A Polar code decoding method for correcting insertion and deletion errors

Abstract

The present invention discloses a polarization code decoding method for correcting insertion and deletion errors, including: mixing information bits of length K and all-zero fixed bits of length N-K according to a preset position index of information bits and fixed bits to obtain a bit sequence; encoding the bit sequence to obtain a transmission sequence of length N; after passing through the IDS channel, the transmission sequence generates a received sequence of length N<supgt;*< / supgt>; a weighted edit distance-based SC decoder corrects insertion and deletion errors in the received sequence and outputs an estimate of the information sequence. The present invention introduces a drift amount into the recursive calculation of the channel transition probability for the insertion and deletion-replacement channel, improves the recursive structure of the traditional SC decoding algorithm, and uses the weighted edit distance to measure the channel transition probability, obtaining good error correction performance and improving the accuracy of information transmission.

Description

Technical Field

[0001] The present invention relates to the field of digital communication error control coding, and particularly to a polarization code decoding method for correcting insertion and deletion errors. Background Art

[0002] Insertion and deletion errors widely exist in various systems. For example, during information transmission, due to the unstable sampling clock of the receiver in the communication system, insertion or deletion errors may occur due to missed sampling or over-sampling by the sampler, resulting in system desynchronization. Insertion and deletion errors may also occur in some storage devices. For example, factors such as manufacturing defects of the medium cause the expected write window to be misaligned with the actual magnetic point position, resulting in insertion and deletion errors. Systems with insertion and deletion errors have memory, and a single insertion and deletion error can trigger sudden substitution errors, seriously damaging the communication quality, while traditional polarization codes cannot correct such errors.

[0003] A polarization code is a channel coding proposed by Professor Arikan based on the channel polarization theory. It is currently the only channel coding that has been theoretically proven to reach the Shannon limit under a binary discrete memoryless channel (B-DMC), and has relatively low encoding and decoding complexities, showing broad development prospects in the fields of new-generation mobile communication, satellite communication, etc. Currently, the research on polarization codes mainly focuses on binary memoryless channels, and there is relatively little research on memoryful insertion and deletion channels.

[0004] In the prior art, Tian Kuangda et al. proposed a polarization code decoding algorithm for a deletion channel, which can only correct deletion errors. Sun He et al. proposed an error correction code scheme for a channel model that can correct insertion, deletion, and additive white Gaussian noise by improving the polarization code decoding algorithm. In practical applications, insertion and deletion errors often occur with a certain probability, that is, there may be multiple insertion and deletion errors in the received sequence, and the number is unknown. Summary of the Invention

[0005] The present invention provides a polarization code decoding method for correcting insertion and deletion errors. For an insertion, deletion, and substitution channel, the present invention introduces a drift amount into the recursive calculation of the channel transition probability, improves the recursive structure of the traditional SC decoding algorithm, and uses the weighted edit distance to measure the channel transition probability, obtaining good error correction performance and improving the accuracy of information transmission. The details are described below:

[0006] A polarization code decoding method for correcting insertion and deletion errors, the method comprising:

[0007] For information bits of length K Mix the all-zero fixed bits of length N-K with the preset information bits and fixed bits according to the position index to obtain a bit sequence

[0008] Encode the bit sequence to obtain a transmission sequence of length N

[0009] The transmission sequence After passing through the IDS channel, a received sequence of length N * is generated

[0010] The SC decoder based on the weighted edit distance corrects the insertion and deletion errors in the received sequence and outputs an estimate of the information sequence

[0011] Among them, the SC decoder based on the weighted edit distance corrects the insertion and deletion errors in the received sequence and outputs an estimate of the information sequence Specifically:

[0012] Calculate the initialization information of the received sequence as the channel transition probability of the 0th layer;

[0013] Recursively calculate the channel transition probability using the initialization information; perform bit-by-bit decoding and decision based on the channel transition probability.

[0014] Among them, the channel transition probability of the 0th layer is:

[0015]

[0016] Among them, represents the weighted edit distance between the i-th bit of the 0th layer and the subsequence The parameters P i 、P d and P s respectively represent the insertion, deletion, and substitution probabilities of the channel. The transmission probability P t =1 - P i - P d , d i is the drift at the i-th point.

