Maximum posterior probability decoding method and system for high-bit-rate convolutional codes

Abstract

The invention belongs to the technical field of space communication and satellite communication, and particularly relates to a maximum posterior probability decoding method and system for a high-bit-rate convolutional code. The method comprises the following steps: converting received high-bit-rate convolutional code word soft information into log-likelihood ratio information; updating of forward information is carried out on the Trellis graph; the backward information is updated on the Trellis graph; according to the updated forward information and backward information, calculating side information of all the Trellis branches; obtaining log-likelihood posterior probability information of each input bit according to the side information of each branch; and obtaining final decoding output by judging logarithm likelihood posterior probability information of each input bit. By adopting the method provided by the invention, the bit error rate of the CCSDS high-bit-rate convolutional code can be reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of space communication and satellite communication, and in particular relates to a maximum a posteriori probability decoding method and system for high-code rate convolutional codes. Background Art

[0002] Satellite-to-ground communications, such as spacecraft tracking and control communications and satellite communications, involve long-distance transmission of information. The received signal power is weak and the received signal-to-noise ratio is low, which will lead to a high data bit error rate and affect the reliable reception of information. Error control coding must be used to reduce the bit error rate of transmitted information. Therefore, channel coding is the key underlying technology of the satellite-to-ground communication system and an important basis for ensuring reliable information transmission.

[0003] Among them, convolutional code, as a code type in channel coding, can be encoded only through simple shift register operations, and usually a single-digit constraint length can obtain considerable coding gain. In terms of decoding, the Viterbi decoding algorithm is used to achieve maximum likelihood decoding of convolutional codes with a relatively low computational complexity. Therefore, it is widely used in various communication systems such as satellite communications and wireless communications. For example, the Consultative Committee for Space Data Systems (CCSDS) uses a feedforward convolutional code with a constraint length of 7 as its recommended channel coding scheme. The initial code rate is 1 / 2, and different hollowing methods can be used to obtain higher code rate coding, which can be used as an alternative coding strategy in variable coded modulation (VCM) or adaptive coded modulation (ACM).

[0004] However, the high-rate convolutional code obtained by the hole-punching has a certain coding gain loss in Viterbi decoding compared with the case without the hole-punching due to the lack of prior information at the hole-punching position. The more holes are punched, the higher the code rate and the greater the coding gain loss. Summary of the invention

[0005] Aiming at the coding gain loss problem of the hollowed-out high-rate convolutional code under Viterbi decoding in the CCSDS standard, the purpose of the present invention is to overcome the above-mentioned defects of the prior art and propose a maximum a posteriori probability decoding method for high-rate convolutional decoding. By performing forward and backward updates of the likelihood information on the Trellis diagram, the posterior information corresponding to each coded bit after receiving the entire coded codeword is finally obtained, thereby improving the bit error performance of the hollowed-out convolutional code.

[0006] In view of this, the present invention proposes a maximum a posteriori probability decoding method for a high-rate convolutional code, comprising:

[0007] Step 1: Convert the received high-rate convolutional codeword soft information into log-likelihood ratio information;

[0008] Step 2: Update the forward information on the Trellis graph;

[0009] Step 3: Update the backward information on the Trellis graph;

[0010] Step 4: Calculate the side information of all Trellis branches based on the updated forward information and backward information;

[0011] Step 5: Based on the side information of each branch, obtain the log-likelihood a posteriori probability information of each input bit;

[0012] Step 6: Obtain the final decoding output by judging the log-likelihood a posteriori probability information of each input bit.

[0013] Preferably, the high-rate convolutional code received in step 1 is ,in, For two outputs, , represents the kth coding block, n is the length of the coding block information bit;

[0014]

[0015] in, , is the modulated output, are independent and have a mean of 0 and a variance of A normally distributed random variable, is the power spectral density of the one-sided noise.

[0016] Preferably, the log-likelihood ratio information in step 1 is , satisfying the following formula:

[0017] .

[0018] Preferably, the step 2 comprises:

[0019] The forward information of the 0th coding block is calculated according to the following formula To initialize:

[0020]

[0021] in, is the state of the convolutional encoder, that is, the different values ​​stored in the encoding shift register, which belongs to the state set , M is the number of states;

[0022] For k from 1 to n, the forward update is performed according to the following formula to obtain the forward information of the current state of the updated k-th coding block: :

[0023]

[0024] in, Indicates the previous state in the Trellis diagram The forward information, and this information is passed through the input information Arrived at the current state ; For input information Arrived at the current state The encoding output codeword is is the log-likelihood ratio information of the k-1th coding block, and m represents the mth bit of the current codeword.

