Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request

Abstract

The present invention discloses an information age optimization method based on polar code incremental redundancy hybrid automatic repeat request, which focuses on the monitoring of spatio-temporal processes in wireless sensor networks, uses the system prediction error as a metric for information freshness, studies the information validity range of sensor nodes, designs a polar code encoding scheme in an actual additive white Gaussian noise channel, and introduces an incremental redundancy hybrid automatic repeat request scheme to optimize the average estimation error of the system, so as to reduce the average information age of the system and expand the information validity range of information packets. And through simulation, it is verified that the proposed method has better information age performance compared with the existing hybrid chase combining automatic repeat request scheme.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular to an information age optimization method based on polar code incremental redundancy hybrid automatic repeat request. Background Art

[0002] Recently, with the progress of massive Internet of Things device connections and portable devices, real-time status information is crucial in many systems (such as wireless sensor network systems), and the receiving end hopes to obtain fresh and accurate information to assist in making quick decisions and accurate predictions. Due to the dense distribution of sensing nodes, the status information obtained by each node often has a certain correlation in the time domain and the space domain. In this case, if the scheduling between sensing nodes with strong information correlation is too frequent, on the one hand, a large number of redundant information packets will congest the system, and the amount of information obtained by the entire system will not increase. On the other hand, frequent sampling will also shorten the lifespan of the sensing nodes. Therefore, in the above systems, we are more concerned about the freshness and effectiveness of information than throughput and transmission delay.

[0003] To measure the freshness of information, the concept of information age is proposed, which is defined as the time interval between the generation moment of the latest status packet and the current timestamp. The time-averaged age metric is adopted to evaluate the performance of the status update system to guide the sampling interval of sensors. Since then, information age has received increasing attention in related fields. Some literature has summarized the contributions of information age in a wide range of information age fields in recent years. Starting from the basic single-server queue, information age measurement methods have been applied to a series of increasingly complex systems, including energy harvesting sensors transmitted through noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. For a spatio-temporal physical process, the information sampled by wireless sensor network nodes often has spatial correlation. Related research has proposed that using the information of a system composed of correlated information sources to adjust the sampling strategy can significantly improve the device lifetime. At the same time, some research has utilized the Markov property of the observed physical phenomenon in the time series and the Gaussian random field characteristics in space, and obtained that the estimation error of using outdated information to estimate the current physical phenomenon is a non-linear function of information age and spatial distance. This gives a joint measurement method for information freshness and prediction effective range. Furthermore, some articles have defined the fault-tolerant sensing coverage of sensing nodes using range correlation, deduced the average information age and the probability of information age exceeding the limit of the sensor monitoring system, and minimized the average energy consumption while ensuring a certain degree of fault-tolerant coverage probability. Most of these technologies focus on queuing systems and focus on deriving the relationship between the sampling frequency of information packets and information age to guide the scheduling and sampling schemes of wireless sensor networks. However, the modeling of these systems is overly idealized and does not consider the channel noise problem of actual communication systems. Channel noise and interference will affect the decoding and reception of information packets. Once the information packet reception fails, it will have a greater impact on the overall information age of the system. These schemes do not consider this point. Even if some articles introduce the decoding success probability, they only model it as a fixed constant and do not conduct in-depth research on it, and cannot be applied to actual communication systems with large noise effects.

[0004] Currently, only a small number of articles use information age as a metric to optimize the source-channel coding process. Under the condition of error-free channels, such schemes measure the semantic characteristics of the source, encode the source after semantic filtering with a prefix code, and design the optimal code length for the weighted sum of the semantic information value (a non-linear function of information age) and the coding cost. Focusing on the impact of the code length of source coding on the information age of the system, the channel is also modeled as an ideal channel condition without considering the impact of channel noise.