[0017] Furthermore, the recursive calculation of the channel transition probability using the initialization information is:

[0018] For the i-th bit of the k-th layer where k ∈ {n, n - 1, …, 1}, it is represented by a set of (m, j) indices, where n = log2N and m ∈ {0, 1, …, 2 n-k-1}, j ∈ {0, 1, …, 2 k-1 -1};

[0019] The following definitions are used in the recursion:

[0020] a = 2 k × m, b = (m + 1) × 2 k ,

[0021]

[0022]

[0023] where k is the number of layers, m is the index of the block where the bit is located, a is the upper bound of the block, b is the lower bound of the block, c is the middle value of a and b, even represents the elements with even indices in and odd represents

[0024] the elements with odd indices in;

[0025]

[0026] If the index is even:

[0027]

[0028] If the index is odd: represents the XOR operation of two bits, Set D = {-d max , …, -2, -1, 0, 1, 2, …, d max}, set B = {0, 1}, d b , d a , d c represent the drift amounts at points b, a, and c respectively, and represent the channel transition probabilities when the index is even or odd respectively, d max represents the maximum drift amount, (k) (u a , …, u a+2j+1 ), represents the (a + 2j)-th bit in the k-th layer,

[0029]

[0029]

[0030] Determine whether the i-th bit is an information bit or a fixed bit. If it is a fixed bit, use 0 as the judgment result; otherwise, assume that the estimates of the first i-1 bits are correct and determine based on the likelihood ratio. Values:

[0031]

[0032] Among them, set A represents the information bit channel index set, A c To represent a fixed bit channel index set, It represents the decoding likelihood ratio of the i-th bit, and its calculation formula is as follows:

[0033]

[0034] The beneficial effects of the technical solution provided by the present invention are:

[0035] 1. The present invention adopts polar codes to correct insertion and deletion errors, improves the traditional SC decoding algorithm by introducing drift, and achieves good error correction performance; improves the accuracy of information transmission, reduces the bit error rate, and ensures the security of channel transmission;

[0036] 2. The present invention expands the application of polarization codes in IDS channels, achieves significant performance gains, and meets various needs in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of polar code encoding and decoding for correcting insertion and deletion errors provided by the present invention;

[0038] Figure 2 A flowchart of SC decoding based on weighted edit distance used in the present invention;

[0039] Figure 3 Schematic diagram of recursive calculation of drift when code length N=8;

[0040] Among them, (a) is the recursive diagram of the polar code in the SC decoding algorithm based on weighted edit distance; (b) is the detailed operation diagram of the dotted rectangle.

[0041] Figure 4 This is a performance simulation comparison chart of the method provided by the present invention and the existing method. DETAILED DESCRIPTION

[0042] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention are described in further detail below.

[0043] For the Insertion / Deletion-Substitution (IDS) channel, an embodiment of the present invention proposes a new polar code decoding method. Based on the traditional Successive Cancellation (SC) decoding method, a drift amount is introduced to correct insertion and deletion errors, and the weighted edit distance is used to measure the transition probability of the channel.

[0044] An embodiment of the present invention intends to design a polar code decoding method for correcting insertion and deletion errors within the framework of SC decoding. Compared with the traditional scheme, the following modifications are made in this embodiment of the present invention:

[0045] First, the transmitted sequence passes through the insertion / deletion-substitution channel;

[0046] Second, a drift amount is introduced in the calculation of the decoding algorithm, which can be used to correct insertion and deletion errors;

[0047] Third, the channel transition probability is calculated from the weighted edit distance.

[0048] Compared with the traditional SC decoding algorithm, this embodiment of the present invention introduces a drift amount in the decoding algorithm to obtain excellent insertion and deletion error correction capabilities, broadening the application range of polar codes.