[0025] Preferably, step 3 comprises:

[0026] According to the following formula, the backward information of the nth coding block is To initialize:

[0027]

[0028] For k from n to 1, the backward update is performed according to the following formula to obtain the backward information of the current state of the kth coding block after the update: :

[0029]

[0030] in, Indicates the next state in the Trellis diagram The backward information is generated by the current state By inputting information arrive; is in the current state Next, by inputting information Arrival Status The encoding output codeword is is the log-likelihood ratio information of the kth coding block.

[0031] Preferably, the side information of all Trellis branches in step 4 is , satisfying the following formula:

[0032]

[0033] in, Indicates from the state Departure, by inputting information Transfer to state The state transfer posterior information corresponding to the corresponding edge, each edge in each branch in the Trellis graph corresponds to a state transfer posterior information.

[0034] Preferably, the log-likelihood a posteriori probability information of each input bit obtained in step 5 is for:

[0035]

[0036] in, and Respectively The binary data u is 0 and 1.

[0037] Preferably, the final decoding output in step 6 is , satisfying the following formula:

[0038]

[0039] in, is the final decoded output of the kth coding block.

[0040] Preferably, step 2 and step 3 are performed simultaneously or in sequence.

[0041] On the other hand, the present invention provides a maximum a posteriori probability decoding system for a high-rate convolutional code, comprising:

[0042] A conversion module, used for converting received high-rate convolutional codeword soft information into log-likelihood ratio information;

[0043] The forward update module is used to update the forward information on the Trellis graph;

[0044] Backward update module, used to update backward information on the Trellis graph;

[0045] A side information calculation module is used to calculate the side information of all Trellis branches based on the updated forward information and backward information;

[0046] A maximum a posteriori information acquisition module is used to obtain the log-likelihood a posteriori probability information of each input bit according to the side information of each branch;

[0047] The decision output module is used to obtain the final decoding output by deciding the logarithmic likelihood a posteriori probability information of each input bit.

[0048] Compared with the prior art, the advantages of the present invention are:

[0049] The present invention obtains the maximum a posteriori likelihood information of each coded bit by performing forward and backward updates of likelihood information on a Trellis graph, thereby improving the bit error performance of a CCSDS high-rate convolutional code. The method of the present invention can reduce the bit error rate of a CCSDS high-rate convolutional code. For a CCSDS convolutional code with an information length of 8920 bits and a code rate of 5 / 6 and 7 / 8, the method can obtain additional coding gains of about 0.2 dB and 0.6 dB, respectively, compared with a Viterbi decoding algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is the CCSDS convolutional coded transmitter information stream;

[0051] Figure 2 It is a flow chart of the maximum a posteriori probability decoding algorithm for high-rate convolutional codes;

[0052] Figure 3 This is the comparison of the bit error rate curve of 7 / 8 code rate CCSDS convolution code;

[0053] Figure 4 This is the comparison of the bit error rate curves of 5 / 6 code rate CCSDS convolutional codes;

[0054] Figure 5 This is the comparison of the bit error rate curve of 3 / 4 code rate CCSDS convolution code;

[0055] Figure 6 This is a comparison of the bit error rate curves of 2 / 3 code rate CCSDS convolutional codes. DETAILED DESCRIPTION

[0056] (1) The convolutional code recommended by the CCSDS standard is a non-systematic code with a code rate of 1 / 2, that is, one bit of information is converted into a two-bit codeword through a two-way feedforward convolution machine with a constraint length of 7, and then high-rate convolutional codes with code rates of 2 / 3, 3 / 4, 5 / 6 and 7 / 8 are obtained through periodic hollowing.

[0057] (2) Figure 1 The information flow from CCSDS convolutional coding to the final received codeword is given. Among them, is the kth input bit, For its corresponding two coded output bits, , n is the information bit length of the coding block.

[0058] (3) The coded output is then binary modulated, and the modulated output is , the specific modulation relationship is as follows:

[0059]

[0060] (4) The modulated information is then passed through an additive white Gaussian noise channel (AWGN) and the output is :

[0061]

[0062] in are independent and have a mean of 0 and a variance of A normally distributed random variable, is the power spectral density of the one-sided noise. That is, the coded codeword in the form of soft information received by the receiving end.