[0005] In an actual transmission system, considering the influence of channel noise, poor channel conditions can lead to errors and losses of information packets during transmission, which will result in a decline in the age-of-information performance of the system. Increasing the code length will increase the probability of decoding success while also increasing the transmission time of the codeword. To minimize the age of information, the code length must be reasonably designed to find a trade-off between the two performance metrics. The automatic repeat request (ARQ) scheme, especially the hybrid automatic repeat request (HARQ) scheme, which combines forward error correction and automatic repeat request technologies, is crucial for providing reliable data transmission in wireless communication systems. As in the literature [1] (A. Arafa, K. Banawan, K. G. Seddik and H. V. Poor, "On Timely Channel Coding with Hybrid ARQ," 2019 IEEE Global Communications Conference (GLOBECOM), 2019, pp. 1-6, doi: 10.1109 / GLOBECOM38437.2019.9013381.) in a communication system based on hybrid automatic repeat request channel coding, with the linear age of information as the optimization objective, different optimization schemes and waiting strategies are obtained according to different conditions of the binary symmetric channel, and how to select the best codeword and the best code length of the maximum distance separable code in the binary symmetric channel is discussed. The literature [2] (M. Xie, Q. Wang, J. Gong and X. Ma, "Age and Energy Analysis for LDPC Coded Status Update With and Without ARQ," in IEEE Internet of Things Journal, vol. 7, no. 10, pp. 10388-10400, Oct. 2020, doi: 10.1109 / JIOT.2020.2989166.) analyzes and compares the performance of the non-automatic repeat request, classical automatic repeat request, truncated automatic repeat request, and truncated hybrid chase combining automatic repeat request schemes using low-density parity-check codes with a fixed redundancy scheme, in terms of the average age of information and the average energy consumption.Reference [3] (M. Xie, J. Gong, Q. Wang, S. Cai and X. Ma, "Reducing Age of Extra Data by Free Riding on Coded Transmission in Multiaccess Networks," 2022 IEEE Wireless Communications and Networking Conference (WCNC), 2022, pp. 1296-1300, doi: 10.1109 / WCNC51071.2022.9771945) studied the performance of low-density parity-check codes in state update vehicle networks and multiaccess network scenarios respectively, and fresher data can be obtained compared with traditional coding schemes. However, the feedback from the receiver to the transmitter and the retransmission process used in automatic repeat request incur significant costs in terms of power efficiency, throughput, computing power and latency. These articles studied the performance differences of information age of different retransmission schemes under different channel codes, providing new ideas for subsequent research. However, some of these codewords have limitations, and some codewords cannot reach the Shannon limit, and are gradually replaced by codes with better performance in actual coding systems, such as polar codes, and the research schemes in the above articles are not applicable to the research of such codewords.

[0006] Polar codes have been selected as a 5G standard and are the only coding method proven to reach the Shannon limit. At present, there are studies on the hybrid chase combining automatic repeat request transmission scheme for polar codes, but the current performance is not optimal. Due to the puncturing pattern variable code rate design of polar codes, better gain can be achieved for the information age. However, due to the channel splitting and channel combining of polar codes and the successive decoding at the decoding end, it is difficult to obtain a closed-form solution for the decoding success probability, which also poses a challenge to finding the optimal polar code coding scheme for the information age. Summary of the Invention

[0007] In view of the problems of the prior art, the present invention proposes an information age optimization method based on the incremental redundancy hybrid automatic repeat request (IR-HARQ) mechanism of polar codes. Compared with the hybrid chase combining automatic repeat request (HCC-ARQ), the incremental redundancy hybrid automatic repeat request technology constructs a lower code rate codeword by adding redundant bits in each retransmission, and can obtain additional coding gain. Due to the application of the puncturing technology, the code rate of polar codes is more flexible, and it can use fewer redundant bits to exchange for greater decoding gain during the retransmission process. Therefore, the incremental redundancy hybrid automatic repeat request retransmission mechanism is also very helpful for the receiver to decode more fresh information packets. Especially considering the scenario where the state needs to be updated in a timely manner, that is, a large number of Internet of Things (IoT) devices need to be relayed to the destination through a multi-hop IoT network, which will reduce the data correctness, and at the same time the network has a high requirement for the freshness of information packets. In order to achieve reliable transmission and reduce the system information age, the present invention adopts the incremental redundancy hybrid automatic repeat request.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] The present invention provides an information age optimization method based on the incremental redundancy hybrid automatic repeat request of polar codes. The coding system uses polar codes for coding and transmits through the incremental redundancy hybrid automatic repeat request transmission mechanism over an additive white Gaussian noise channel. The information age optimization steps are as follows:

[0010] S1. Establish a non-linear function regarding the system average estimation error, information age, and the information validity range of each node; for the successive cancellation (SC) decoding of polar codes, use Gaussian estimation to give the decoding success probabilities of the first transmission and retransmissions.

[0011] S2. Under the known maximum number of retransmissions and physical channel conditions, use the system estimation error as a metric for information freshness, and establish an optimization objective between the system average estimation error and the polar code length: find the optimal polar code length to minimize the system average estimation error while ensuring that the information validity range of each node remains unchanged.

[0012] S3. Use the greedy algorithm to find the optimal polar code length for the optimization objective.

[0013] Furthermore, the system consists of a wireless sensor network. The source coding encodes the information packet into a K-bit state update message u, and the state update message is encoded into an L-bit packet c using polar codes. After channel modulation, it becomes the transmitted signal x and is transmitted through the additive white Gaussian noise channel w. The sampling strategy of the coding system is the zero-waiting strategy.

