Polarization code belief propagation decoding method for correcting insertion and deletion errors

Abstract

The invention discloses a polarization code belief propagation decoding method for correcting insertion and deletion errors, and relates to the field of digital communication error control coding. The method comprises the following steps: mixing information bits with the length of 1 and all-zero frozen bits with the length of 1 according to position indexes of preset information bits and fixed bits to obtain a bit sequence; encoding the bit sequence to obtain a sending sequence with the length of 1; the sending sequence is transmitted through an IDS channel to obtain a receiving sequence with the length of the IDS channel; and carrying out insertion and deletion error correction processing on the receiving sequence through a BP decoder based on a weighted Lelwstein distance, and outputting an information sequence estimated value. According to the method, the drift distance is introduced, and the weighted Levinstein distance is adopted as probability measurement, so that the problem that insertion and deletion errors cannot be corrected by a traditional BP decoding algorithm is solved. The inherent problem of an SC framework is also avoided, and the error correction capability is improved; and through parallel operation, the decoding time delay is reduced, and the unit time processing capacity is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of digital communication error control coding, in particular to a polar code belief propagation decoding method for correcting insertion and deletion errors. BACKGROUND

[0002] Insertion and deletion errors are usually caused by unstable receiver sampling clock or storage device defects. These errors make the channel have memory characteristics, and a single insertion or deletion can trigger a burst substitution error, causing the traditional polar code to fail and seriously affecting the communication quality. Therefore, the traditional polar code, LDPC code and other non-memory channel coding schemes have a sharp deterioration in error correction performance in such scenarios.

[0003] Polar code is the first constructed coding method that is strictly proven to approach the Shannon capacity limit. Its core is to decompose the original channel into a set of high-reliability and low-reliability sub-channels through channel polarization theory. Because of its low encoding and decoding complexity and provable capacity reachability, polar code was adopted by 3GPP as the standard coding scheme for control channels in the 5G enhanced mobile broadband scenario in 2016. At present, the research of polar code is mainly aimed at binary non-memory channels, and there is less research on insertion and deletion channels with memory.

[0004] In the prior art, for synchronization distortion caused only by deletion errors, a polar code successive cancellation (SC) decoding algorithm can be used, and an improved polar code SC decoding algorithm can solve the insertion, deletion and substitution (IDS) problem, but the channel model of this algorithm does not fully consider the complex characteristics in actual communication, resulting in a gap between the model and the actual scene, and its core is to perform decoding through a serial and recursive method. However, when dealing with insertion or deletion errors, there is an inherent structural limitation. Once a bit decision error is caused by synchronization error, the error will propagate and amplify, causing all subsequent decoding to fail, and the error correction capability is limited. SUMMARY

[0005] The purpose of the present application is to provide a polar code belief propagation decoding method for correcting insertion and deletion errors, which aims to solve or improve at least one of the above technical problems.

[0006] To achieve the above purpose, the present application provides the following scheme: A polar code belief propagation decoding method for correcting insertion and deletion errors, comprising: mixing information bits with a length of and all-zero frozen bits with a length of according to the position index of the preset information bits and fixed bits to obtain a bit sequence ;

[0007] Bit sequence Encoding yields a length of Sending sequence ; Send sequence The length obtained after transmission through the IDS channel is Received sequence ; The received sequence is processed by a BP decoder based on weighted Lewinstein distance. Perform correction of insertion and deletion errors, and output an estimated value of the information sequence; Specifically, the correction of insertion and deletion errors includes: The received sequence is calculated using a BP decoder based on weighted Lewinstein distance. The initialization information is used to iteratively calculate the left information probability and right information probability of each layer, and the output information sequence estimate is determined based on the probability of the last iteration.

[0008] Optionally, the position index of the fixed bit is determined using the Gaussian approximation method.

[0009] Optionally, the encoding method employs the construction of a generator matrix.

[0010] Optionally, the sequence to be sent The length obtained after transmission through the IDS channel is Received sequence Specifically, it includes: Send sequence The code in Transmission probability is obtained through insertion and deletion-substitution channels. , where the parameters and These represent the insertion and deletion probabilities of the channel, respectively; Define state For the first i The amount of drift per bit, Equal to sent bits Up to be sent bits The number of insertions minus the number of prunings in the sequence. exist Take the value from, where Total Each possible value This represents the maximum drift.