[0063] Figure 2 It is a flowchart of the convolutional decoding algorithm based on maximum a posteriori probability. The detailed decoding process is described as follows:

[0064] (5) First, convert the codeword information at the receiving end into log-likelihood ratio (LLR) information :

[0065]

[0066] (6) Then perform forward information on the Trellis graph Update:

[0067] (7) First, perform the following steps to Initialize, is the forward information of the 0th coding block:

[0068]

[0069] in, is the state of the convolutional encoder, that is, the different values ​​stored in the encoding shift register, which belongs to the state set , M is the number of states. The number of bits of the CCSDS convolutional code shift register is 6, corresponding to 64 states, that is, , arranged in order of value: , This is the state corresponding to the register being all zeros.

[0070] (8) Then for k from 1 to n, perform The forward update of is calculated as follows:

[0071]

[0072] in Indicates the previous state in the Trellis diagram The forward information, and this information is passed through the input information Arrived at the current state For input information Arrived at the current state The encoding output codeword is is the log-likelihood ratio information of the k-1th coding block, and m represents the mth bit of the current codeword.

[0073] (9) Then perform backward information on the Trellis graph Update:

[0074] (10) First, perform the following steps to To initialize:

[0075]

[0076] (11) Then for k from n to 1, The backward update of is calculated as follows:

[0077]

[0078] in Indicates the next state in the Trellis diagram The backward information is generated by the current state By inputting information arrive; is in the current state Next, by inputting information Arrival Status The encoding output codeword when .

[0079] (12) In actual operation and implementation, forward update and backward update can be performed in time-sharing or simultaneously. Time-sharing only requires one computing unit, while simultaneous operation requires two computing units to perform parallel calculations. Compared with time-sharing, simultaneous operation can nearly double the decoding throughput.

[0080] (13) When all and After the update is completed, the following formula can be used to calculate all Trellis branches The posterior probability of the state transition is in the form of log-likelihood: :

[0081]

[0082] in Indicates from the state Departure, by inputting information Transfer to state The state transfer posterior information corresponding to the corresponding edge, each edge in each branch in the Trellis graph corresponds to a state transfer posterior information.

[0083] (14) According to , the following formula is used to calculate the log-likelihood a posteriori probability information of each input bit, and its log-likelihood ratio form is expressed as :

[0084]

[0085] (15) Finally, the following formula is used to make a decision and obtain the final decoding output :

[0086]

[0087] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0088] Example 1

[0089] Embodiment 1 of the present invention proposes a maximum a posteriori probability decoding method for a high-rate convolutional code, comprising the following steps:

[0090] Step 1: Convert the received high-rate convolutional codeword soft information into log-likelihood ratio information;

[0091] Step 2: Update the forward information on the Trellis graph;

[0092] Step 3: Update the backward information on the Trellis graph;

[0093] Step 4: Calculate the side information of all Trellis branches based on the updated forward information and backward information;

[0094] Step 5: Based on the side information of each branch, obtain the log-likelihood a posteriori probability information of each input bit;

[0095] Step 6: Obtain the final decoding output by judging the log-likelihood a posteriori probability information of each input bit.

[0096] Figure 3~Figure 6 The bit error rate curves of the CCSDS high-rate convolutional code using the method proposed in this paper are given respectively, where Figure 3 This is the comparison of the bit error rate curve of 7 / 8 code rate CCSDS convolution code. Figure 4 This is the comparison of the bit error rate curve of 5 / 6 code rate CCSDS convolution code. Figure 5 This is the comparison of the bit error rate curve of 3 / 4 code rate CCSDS convolution code. Figure 6The figure is a comparison of the bit error rate curves of 2 / 3 code rate CCSDS convolutional codes. For comparison, the figure also shows the bit error rate curve of the Viterbi soft decoding algorithm and the Shannon limit of binary input at the corresponding code rate. As can be seen from the figure, the proposed method in this paper does have better decoding performance than the Viterbi decoding algorithm under high code rate conditions, and the higher the code rate (the more hollowing), the better the performance, especially when the code rate is 5 / 6 and 7 / 8, the proposed method in this paper can obtain about 0.2dB and 0.6dB coding gain (BER=1e-6) respectively compared with the Viterbi decoding algorithm. In addition, the performance of the Viterbi algorithm at high code rate will be greater than 4dB away from the Shannon limit, especially when the code rate is 7 / 8, the performance of the Viterbi algorithm is about 4.4dB away from the Shannon limit, while the proposed method in this paper can keep the performance of CCSDS convolutional codes with code rates of 5 / 6 and 7 / 8 within 4dB of the Shannon limit.

[0097] Table 1 shows the Eb / N0 required for CCSDS convolutional codes with different code rates to achieve a bit error rate of 1e-6 using the method proposed in this paper and the Viterbi decoding algorithm, and its difference with the corresponding Shannon limit.