[0049] The following will make a detailed description of a polar code decoding method for correcting insertion and deletion errors provided by an embodiment of the present invention in conjunction with the accompanying drawings. See the following description for details:

[0050] As Figure 1 shown, the method includes the following four steps:

[0051] (1) Mix the information bits of length K and the all-zero fixed bits of length N-K according to the pre-set position indexes of the information bits and the fixed bits to obtain the bit sequence

[0052] (2) Encode the bit sequence to obtain the transmitted sequence of length N

[0053] (3) The transmitted sequence passes through the IDS channel to generate the received sequence of length N *

[0054] (4) Based on the SC decoder with weighted edit distance, correct the insertion and deletion errors in the received sequence and output the estimate of the information sequence

[0055] ​Among them, step (4) includes:

[0056] (4.1) Calculate the initialization information of the received sequence ;

[0057] Among them, this initialization information serves as the channel transition probability of the 0th layer.

[0058] (4.2) Recursively calculate the channel transition probability using the initialization information;

[0059] (4.3) Decode and make a decision bit by bit according to the channel transition probability.

[0060] During specific decoding, decide whether it is 0 or 1 according to the transition probability of the nth recursive layer.

[0061] The specific implementation processes of the above four steps are introduced separately as follows:

[0062] Step (1) uses the Gaussian approximation method to determine the position index of the fixed bits (well-known to those skilled in the art);

[0063] Step (2) encoding includes constructing a generator matrix, which is the same as the traditional encoding method (well-known to those skilled in the art);

[0064] The transmission sequence in step (3) generates a received sequence of length N * through the insertion and deletion - substitution channel The steps include:

[0065] Transmit the codeword x i through the insertion and deletion - substitution channel, and the parameters P i , P d and P s represent the insertion, deletion, and substitution probabilities of the channel respectively, and the transmission probability P t = 1 - P i - P d .

[0066] Define the state d i as the drift amount at point i, and d i is equal to the number of insertions minus the number of deletions in the sequence between the transmitted bit x0 and the bit x i to be transmitted. The value of d i is taken from the set D = {-d max , …, -2, -1, 0, 1, 2, …, d max}. Among them, d i has a total of 2d max +1 values, and d max is the maximum drift amount.

[0067] In step (4.1), calculate the received sequence The steps for initializing the information are specifically as follows:

[0068] Let k = 0, and calculate the channel transition probability of the 0th layer.

[0069]

[0070] Among them, denotes the weighted edit distance between and the subsequence

[0071] which is calculated by the dynamic programming method.

[0072] (4.2.1) For the i-th bit of the k-th layer where k ∈ {n, n - 1,..., 1}, its index can be represented by a group (m, j), where n = log2N, m ∈ {0, 1,..., 2 n-k - 1}, and j ∈ {0, 1,..., 2 k-1 - 1}

[0073] The following definitions are needed in the recursion:

[0074] a = 2 k × m, b = (m + 1) × 2 k ,

[0075]

[0076]

[0077] Among them, k is the layer number, m is the index of the block where the bit is located, a is the upper bound of the block, b is the lower bound of the block, and c is the middle value of a and b. denotes the sequence u of the k-th layer (k) (u a ,..., u a+2j+1 ), even denotes the elements with even indices in and odd denotes

[0078] According to the parity of the bit index, the channel transition probability can be calculated by the following two recursive formulas:

[0079] If the index is even:

[0080]

[0081] Conversely, if the index is odd:

[0082]

[0083] Among them, represents the exclusive - or operation of two bits, represents the sequence Set D = {-d max , …, -2, -1, 0, 1, 2, …, d max}, set B = {0, 1}, d b , d a , d c represent the drift amounts of point b, point a, and point c respectively, and represent the channel transition probabilities when the index is even or odd respectively, represents the sequence d max represents the maximum drift amount.

[0084] The specific steps of bit - by - bit decoding and decision - making according to the channel transition probability in step (4.3) are as follows:

[0085] Judge each bit of the source sequence in order. First, determine whether the i - th bit is an information bit or a fixed bit. If it is a fixed bit, directly use 0 as the discrimination result; otherwise, assume that the estimations of the previous i - 1 bits are all correct, and determine the value of :

[0086]

[0087] Among them, set A represents the information - bit channel index set, A c is the fixed - bit channel index set, represents the decoding likelihood ratio of the i - th bit, and its calculation formula is as follows:

[0088]

[0089] In the embodiment of the present invention, a polar code with a code length N of 512 bits and a code rate of 0.5 is selected as a special case to introduce a polar - code decoding method for correcting insertion and deletion errors. In the simulation, the fixed - bit position index is calculated by the Gaussian approximation method, the encoding algorithm is the same as the traditional algorithm, the maximum number of insertion errors I for each bit in the channel is 2, P i = P d , and the maximum drift amount d max = 5.