[0011] Optionally, the calculation of the received sequence using a BP decoder based on weighted Levenstein distance... The initialization information is used to iteratively calculate the left and right information probabilities of each layer, and the estimated information sequence value is output based on the probability of the last iteration. Specifically, this includes: The first step is to calculate the received sequence using a BP decoder based on weighted Levenstein distance. Initialization information: (1) Calculate the left information probability of layer 0: ; In the formula, Indicates the 0th layer bits and subsequence The weighted Levenstein distance between them, parameters , and These represent the insertion, deletion, and substitution probabilities of the channel, and the transmission probability, respectively. , for The amount of drift at the point, It represents the probability of updating to the left; (2) Calculate the first Right information probability of layer: ; In the formula, Represents the set of frozen bit channel indices. Represents the set of information bit channel indices. , , , It represents the probability of updating to the right. For the first N The amount of drift per bit; The second step is to iteratively calculate the left and right information probabilities of each layer using the initialization information: For the The bits of the layer are composed of a set Represents an index, where , , For the first k The bits of layer +1 are composed of a set of Represents an index, where , ; The following definitions are used in the calculation: For the layer: , , , ; For the kLayer +1: , , , ; wherein, is the number of layers, m is the set of all blocks in the k th layer, is the set of all blocks in the k th layer, is the upper bound of blocks in the k th layer, is the lower bound of blocks in the k th layer, is the middle value of and , is the upper bound of blocks in the k th layer, is the lower bound of blocks in the k th layer, is the middle value of and , ; First, the left information probability of all nodes is updated: (1) The calculation formula of the left information probability of bits in even index position is: ; (2) The calculation formula of the left information probability of bits in odd index position is: ; Then, the right information probability of all nodes is updated: (1) The calculation formula of the right information probability of bits between the upper bound and the middle value is: ; (2) The calculation formula of the right information probability of bits between the middle value and the lower bound is: ; wherein, denotes the sequence , the set , , , denotes the drift of points, points and points respectively, , , denotes point, Point and The amount of drift at the point, Indicates the maximum drift amount. Indicates the first The first layer 1 bit; The iterative computation process follows a two-way message propagation mechanism. Propagate from right to left, layer by layer, starting from the initial node. The message is passed from left to right layer by layer from the termination node. When bidirectional probability synchronization covers all nodes, it is recorded as a complete iteration. The iteration continues until the preset number of iterations is reached or the message convergence condition is met. The third step is to output an estimated information sequence based on the probability decision made in the last iteration: First determine the first If the bit is an information bit or a frozen bit, then 0 is used as the final decision; if it is an information bit, then the likelihood ratio is used for the decision. Value: ; in, Indicates the first The likelihood ratio of each position is calculated using the following formula: .

[0012] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a polar code confidence propagation decoding method for correcting insertion and pruning errors. The method includes decoding a polar code of length... Information bits and length are The all-zero frozen bits are mixed according to the preset position indices of the information bits and fixed bits to obtain the bit sequence. ; for bit sequences Encoding yields a length of Sending sequence ; will send sequence The length obtained after transmission through the IDS channel is Received sequence The received sequence is processed by a BP decoder based on weighted Levenstein distance. This invention corrects insertion and pruning errors and outputs an estimated information sequence. By introducing a drift factor and using weighted Levenstein distance as a probability metric, this invention solves the problem that traditional BP decoding algorithms cannot correct insertion and pruning errors. Furthermore, this invention effectively avoids the inherent problems of the SC framework through an iterative update mechanism, improving error correction capability; and reduces decoding latency and increases processing throughput per unit time through parallel operations. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only represent some of the embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without any creative effort.

[0014] Figure 1 The system block diagram of the polar code decoding method for correcting insertion and deletion errors in the embodiment; Figure 2 The schematic diagram of the iteration calculation of the BP decoding algorithm based on WLD containing a drift amount in the embodiment; Figure 3 The performance simulation comparison diagram of the method and the conventional BP decoding algorithm in the embodiment; Figure 4 The performance simulation comparison diagram of the method and the SC decoding algorithm based on WLD in the embodiment. DETAILED DESCRIPTION

[0015] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments only represent some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort fall within the protection scope of the present application.