[0098] surface Performance comparison table of CCSDS convolutional codes with different code rates using the proposed method and Viterbi algorithm

[0099]

[0100] Example 2

[0101] Embodiment 2 of the present invention provides a maximum a posteriori probability decoding system for a high-rate convolutional code, which is implemented based on the method of embodiment 1. The system includes:

[0102] A conversion module, used for converting received high-rate convolutional codeword soft information into log-likelihood ratio information;

[0103] The forward update module is used to update the forward information on the Trellis graph;

[0104] Backward update module, used to update backward information on the Trellis graph;

[0105] A side information calculation module is used to calculate the side information of all Trellis branches based on the updated forward information and backward information;

[0106] A maximum a posteriori information acquisition module is used to obtain the log-likelihood a posteriori probability information of each input bit according to the side information of each branch;

[0107] The decision output module is used to obtain the final decoding output by deciding the logarithmic likelihood a posteriori probability information of each input bit.

[0108] It is worth noting that in the embodiment of the above system, the modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of the functional modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of the present invention.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A maximum a posteriori probability decoding method for a high-rate convolutional code, comprising: Step 1: Convert the received high-rate convolutional codeword soft information into log-likelihood ratio information; Step 2: Update the forward information on the Trellis graph; Step 3: Update the backward information on the Trellis graph; Step 4: Calculate the side information of all Trellis branches based on the updated forward information and backward information; Step 5: Based on the side information of each branch, obtain the log-likelihood a posteriori probability information of each input bit; Step 6: Obtain the final decoding output by judging the log-likelihood a posteriori probability information of each input bit.

2. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 1, characterized in that: The high-rate convolutional code received in step 1 is ,in, For two outputs, , represents the kth coding block, n is the length of the coding block information bit; in, , is the modulated output, are independent and have a mean of 0 and a variance of A normally distributed random variable, is the power spectral density of the one-sided noise.

3. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 2, characterized in that: The log-likelihood ratio information in step 1 is , satisfying the following formula: 。 4. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 3, characterized in that: The step 2 comprises: According to the following formula, the forward information of the 0th coding block is To initialize: in, is the state of the convolutional encoder, that is, the different values ​​stored in the encoding shift register, which belongs to the state set , M is the number of states; For k from 1 to n, the forward update is performed according to the following formula to obtain the forward information of the current state of the updated k-th coding block: : in, Indicates the previous state in the Trellis diagram The forward information, and this information is passed through the input information Arrived at the current state ; For input information Arrived at the current state The encoding output codeword is is the log-likelihood ratio information of the k-1th coding block, and m represents the mth bit of the current codeword.

5. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 4, characterized in that: The step 3 comprises: According to the following formula, the backward information of the nth coding block is To initialize: For k from n to 1, the backward update is performed according to the following formula to obtain the backward information of the current state of the kth coding block after the update: : in, Indicates the next state in the Trellis diagram The backward information is generated by the current state By inputting information arrive; is in the current state Next, by inputting information Arrival Status The encoding output codeword is is the log-likelihood ratio information of the kth coding block.

6. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 5, characterized in that: The side information of all Trellis branches in step 4 is , satisfying the following formula: in, Indicates from the state Departure, by inputting information Transfer to state The state transfer posterior information corresponding to the corresponding edge, each edge in each branch in the Trellis graph corresponds to a state transfer posterior information.

7. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 6, characterized in that: The log-likelihood a priori probability information of each input bit obtained in step 5 is for: in, and Respectively The binary data u is 0 and 1.

8. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 7, characterized in that: The final decoding output in step 6 is , satisfying the following formula: in, is the final decoded output of the kth coding block.

9. The maximum a posteriori probability decoding method for high-rate convolutional codes according to claim 1, characterized in that: The steps 2 and 3 are performed simultaneously or in sequence.

10. A maximum a posteriori probability decoding system for high-rate convolutional codes, characterized in that: include: A conversion module, used for converting received high-rate convolutional codeword soft information into log-likelihood ratio information; The forward update module is used to update the forward information on the Trellis graph; Backward update module, used to update backward information on the Trellis graph; A side information calculation module is used to calculate the side information of all Trellis branches based on the updated forward information and backward information; A maximum a posteriori information acquisition module is used to obtain the log-likelihood a posteriori probability information of each input bit according to the side information of each branch; and The decision output module is used to obtain the final decoding output by deciding the logarithmic likelihood a posteriori probability information of each input bit.

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