[0014] Furthermore, the expression of the system average estimation error in step S1 is:

[0015]

[0016] Among them, α and β are the scaling parameters in time and space respectively, l is the straight-line distance between the information packet and the prediction point, E[X], E[X 2 , and E[Q] are the expected values of the random variables X, X 2 , and Q respectively. X is the time period from the generation of the first packet to the successful decoding of the last packet at the receiving end, X 2 is the second moment of X, and Q is the time period from the generation to the last reception of the successfully received packet;

[0017]

[0018]

[0019]

[0020]

[0021] Among them, x is the set composed of all possible time periods, the maximum number of retransmissions is T, and the code length of each transmission is l i , i = 1, 2,..., T, p f is the probability of successful decoding of the f-th transmission, k is an integer, is an integer less than k.

[0022] Furthermore, the polar code incremental redundancy hybrid automatic repeat request transmission mechanism is as follows:

[0023] A matrix of size 2N is represented as G N is the generator matrix, where is a polarization matrix of size N*N, represents the n-th Kronecker product of the matrix , and there is a recurrence formula Utilize the lower triangular property and high structural property of the polarization matrix to expand the small polarization matrix into a larger polarization matrix to carry the redundant bits for retransmission, and combine the redundant bits during the decoding process to obtain a more reliable bit channel to increase the decoding success probability.

[0024] Furthermore, the polar code incremental redundancy hybrid automatic repeat request transmission method is as follows: Assume that the initial transmission code rate of the polar codeword c is K / M 1 , if the decoding is not successful, transmit the extended polar code c with an arbitrary extended length of ΔM bit through the polarization matrix 2 , and the decoder jointly decodes c 1 , c 2 for decoding, and the information bit channel set is composed of c 1 , c 2It is determined that the information bits are still transmitted through the K most reliable information bit channels, and the decoding end efficiently decodes the polar code with a code rate of K / (M + ΔM) until a successful decoding signal ACK is sent back or the maximum number of retransmissions T is reached.

[0025] Furthermore, parity check or dynamic frozen bit channels are used to represent the frozen bits.

[0026] Furthermore, in step S1, the error probability of the i-th bit is expressed according to the Gaussian estimation as:

[0027]

[0028] where B i is the i-th bit error event, is the average value of the log-likelihood (LLR) of u i obtained by the SC decoder, which is obtained through SC decoding and calculated according to the following recursive relation:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] where, is the log-likelihood (LLR) value of u i obtained by the SC decoder, σ is the standard deviation of the channel Gaussian noise, and m is the mean value of the channel Gaussian noise.

[0035] Furthermore, the optimization problem in step S2 is expressed as:

[0036]

[0037] where, α and β are the scaling parameters in time and space respectively, ρ is the bit transmitted through each channel, that is, the transmission time is proportional to the code length; p f is the decoding success probability of the f-th transmission; T is the maximum number of retransmissions, the code length of each transmission is l i , i = 1, 2,..., T, the coding length; N is the maximum number of retransmissions of the system, d is the information validity range of each node, k is an integer, is an integer less than k.

[0038] Furthermore, the optimization algorithm in step S3 is:

[0039] Based on the bit length K of the source status information, the current channel condition signal-to-noise ratio SNR, the estimated distance d, and the maximum number of retransmissions N set by the coding system as the input quantities of the algorithm; initialize the global variable optimal system estimation error to infinity and set the optimal code length vector to a zero vector; then enter a loop, and in each loop, increase the code length by 1 in sequence according to the retransmission order; calculate the channel Gaussian noise variance through the formula σ 2 =10 -sNR / 10 / 2; for each retransmission, calculate the total polar code length and the mother code length, and use Gaussian estimation to update the index set of the set information bits according to the parameter matrix (M i ,l i ,K,σ 2 ). According to the parameter matrix calculate the block error rate P t (ε), and finally calculate the average estimation error and compare it with the global variable. If the error is smaller, set the optimal error to the result of this calculation and pass the code length to the optimal code length. Continue the above loop until the optimal code length is found.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] The information age optimization method based on polar code incremental redundancy hybrid automatic repeat request proposed by the present invention first considers the impact of coding cost on real-time tracking performance under actual channel conditions, models the source as a Gaussian stationary source, and through considering the spatio-temporal correlation of the source, derives the average error of a certain transmission information packet predicting its nearby state within a period of time, which is a non-linear function of the information age. This measurement method hopes that the system can successfully transmit information with better timeliness compared with the traditional measurement method, and has better performance compared with the traditional linear information age.