[0016] The purpose of the present application is to provide a polar code belief propagation decoding method for correcting insertion and deletion errors, aiming to solve or improve at least one of the above technical problems.

[0017] In order to make the above purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0018] As shown in Figure 1 The present application provides a polar code belief propagation decoding method for correcting insertion and deletion errors. Compared with the conventional scheme, the embodiments of the present application make the following modifications: First, the transmission sequence passes through an IDS channel.

[0019] Second, a drift amount is introduced in the calculation of the decoding algorithm, which can be used to correct insertion and deletion errors.

[0020] Third, the weighted Levenshtein distance is used as a probability metric.

[0021] Compared with the traditional BP decoding algorithm, the embodiments of the present invention introduce drift amount into the decoding algorithm to obtain insertion and pruning error correction capabilities, thus broadening the application scope of polar codes.

[0022] The following is a detailed description of a polar code decoding method for correcting insertion and deletion errors provided by an embodiment of the present invention, with reference to the accompanying drawings. See the description below for details: like Figure 1 As shown, the method includes the following four steps: Step 1. Bit sequence generation: Generate a bit sequence of length... Information bits and length are The all-zero frozen bits are mixed according to the preset positions of the information bits and fixed bits to obtain a bit sequence. .

[0023] Step 2. Polar code encoding: Encode the bit sequence to obtain a length of... Sending sequence .

[0024] Step 3. IDS Channel Transmission: The transmitted sequence, after being transmitted through the IDS channel, yields a sequence of length... Received sequence .

[0025] Step 4. WLD-based BP decoder: The received sequence is processed using a WLD-based BP decoder. This step (4) includes: Step 4.1 Calculate the initialization information of the received sequence to initialize the left information probability and right information probability in the BP decoding algorithm.

[0026] Step 4.2 Iteratively calculate the left information probability and right information probability of each layer using the initialization information.

[0027] Step 4.3 Based on the probability decision of the last iteration, output the estimated value of the information sequence.

[0028] The following describes the specific implementation process of the above four steps: Step 1 uses the Gaussian approximation method to determine the position index of the fixed bit.

[0029] The encoding in step 2 includes constructing a generator matrix, which is the same as the traditional encoding method.

[0030] Transmission sequence in step 3 The length of the insertion and pruning-substitution channel is... Received sequence The process includes: Send code Through insertion and deletion-substitution channels, parameters , and denote the insertion, deletion and substitution probabilities of the channel, respectively, the transmission probability .

[0031] Define the state as the drift of the point, equal to the number of insertions minus the number of deletions in the sequence between the transmitted bit and the bit to be transmitted . The value of is taken from the set . There are values, and the maximum drift

[0032] The steps in step 4 are described in detail: Step 4.1: Calculate the initialization information of the received sequence : (1) Let , calculate the left information probability of the 0th layer.

[0033] ; In the formula, denotes the weighted Levenshtein distance between the th bit of the 0th layer and the subsequence , parameters , and denote the insertion, deletion and substitution probabilities of the channel, respectively, the transmission probability , is the drift of the point, and refers to the probability of updating to the left.

[0034] (2) Let , calculate the right information probability of the th layer.

[0035] ; In the formula denotes the frozen bit channel index set, denotes the information bit channel index set, , , and refers to the probability of updating to the right, is the drift of the N th bit.

[0036] Step 4.2: Use the initialization information to iteratively calculate the left information probability and the right information probability of each layer:​ For the first layer, the index is represented by a set of , , ; for the first k +1 layer, the index is represented by a set of .

[0037] The following definitions are used in the calculation: For the first layer: , , , ; For the first k +1 layer: , , , .

[0038] In the formula, is the number of layers, m is the set of all blocks in the first k layer, is the set of all blocks in the first k +1 layer, is the upper bound of the block in the first k layer, is the lower bound of the block in the first k layer, is the intermediate value of and , is the upper bound of the block in the first k +1 layer, is the lower bound of the block in the first k +1 layer, is the intermediate value of and .

