the above method.

[0224] The computer program product of the readable storage medium provided in the embodiment of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the method described in the previous method embodiment. The specific implementation can be referred to the previous method embodiment and will not be repeated here.

[0225] If the functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0226] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the above-described embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-described embodiments within the technical scope disclosed by the present invention, or replace some of the technical features therein with equivalents. Such modifications, changes, or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A polar code construction method based on parallel polarization of underwater acoustic channels, characterized in that: Applied to an OFDM underwater acoustic communication system, the OFDM underwater acoustic communication system includes a transmitter, an OFDM parallel underwater acoustic channel, and a receiver, and the method includes: Step 1: performing an encoding operation on a current sample transmission sequence at the transmitting end to obtain a polar code encoding sequence, and sending a first OFDM signal including the polar code encoding sequence to the receiving end via the OFDM underwater acoustic communication system; Step 2: performing polarization processing on the OFDM parallel underwater acoustic channel to obtain multiple polarization sub-channels, and performing reliability analysis on the polarization sub-channels based on the first OFDM signal sent by the transmitting end and the first OFDM signal received by the receiving end to obtain a polar code construction result; Step 3: For any sequence to be transmitted at the transmitting end, combining characteristic information of the polar code construction result, determining whether the sequence to be transmitted meets the calling conditions of the polar code construction result, where the characteristic information is used to describe the timeliness and reliability distribution of the polar code construction result; Step 4: If the judgment result of step 3 is yes, select a target polarization subchannel according to the polar code construction result, and send the sequence to be transmitted from the transmitting end to the receiving end. If the judgment result of step 3 is no, repeat steps 1 to 2 to obtain a new polarization code construction result. According to the new polarization code construction result, send the sequence to be transmitted from the transmitting end to the receiving end through the target polarization subchannel. The calling conditions include: the transmission time of the sequence to be transmitted is within the valid time of the polar code construction result; the relative movement speed of the transmitting end and the receiving end at the transmission time matches the relative speed scenario of the polar code construction result; and the code length of the sequence to be transmitted matches the code length scenario of the polar code construction result. The timeliness is used to describe the validity period of the polar code construction result. The reliability distribution law is used to describe the relative speed scenario and code length scenario matched by the polar code construction result. The relative speed scenario includes multiple motion speeds associated with the polar code construction result. The code length scenario includes multiple code lengths associated with the polar code construction result. Determining whether the sequence to be transmitted meets the calling condition of the polar code construction result based on the characteristic information of the polar code construction result includes: determining that the sequence to be transmitted meets the calling condition of the polar code construction result if a transmission time of the sequence to be transmitted is within a valid time of the polar code construction result; and a relative motion speed between the transmitting end and the receiving end at the transmission time is consistent with any one of multiple relative motion speeds associated with the polar code construction result; and a code length of the sequence to be transmitted is consistent with any one of multiple code lengths associated with the polar code construction result.

2. The polar code construction method based on parallel polarization of underwater acoustic channel according to claim 1, characterized in that: The method further includes performing reliability analysis on the polarization subchannel based on the first OFDM signal sent by the transmitting end and the first OFDM signal received by the receiving end to obtain a polar code construction result, including: After performing BPSK modulation on the first OFDM signal received by the receiving end, recursively decode the signal using a serial cancellation decoder based on a path metric according to a factor graph to determine a log-likelihood value corresponding to the polarization subchannel, thereby determining a log-likelihood ratio corresponding to the polarization subchannel; determining a Bhattacharyya parameter estimate corresponding to the polarimetric subchannel according to the log-likelihood ratio, where the Bhattacharyya parameter estimate is negatively correlated with reliability of the polarimetric subchannel; Multiple target polarization subchannels are selected in ascending order of the Bhattacharyya parameter estimation values ​​to obtain a polar code construction result. The target polarization subchannel is used to transmit information bits, and the remaining polarization subchannels are used to transmit frozen bits.

3. The polar code construction method based on parallel polarization of underwater acoustic channel according to claim 2, characterized in that: Recursively decoding the polarization subchannel using a serial cancellation decoder based on a path metric according to a factor graph to determine a log-likelihood value corresponding to the polarization subchannel includes: The log-likelihood value corresponding to the polarization sub-channel is determined according to the following formula: ； in, is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the depth in the factor graph Node Group Nodes in The log-likelihood value of is the bit decision value.