[0042] Secondly, the invention combines the information age with the hybrid automatic repeat request transmission of polar codes for the first time, and studies the performance of the incremental redundancy hybrid automatic repeat request technology with higher coding gain in polar codes in real-time state update systems. The present invention derives the relationship between the non-linear function related to the information age, the maximum number of retransmissions, the polar code length, the redundant bits, and the decoding success probability under the polar code incremental redundancy hybrid automatic repeat request transmission mechanism, and establishes an optimization problem between the system average estimation error and the code length under a given transmission scheme. For the SC decoding of polar codes, the decoding success probabilities of the first transmission and retransmission are given by Gaussian estimation, and the optimal code length of the polar code incremental redundancy hybrid automatic repeat request transmission scheme is found by the greedy algorithm. Compared with other retransmission mechanisms (non-automatic repeat request, classical automatic repeat request, truncated automatic repeat request, and truncated hybrid chase combining automatic repeat request), the system estimation error of the proposed scheme is the smallest under various channel conditions.

[0043] Finally, the present invention verifies the advantages of the above-mentioned proposed metric and the incremental redundancy hybrid automatic repeat request transmission mechanism in real-time tracking performance through simulation experiments, and obtains that the system error of the information packet for predicting different distances can obtain the information validity coverage range according to the upper bound of the error tolerance, providing a basis for the subsequent scheduling of the sensor network and the deployment of the sensor network topology.

[0044] In summary, the present invention studies the value of the age of information for system prediction of a stationary Gaussian source in a real-time state update system. Focusing on the monitoring of spatio-temporal processes in wireless sensor networks, using the system prediction error as a metric for information freshness, studying the information validity range of sensor nodes, designing a polarization code encoding scheme in an actual additive white Gaussian noise channel, and introducing an incremental redundancy hybrid automatic repeat request scheme to optimize the average estimation error of the system, so as to reduce the average age of information of the system and expand the information validity range of information packets. The present invention proposes a method for designing the code length of polarization codes in channel coding, so that the average age of information of the system for a period of time is minimized. The simulation results show that the retransmission scheme of IR-HARQ using polarization codes in an actual communication system against channel noise has obvious performance improvement in enhancing the information freshness of the entire system, compared with the hybrid tracking combining automatic repeat request, non-automatic repeat request and classical automatic repeat request schemes proposed in previous studies. The research results have practical value for communication systems that actually use polarization code encoding and SC decoder decoding. Moreover, the present invention considers the information correlation of sensor nodes in wireless sensor networks, and obtains the estimation error of information packets for predicting information of nodes at different distances, and can obtain the information validity coverage range according to the upper bound of the error tolerance, providing a basis for the subsequent scheduling of the sensor network and the deployment of the sensor network topology. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings.

[0046] Figure 1 It is a general coding-based real-time state update monitoring system diagram provided by an embodiment of the present invention.

[0047] Figure 2 It is an information validity range diagram provided by an embodiment of the present invention.

[0048] Figure 3 It is an evolution diagram of the error of a single information packet for prediction over time provided by an embodiment of the present invention.

[0049] Figure 4 The polarization matrix G with code lengths M = 8, 12, and 16 provided by the embodiments of the present invention M 。

[0050] Figure 5 The performance curves of the objective function at the optimal code length for transmitting using polar codes under different retransmission mechanisms (ARQ, non - ARQ, puncturing HARQ - CC, no puncturing IR - HARQ, puncturing IR - HARQ) provided by the embodiments of the present invention

[0051] Figure 6 The performance curves of the objective function at a fixed code length for transmitting using polar codes under different retransmission mechanisms provided by the embodiments of the present invention Detailed implementation manners

[0052] To better understand the technical solution, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described examples are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art based on this application belong to the scope of protection of the present invention.

[0053] 1 System model

[0054] We consider a real - time status update system where a single sensor in a wireless sensor network transmits monitoring information through a wireless channel. Source coding encodes the information packet into K - bit status update information u, and the status update information is encoded into an L - bit packet c using polar codes. After channel modulation, it becomes the transmitted signal x and is transmitted through an additive white Gaussian noise channel w. The receiving end demodulates the received signal y to obtain ĉ and then decodes it to û to recover the transmitted status update information.

[0055] We assume that the signal ACK / NACK indicating whether each transmission is successful is transmitted through a noiseless channel, and the time consumed by its transmission is not considered. When the sensor end receives the NACK signal, it will decide whether to re - transmit the failed packet or transmit a new data packet according to the maximum number of re - transmissions N. After receiving the ACK signal, the sensor will immediately collect the current status and transmit it, which is the zero - waiting strategy. Adopting this sampling strategy in the present invention can simplify the subsequent derivation process on the one hand, and on the other hand, the zero - waiting strategy has also been proven to be the information - age - optimal sampling strategy for the hybrid automatic repeat request transmission mechanism in most cases.