[0039] First, complete the left information probability update of all nodes: (1) The calculation formula of the left information probability of the bit in the even index position is: ; (2) The calculation formula of the left information probability of the bit in the odd index position is: ; Next, complete the right information probability update of all nodes: (1) The calculation formula of the right information probability of the bit located at the upper bound​​​​​ The calculation formula of the bit right information probability between the median and the lower bound is as follows: (2) The calculation formula of the bit right information probability between the median and the lower bound is as follows: In the formula, the maximum drift amount represents the sequence , the set , , , respectively represents the drift amount of the point, the point and the point, , , respectively represents the drift amount of the point, the point and the point, represents the maximum drift amount, represents the bit of the layer.

[0040] The iteration process follows a bidirectional message propagation mechanism, propagates from right to left layer by layer from the starting node, propagates from left to right layer by layer from the ending node, and when the bidirectional probability synchronously covers all nodes, that is, the global update from right to left and from left to right is completed, it is recorded as one complete iteration. The iteration continues until a preset number of times or message convergence is reached.

[0041] Step 4.3: According to the probability decoding and decision of the last iteration, the information sequence estimation value is output: First, it is determined whether the bit is an information bit or a frozen bit. If it is a frozen bit, 0 is directly taken as the final decision result; otherwise, if it is an information bit, the value of the likelihood ratio decision is used: In the formula, the likelihood ratio of the bit is represented by , and the calculation formula is as follows: .

[0042] The above decoding process is shown in Figure 2 .

[0043] ​​The code length of the embodiment of the present application is 512 bits, the code rate of the polar code is 0.5, and the polar code is a special case. N A polar code BP decoding method for correcting insertion and deletion errors is described. In the simulation, the frozen bit position index is determined by the Gaussian approximation method, the encoding process is consistent with the traditional algorithm, and the maximum number of insertion errors of each bit in the channel is set to 5. I The maximum drift is limited according to the maximum number of insertion errors. .

[0044] Figure 3 The performance curves of the system's frame error rate and bit error rate with the change of insertion and deletion probabilities are shown under the condition that the substitution probability is 0. The frame error rate refers to the number of error frames divided by the total number of transmitted frames, and the bit error rate refers to the number of error bits divided by the total number of transmitted bits. The results show that as the insertion and deletion probabilities decrease, the system performance is significantly improved. Under the same insertion and deletion probabilities, the traditional BP decoding method fails to adapt to synchronous errors; in contrast, the method of the present application has lower frame error rate and bit error rate, and exhibits obvious performance gain. This verifies the ability of the method to effectively correct errors in the IDS channel and its excellent error performance.

[0045] Figure 4 The performance curves of the system's frame error rate with the change of insertion and deletion probabilities are shown under the condition that the substitution probability is 0. The results show that the frame error rate of the BP decoding algorithm of the present application is significantly reduced compared with the SC decoding algorithm based on WLD, and the system performance is improved.

[0046] It can be seen that first, the present application uses polar code based on WLD to correct insertion and deletion errors, and improves the traditional BP algorithm by introducing drift, achieving good error correction performance and ensuring the reliability of information transmission. Second, the BP decoding algorithm used in the present application fully utilizes the parallelism advantage of message passing compared with the SC decoding algorithm. This feature reduces the decoding delay and improves the processing capacity per unit time. In addition, even in the harsh channel conditions of code length , , , the number of iterations can be stably controlled within 5 to 10 times. Finally, compared with the improved SC decoding algorithm based on WLD, the improved BP decoding algorithm based on WLD of the present application achieves lower frame error rate under the same channel conditions through iterative message passing.

[0047] Each embodiment in the specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts of each embodiment can be referred to each other.

[0048] ​The principles and implementations of the present application are described in the specific examples in this article, and the above examples are only used to help understand the core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation and application range will be changed. Therefore, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A polar code confidence propagation decoding method for correcting insertion and pruning errors, characterized in that, include: The length is Information bits and length are The all-zero frozen bits are mixed according to the preset position indices of the information bits and fixed bits to obtain the bit sequence. ; Bit sequence Encoding yields a length of Sending sequence ; Send sequence The length obtained after transmission through the IDS channel is Received sequence ; The received sequence is processed by a BP decoder based on weighted Lewinstein distance. Perform correction of insertion and deletion errors, and output an estimated value of the information sequence; Specifically, the correction of insertion and deletion errors includes: The received sequence is calculated using a BP decoder based on weighted Lewinstein distance. The initialization information is used to iteratively calculate the left information probability and right information probability of each layer, and the output information sequence estimate is determined based on the probability of the last iteration.