[0090] Figure 4The curves of the frame error rate and bit error rate of the system varying with the insertion / deletion probability are given under the same substitution probability. The frame error rate is the number of error frames divided by the total number of transmitted frames, and the bit error rate is the number of error bits divided by the total number of transmitted bits. It can be seen from the figure that as the insertion / deletion probability decreases, the system performance is significantly improved. At the same time, under the same insertion / deletion probability, the traditional SC decoding method is not applicable, and the method proposed in the present invention has a lower frame error rate and bit error rate, showing an obvious performance gain. This shows that the polar code decoding method described in the present invention can effectively correct errors in the insertion / deletion-substitution channel and has good error performance.

[0091] Those skilled in the art can understand that the drawings are only schematic diagrams of a preferred embodiment, and the serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0092] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A polarization code decoding method for correcting insertion and deletion errors, characterized in that, The method includes: The information bits of length K and the all-zero fixed bits of length N - K are mixed according to the preset position indexes of the information bits and the fixed bits to obtain a bit sequence Encode the bit sequence to obtain a transmission sequence of length N Transmission sequence After passing through the IDS channel, a received sequence of length N is generated * is generated SC decoder based on weighted edit distance, correcting insertion and deletion errors in the received sequence and outputting an estimate of the information sequence and outputting an estimate of the information sequence Among them, the SC decoder based on weighted edit distance corrects insertion and deletion errors in the received sequence and outputs an estimate of the information sequence Specifically: Calculate the received sequence of the initialization information as the channel transition probability of the 0th layer; Recursively calculating the channel transition probability using the initialization information; performing bit-by-bit decoding and decision-making based on the channel transition probability; wherein, the channel transition probability of the 0th layer is: Among them, represents the i-th bit of the 0-th layer and the weighted edit distance between the subsequence with parameter P i , P d and P s respectively represent the insertion, deletion and substitution probabilities of the channel, and the transmission probability P t = 1 - P i - P d , d i is the drift at point i; wherein, the recursively calculating the channel transition probability using the initialization information is: For the \(i\)-th bit of the \(k\)-th layer where \(k\in\{n,n - 1,\ldots,1\}\), the index is represented by a set \((m,j)\), where \(n=\log_2N\), \(m\in\{0,1,\ldots,2 n-k-1 \}\), \(j\in\{0,1,\ldots,2 k-1 - 1\}\); The following definitions are used in the recursion: where k is the number of layers, m is the index of the block where the bit is located, a is the upper bound of the block, b is the lower bound of the block, c is the middle value of a and b, even represents the elements with even indices in and odd represents the elements with odd indices in; If the index is even: If the index is odd: Among them, represents the exclusive OR operation of two bits, represents a sequence Set D = {-d max ,…,-2,-1,0,1,2,…,d max}, Set B = {0,1}, d b , d a , d c represent the drift amounts of point b, point a, and point c respectively, and represent the channel transition probabilities when the index is even or odd respectively, represents a sequence d max represents the maximum drift amount, represents the sequence u of the k-th layer (k) (u a ,…,u a+2j+1 ), represents the (a + 2j)-th bit of the k-th layer, represents the transition probability of the branch.

2. The polarization code decoding method for correcting insertion and deletion errors according to claim 1, characterized in that, The performing bit-by-bit decoding and decision-making based on the channel transition probability is: Determine whether the i-th bit is an information bit or a fixed bit. If it is a fixed bit, use 0 as the discrimination result; otherwise, assuming that the estimations of the first i - 1 bits are all correct, determine according to the likelihood ratio value: Among them, the set A represents the information bit channel index set, A c represents the fixed bit channel index set, represents the decoding likelihood ratio of the i-th bit, and its calculation formula is as follows:

Images