[0056] 1.1 System estimation error model

[0057] The system consists of a wireless sensor network. The physical phenomena monitored by the network are spatially distributed and vary over time. We represent the information collected at the 3D physical space position x at time t as Z(x, t). The physical phenomena observed by the sensors are generally affected by multiple factors and have a certain degree of randomness. According to the central limit theorem, without loss of generality, it is considered that the observed value Z at position x at time t follows a standard Gaussian distribution. Assuming that within the observed region, the correlation of the random variables to be observed is spatio-temporally uniform and decays exponentially with spatio-temporal intervals, the covariance between the information Z(x, t) and the information Z(x + d, t + Δt) at a point with a distance d from it at the current time can be written as:

[0058] ρ(d, Δτ) = e -αΔτ-βd (1)

[0059] If the system uses outdated information to predict the current physical phenomena, a system prediction error will occur. The magnitude of this error depends on the age of the information and the distance between the prediction point and the information source, and can be expressed as:

[0060] ∈(d, Δτ) - 1 - ρ(d, Δτ) 2 = 1 - e -2αΔτ-2βd (2)

[0061] According to the fault-tolerant sensing coverage range of the sensing nodes, the upper bound of the error tolerance of the system is defined as ε,

[0062] ∈(d, Δτ) < ε (3)

[0063] According to Equation (2), we can obtain

[0064]

[0065] As Figure 2 shown, the range of information validity decreases as the age of the information packet increases. Therefore, it is important to design a channel coding scheme to make the range of information validity cover a wider area within a certain period of time, which will guide the sensor deployment and scheduling schemes.

[0066] Next, we will derive the specific expression of the system estimation error in the actual coding system within a certain period of time. Since the influence of channel noise in the actual coding system cannot be ignored and will hinder the successful reception of information packets, a retransmission mechanism is often used in practice to combat channel noise and ensure accurate information transmission. However, the freshness of the information will inevitably decrease during the retransmission process. How to design a reasonable retransmission scheme to minimize the age of the information within a certain period of time is the key issue to be focused on in the following. In the present invention, we use a non-linear function of the age of the information for the system estimation error to measure.

[0067] The sampling strategy of the system is the zero-waiting strategy, and the transmission strategy is the truncated incremental redundancy hybrid automatic repeat request scheme. That is, if the current information packet still cannot be decoded successfully after reaching the maximum number of retransmissions, the current state is sampled as a new information packet for transmission. The evolution of the prediction error of the system over time is as shown in Figure 2 shown, where t i is the generation time of the i-th information packet, is the successful reception time of the i-th information packet, where the maximum number of retransmissions of the system is set to N, is the time when the i-th information packet exceeds the maximum number of retransmissions, and the current state is sampled as a new information packet. The average error of the system over a period of time can be expressed as the quotient of the area R i formed by the system error of the i-th transmission and the time period X i from the generation of the first packet to the successful decoding of the last packet at the receiving end in the i-th transmission:

[0068]

[0069] The area R i formed by the system error of the i-th transmission can be derived according to the integral:

[0070]

[0071] Then we calculate E[R i as follows,

[0072] E[R i = (1 - e -2βd )E[X] + αe -2βd E[X 2 + 2αe -2βd E[X]E[Q] (7)

[0073] Substituting equation (7) into (5), we can obtain the expression of the average prediction error:

[0074]

[0075] Among them, E[X2], E[X], and E[Q] in equation (8) depend on the specific coding scheme.

[0076] 1.2 Polar Code Incremental Redundancy Hybrid Automatic Repeat Request Transmission Model

[0077] Polar codes have the basic coding elements of general binary linear block codes, so their generator matrices can be explicitly written to complete the coding. A binary polar code with a code length of N = 2 n can be constructed as:

[0078]

[0079] Among them, is the information bit vector, is the codeword vector after polar code encoding, and G N is the generating matrix, where is the polarization matrix of size N*N, represents the matrix of the n-th Kronecker product, and there is a recurrence formula Consider a binary-input discrete memoryless channel which can be represented as W: X→Y, X = {0, 1} is the set of input symbols, Y is the set of output symbols, and the transition probability is W(y|x), x ∈ X, y ∈ Y. After channel combining and splitting, the channel capacities of each sub-channel show a trend of polarization. As the code length increases, the capacities of some sub-channels tend to 1, while the capacities of the remaining sub-channels tend to 0. Let the set with cardinality K be a subset containing the row indices of the generating matrix G N , corresponding to the K most reliable bit channels. This set represents the information bit channel set. The corresponding set represents the frozen bit channel set. Information is carried on the elements with index values in the set, and the remaining positions store the frozen bits (0 or 1) known in advance by the codec. According to the QUP algorithm, the N-bit codeword can be punctured into an L-bit codeword, where L < N, to achieve a more flexible transmission rate.