4. The polar code construction method based on parallel polarization of underwater acoustic channel according to claim 2, characterized in that: Determining a Bhattacharyya parameter estimate corresponding to the polarization subchannel according to the log-likelihood ratio includes: If the log-likelihood ratio corresponding to the polarized subchannel is greater than or equal to 1, taking the square root of the reciprocal of the log-likelihood ratio as the index value corresponding to the polarized subchannel; or, if the log-likelihood ratio corresponding to the polarized subchannel is less than 1, taking the square root of the log-likelihood ratio as the index value corresponding to the polarized subchannel; Statistics are performed on all the indicator values ​​to obtain an expected indicator value, and the expected indicator value is used as a Bhattacharyya parameter estimate corresponding to the polarimetric sub-channel.

5. The polar code construction method based on parallel polarization of underwater acoustic channel according to claim 1, characterized in that: The method further comprises: performing, at the transmitting end, an encoding operation on the current sample transmission sequence to obtain a polar code encoding sequence, and sending a second OFDM signal including the polar code encoding sequence to the receiving end via the OFDM underwater acoustic communication system; Performing polarization processing on the OFDM parallel underwater acoustic channel to obtain a plurality of polarization sub-channels; Determining, by means of a channel transfer probability function and its statistical characteristics, a channel transfer probability value corresponding to a subcarrier included in the OFDM parallel underwater acoustic channel based on the second OFDM signal sent by the transmitting end and the second OFDM signal received by the receiving end, and determining the channel transfer probability value corresponding to the polarization subchannel based on the channel transfer probability value corresponding to the subcarrier; Based on the channel transition probability value corresponding to the subcarrier and the channel transition probability value corresponding to the polarization subchannel, the channel capacity and Bhattacharyya parameter corresponding to the subcarrier and the channel capacity and Bhattacharyya parameter corresponding to the polarization subchannel are determined, respectively, to determine a reliability distribution law corresponding to the polarization subchannel.

6. A polar code construction device based on parallel polarization of underwater acoustic channel, characterized in that: Applied to an OFDM underwater acoustic communication system, the OFDM underwater acoustic communication system includes a transmitter, an OFDM parallel underwater acoustic channel and a receiver, and the device includes: a first signal transmission module, configured to perform an encoding operation on a current sample transmission sequence at the transmitting end to obtain a polar code encoding sequence, and transmit a first OFDM signal including the polar code encoding sequence to the receiving end via the OFDM underwater acoustic communication system; a polarization code construction module, configured to perform polarization processing on the OFDM parallel underwater acoustic channel to obtain a plurality of polarization sub-channels, and perform reliability analysis on the polarization sub-channels based on the first OFDM signal sent by the transmitting end and the first OFDM signal received by the receiving end to obtain a polarization code construction result; a call determination module, configured to determine, for any sequence to be transmitted at the transmitting end, whether the sequence to be transmitted meets a call condition for the polar code construction result, based on characteristic information of the polar code construction result, where the characteristic information is used to describe the timeliness and reliability distribution pattern of the polar code construction result; a second signal transmission module, configured to, if a judgment result of the calling judgment module is yes, select a target polarization sub-channel according to the polar code construction result, and send the sequence to be transmitted from the transmitting end to the receiving end; and, if a judgment result of the calling judgment module is no, repeatedly execute the first signal transmission module to the polar code construction module to obtain a new polar code construction result, and send the sequence to be transmitted from the transmitting end to the receiving end through the target polarization sub-channel according to the new polar code construction result; The calling conditions include: the transmission time of the sequence to be transmitted is within the valid time of the polar code construction result; the relative movement speed of the transmitting end and the receiving end at the transmission time matches the relative speed scenario of the polar code construction result; and the code length of the sequence to be transmitted matches the code length scenario of the polar code construction result. The timeliness is used to describe the validity period of the polar code construction result. The reliability distribution law is used to describe the relative speed scenario and code length scenario matched by the polar code construction result. The relative speed scenario includes multiple motion speeds associated with the polar code construction result. The code length scenario includes multiple code lengths associated with the polar code construction result. The calling judgment module is specifically configured to determine that the sequence to be transmitted meets the calling condition of the polar code construction result if a transmission time of the sequence to be transmitted is within a valid time of the polar code construction result; a relative motion speed between the transmitting end and the receiving end at the transmission time is consistent with any one of multiple relative motion speeds associated with the polar code construction result; and a code length of the sequence to be transmitted is consistent with any one of multiple code lengths associated with the polar code construction result.

7. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores computer-executable instructions that can be executed by the processor, and the processor executes the computer-executable instructions to implement the polarization code construction method based on parallel polarization of an underwater acoustic channel according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions. When the computer-executable instructions are called and executed by the processor, the computer-executable instructions prompt the processor to implement the polarization code construction method based on parallel polarization of an underwater acoustic channel according to any one of claims 1 to 5.

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