2. The polar code confidence propagation decoding method for correcting insertion and pruning errors according to claim 1, characterized in that, The position index of the fixed bit is determined using the Gaussian approximation method.

3. The polar code confidence propagation decoding method for correcting insertion and pruning errors according to claim 1, characterized in that, The encoding method employs the construction of a generator matrix.

4. The polar code confidence propagation decoding method for correcting insertion and pruning errors according to claim 1, characterized in that, The sequence to be sent The length obtained after transmission through the IDS channel is Received sequence Specifically, it includes: Send sequence The code in Transmission probability is obtained through insertion and deletion-substitution channels. , where the parameters and These represent the insertion and deletion probabilities of the channel, respectively; Define state For the first i The amount of drift per bit, Equal to sent bits Up to be sent bits The number of insertions minus the number of prunings in the sequence. exist Take the value from, where Total Each possible value This represents the maximum drift.

5. The polar code confidence propagation decoding method for correcting insertion and pruning errors according to claim 1, characterized in that, The received sequence is calculated using a BP decoder based on weighted Lewinstein distance. The initialization information is used to iteratively calculate the left and right information probabilities of each layer, and the estimated information sequence value is output based on the probability of the last iteration. Specifically, this includes: The first step is to calculate the received sequence using a BP decoder based on weighted Levenstein distance. Initialization information: (1) Calculate the left information probability of layer 0: ； In the formula, Indicates the 0th layer bits and subsequence The weighted Levenstein distance between them, parameters , and These represent the insertion, deletion, and substitution probabilities of the channel, and the transmission probability, respectively. , for The amount of drift at the point, It represents the probability of updating to the left; (2) Calculate the first Right information probability of layer: ； In the formula, Represents the set of frozen bit channel indices. Represents the set of information bit channel indices. , , , It represents the probability of updating to the right. For the first N The amount of drift per bit; The second step is to iteratively calculate the left and right information probabilities of each layer using the initialization information: For the The bits of the layer are composed of a set Represents an index, where , , For the first k The bits of layer +1 are composed of a set of Represents an index, where , ; The following definitions are used in the calculation: For the layer: , , , ; For the k +1 floor: , , , ; In the formula, For the number of floors, m For the first k The set of all blocks in a layer. For the first k The set of all blocks in layer +1, For the first k The upper bound of the block in the layer, For the first k The lower bound of the block in the layer. for and The median value, For the first k The upper bound of the block in layer +1. For the first k The lower bound of the block in layer +1 for and The median value, ; First, update the left information probability of all nodes: (1) The formula for calculating the probability of the left information of a bit at an even index position is: ； (2) The formula for calculating the probability of left information of bits at odd index positions is: ； Next, update the right information probability of all nodes: (1) Located at the upper boundary With median The formula for calculating the probability of right-hand information between bits is: ； (2) Located at the median and the lower world The formula for calculating the probability of right-hand information between bits is: ； In the formula, Represents a sequence ,gather , , , They are respectively represented as point, Point and The amount of drift at the point, , , They are respectively represented as point, Point and The amount of drift at the point, Indicates the maximum drift amount. Indicates the first The first layer 1 bit; The iterative computation process follows a two-way message propagation mechanism. Propagate from right to left, layer by layer, starting from the initial node. The message is passed from left to right layer by layer from the termination node. When bidirectional probability synchronization covers all nodes, it is recorded as a complete iteration. The iteration continues until the preset number of iterations is reached or the message convergence condition is met. The third step is to output an estimated information sequence based on the probability decision made in the last iteration: First determine the first If the bit is an information bit or a frozen bit, then 0 is used as the final decision; if it is an information bit, then the likelihood ratio is used for the decision. Value: ； in, Indicates the first The likelihood ratio of each position is calculated using the following formula: 。

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