[0080] For the proposed adaptive hybrid automatic repeat request transmission scheme of polar codes, it is mainly based on the channel polarization phenomenon, and more reliable bit channels are generated by increasing the code length. Since the mother code of length 2 m is the sub-vector of the mother code of length 2 m+x and the last 2 m codeword bits, the last 2 m+x codeword bits of a 2 m codeword itself is a smaller polar mother codeword, and the polar decoder can recursively combine several short codewords (2 m bits) into a longer (2 m+x bits) at the input LLR stage. In particular, using the lower triangular property and high structural nature of the polarization matrix, the hybrid automatic repeat request retransmission mechanism of polar codes can be designed.

[0081] A matrix of size 2N can be represented as As Figure 3 shown, G 8 can be regarded as a sub-matrix of G 12 , and can also be regarded as G 16Sub - matrices. This property of the generating matrix can be utilized to expand a small polarization matrix into a larger one to carry redundant bits for re - transmission. By this method, more reliable bit channels can be obtained by combining redundant bits during the decoding process to increase the decoding success probability.

[0082] As Figure 1 shown, assume that the initial transmission code rate is \(K / M\) for the polarization codeword \(c\) 1 . If the decoding is not successful, an extended polar code \(c\) 2 with an arbitrary extended length \(\Delta M\) bits is transmitted through the polarization matrix. The decoder jointly decodes \(c\) 1 and \(c\) 2 . At this time, the set of information - bit channels is determined by \(c\) 1 and \(c\) 2 . The information bits are still transmitted on the K most reliable information - bit channels. The decoder efficiently decodes the polarization code with a code rate of \(K / (M + \Delta M)\) until the decoding is successful and an ACK is sent back or the maximum re - transmission times \(T\) is reached.

[0083] In the present invention, the concept of parity - check or dynamic frozen - bit channels is borrowed to represent frozen bits, and their values are determined by some of the previous information bits. Therefore, the new information - bit channels are always placed before the original part of the extended part used for the previous transmission. In this way, the new information bits are first decoded by SC decoding, and the corresponding less reliable information bits become parity - check frozen bits, which means that the information bits are placed on the most reliable bit channels for re - transmission, and the less reliable bit channels of the previous transmission naturally become frozen bits. The performance is determined by the re - transmission of the constructed low - rate code, which enjoys the full coding gain.

[0084] 1.3 Gaussian Estimation of Bit - Error Rate Analysis

[0085] According to the polarization - code encoding principle, the construction of a polarization code is a problem of polarization - channel selection, and the selection of polarization channels is actually based on the criterion of optimizing the SC decoding performance. According to the polarization - channel transition - probability function, the polarization channels are not independent of each other but have a definite dependence relationship: the polarization channels with larger channel numbers depend on all the polarization channels with smaller numbers than theirs. Based on this dependence relationship between polarization channels, when the SC decoding algorithm makes a decoding decision on each bit, it is necessary to assume that the results obtained from the previous steps of decoding are correct. And it is under this decoding algorithm that the polarization code is proven to be capacity - achieving. Therefore, for polarization codes, the most suitable decoding algorithm should be based on SC decoding, and only this type of decoding algorithm can make full use of the structure of polarization codes and at the same time ensure capacity - achieving when the code length is long enough. In this paper, SC decoding is used to calculate the decoding error rate.

[0086] We denote as \(u\)i For the corresponding decoding result, the i-th bit error can be represented as event B i :

[0087]

[0088] Then The probability of unsuccessful decoding can be expressed as:

[0089]

[0090] The research scenario of the present invention is an actual additive white Gaussian noise channel. Under a binary additive white Gaussian noise channel, the probability density function of the LLR value in density evolution can be approximated by a cluster of Gaussian distributions with a variance twice the mean, thus simplifying it into the calculation of the one-dimensional mean and greatly reducing the computational complexity. This simplified calculation of density evolution is the Gaussian approximation. According to the Gaussian approximation, the error probability of the i-th bit is:

[0091]

[0092] where can be obtained through SC decoding and can be calculated according to the following recurrence relation:

[0093]

[0094]

[0095]

[0096]

[0097] where The function adopts an improved AGA function:

[0098]

[0099] 2 System objective modeling

[0100] In the previous section, based on the SC decoding principle of polar codes and the method of Gaussian estimation, we obtained the bit error rate of each transmission based on the IR-HARQ retransmission mechanism. Next, we can solve for E[X 2 , E[X], and E[Q].

[0101] Recalling the previous section, in the truncated incremental redundancy hybrid automatic repeat request transmission mechanism, X kFor the k-th transmission, it is the time period from the generation of the first packet to the successful decoding of the last packet at the receiving end. The coding system uses polar codes for encoding and an incremental redundancy hybrid automatic repeat request transmission mechanism for transmission. Let the maximum number of retransmissions be T, and the code length for each transmission be l i , i = 1, 2,..., T, each channel transmits ρ bits, that is, the transmission time is proportional to the code length. The possible values of the random variable X can be deduced as follows:

[0102]

[0103] where p f is the probability of successful decoding for the f-th transmission, p f = 1 - P(ε), and P(ε) can be obtained from the recurrence formula derived in formula (10). Then, we can calculate the expected values of the random variables X and X 2

[0104]

[0105]

[0106] Q is the time period from the generation of the successfully received packet to the final reception. Similarly, we can get:

[0107]

[0108]

[0109]

[0110] Substituting into we can get

[0111]

[0112] where

[0113] From the final expression (23), it can be seen that in each transmission (the first transmission and retransmissions), increasing the coding length and decreasing the code rate k / n can help the decoder perform efficient decoding and increase the decoding success rate p f , and fresh information packets can be obtained with fewer retransmission rounds, which helps to reduce the system estimation error; however, at the same time, the cost of increasing the code length is an increase in transmission time, which also leads to a decrease in the freshness of information packets. This requires us to make a trade-off between transmission time and decoding success probability.

[0114] Naturally, the optimization problem in this paper is established as: given the maximum number of retransmissions T and the physical channel condition (CSI), find the optimal puncturing length L = 2 of the polar code encoding​s -N p and the retransmission code length, so that when ensuring that the effective range d of each node information remains unchanged, the average system estimation error is minimized, that is:

[0115]

[0116] 3 Optimization Algorithm

[0117] According to the derived formula, when the signal-to-noise ratio of the physical channel condition, the code length under the incremental redundancy hybrid automatic repeat request transmission mechanism, and the maximum allowed number of retransmissions are known, we can calculate and estimate the optimization objective. Therefore, when the maximum number of retransmissions of the system and the physical channel condition are known, the present invention uses a greedy algorithm to search for the optimal code length, and the specific algorithm flow is shown in Table 1.

[0118] Table 1

[0119]

[0120]

[0121] The specific process is as follows: The bit length K of the source state information, the signal-to-noise ratio SNR of the current channel condition, the estimated distance d, and the maximum number of retransmissions N set by the coding system are used as the input quantities of the algorithm. Initialize the global variable of the optimal system estimation error to infinity, and set the optimal code length vector to a zero vector. Then enter the loop, and in each loop, increase the code length by 1 in sequence according to the retransmission order. Calculate the channel Gaussian noise variance through the formula σ 2 =10 -SNR / 10 / 2. For each retransmission, calculate the total polar code length and the mother code length, and use Gaussian estimation to update the index set of the set information bits according to the parameter matrix (M i ,l i ,K,σ 2 ). Use formula (11 - 16) to calculate the block error rate P (ε) according to the parameter matrix t . Finally, calculate the average estimation error according to formula (23) and compare it with the global variable. If the error is smaller, set the optimal error to the result of this calculation, and pass the code length to the optimal code length. Continue the above loop until the optimal code length is found.

[0122] The information age optimization method of the present invention focuses on the monitoring of spatio-temporal processes in wireless sensor networks, uses the system prediction error as a metric for information freshness, studies the effective range of information of sensor nodes, designs a polar code coding scheme in an actual additive white Gaussian noise channel, and introduces an incremental redundancy hybrid automatic repeat request scheme to optimize the average estimation error of the system, so as to reduce the average information age of the system and expand the effective range of information of information packets.

[0123] In the present invention, it is different from the prior art in many aspects. First, the research on the age of information in the present invention is based on an actual additive white Gaussian noise channel, and the commonly used polar code is used as the coding scheme to combat channel noise. Second, the present invention focuses on the spatio-temporal correlation of physical processes, establishes a non-linear function of the system evaluation error with respect to the age of information and distance, and uses it as the metric and optimization objective. Third, the present invention adopts an incremental redundancy hybrid automatic repeat request transmission scheme during the channel transmission process, and obtains the code length and redundant bit length that minimize the optimization objective through an algorithm. And through simulation, it is verified that it has better age-of-information performance compared with the hybrid chase combine automatic repeat request scheme in the prior art (reference [3]). The simulation diagram is as Figure 5 and Figure 6 shown.

[0124] The above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request, characterized in that, the coding system uses polar code coding and transmits through an additive white Gaussian noise channel using an incremental redundancy hybrid automatic repeat request transmission mechanism. The information age optimization steps are as follows: S1. Establish a non-linear function regarding the system average estimation error, information age, and the information validity range of each node; for the SC decoding of polar codes, use Gaussian estimation to give the decoding success probabilities of the first transmission and retransmission; the expression of the system average estimation error is: where α and β are the scaling parameters in time and space respectively, l is the straight-line distance between the information packet and the prediction point, E[X], E[X 2 , and E[Q] are the expected values of the random variables X, X 2 , and Q respectively, X is the time period from the generation of the first packet to the successful decoding at the receiving end of the last packet, X 2 is the second moment of X, and Q is the time period from the generation to the final reception of the successfully received packets; S2. Under the known maximum number of retransmissions and physical channel conditions, use the system average estimation error as a metric for information freshness, and establish an optimization objective between the system average estimation error and the polar code length: find the optimal polar code length to minimize the system average estimation error while ensuring that the information validity range of each node remains unchanged; The optimization objective of step S2 is expressed as: Among them, α and β are the scaling parameters in time and space respectively, ρ is the number of bits transmitted per channel, that is, the transmission time is proportional to the code length; p f is the decoding success probability of the f-th transmission; T is the maximum number of retransmissions, and the code length of each transmission is l i , i = 1, 2,..., T, the coding length; N is the maximum number of retransmissions of the system, d is the information validity range of each node, k is an integer, is an integer less than k; S3. Use the greedy algorithm to find the optimal polar code length of the optimization objective.

2. The Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request according to claim 1, characterized in that, the system consists of a wireless sensor network. The source coding encodes the information packet into a K-bit status update message u. The status update message is encoded into an L-bit packet c using a polar code, modulated through the channel to become the transmitted signal x, and transmitted through the additive white Gaussian noise channel w. The sampling strategy of the coding system is the zero-waiting strategy.

3. The Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request according to claim 1, characterized in that, in step S1: Among them, \(x\) is the set composed of all possible time periods, the maximum number of retransmissions is \(T\), and the code length of each transmission is \(l\). i , \(i = 1, 2, \cdots, T\), \(p\) f is the probability of successful decoding of the \(f\)-th transmission, \(k\) is an integer, is an integer less than \(k\).

4. The Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request according to claim 1, characterized in that, the polar code incremental redundancy hybrid automatic repeat request transmission mechanism is: A matrix of size 2N is represented as G N as the generating matrix, where is a polarization matrix of size N*N, denotes the n-th Kronecker product of the matrix with the recurrence formula By utilizing the lower triangular property and high structural property of the polarization matrix, the small polarization matrix is extended to a larger polarization matrix to carry redundant bits for retransmission, and the redundant bits are combined during the decoding process to obtain a more reliable bit channel, so as to increase the decoding success probability.

5. The Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request according to claim 1, characterized in that, The method for polar code incremental redundancy hybrid automatic repeat request transmission is as follows: Assume that the initial transmission code rate is K / M for the polar codeword c 1 , if the decoding is unsuccessful, transmit the extended polar code c with an arbitrary extension length of ΔM bits through the polarization matrix 2 , and the decoder jointly decodes c 1 , c 2 . The information bit channel set is determined by c 1 , c 2 . The information bits are still transmitted on the K most reliable information bit channels. The decoding end efficiently decodes the polar code with a code rate of K / (M + ΔM) until a successful decoding signal ACK is returned or the maximum retransmission count T is reached.

6. The Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request according to claim 5, characterized in that, use parity check or dynamic frozen bit channels to represent frozen bits.

7. The Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request according to claim 1, characterized in that, in step S1, according to Gaussian estimation, the error probability of the i-th bit is expressed as: Among them, B i is the i-th bit error event, is the average of the log-likelihood (LLR) of u i obtained by the SC decoder, obtained through SC decoding, and obtained according to the following recurrence relation: wherein, is the log-likelihood ratio (LLR) value of u obtained by the SC decoder, σ is the standard deviation of the channel Gaussian noise, and m is the mean value of the channel Gaussian noise. i ​ 8. The Information Age Optimization Method Based on Polar Code Incremental Redundancy Hybrid Automatic Repeat Request according to claim 1, characterized in that, the optimization algorithm of step S3 is: Based on the bit length K of the source status information, the current channel condition signal-to-noise ratio SNR, the estimated distance d, and the maximum number of retransmissions N set by the coding system as the input quantities of the algorithm; initialize by setting the global variable of the optimal system average estimation error to infinity and the optimal code length vector to the 0 vector; then enter a loop, and in each loop, increase the code length by 1 in sequence according to the retransmission order; calculate the channel Gaussian noise variance through the formula σ 2 = 10 -SNR / 10 / 2; for each retransmission, calculate the total polar code length and the mother code length, and use Gaussian estimation to update the index set of the set information bits according to the parameter matrix (M i , l i , K, σ 2 ); Calculate the block error rate P (ε) according to the parameter matrix t . Finally, calculate the average estimation error and compare it with the global variable. If the error is smaller, set the optimal error to the result of this calculation and pass the code length to the optimal code length; continue the above loop until the optimal code length is found.

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