CN102164025B - Coder based on repeated coding and channel polarization and coding/decoding method thereof - Google Patents

Abstract

An encoder based on repetition coding and channel polarization and its encoding and decoding method, the encoder includes two encoding modules with the same structure, and each encoding module is provided with a repetition encoder group whose output port number is m*L ( It consists of L repetition encoders arranged in sequence with the number of repetitions m), a bit position mapper with a length of N, and a channel polarization device with a length of N. The two encoding modules are located between the repetition encoder and the bit Coding mode selectors between position mappers are connected as one. On the basis of the encoder, the present invention proposes a specific method for channel encoding and decoding by embedding repetitive codes in the channel polarization process. Compared with the limited-length polar codes of the current prior art, the encoding and decoding method of the present invention has almost no Under the premise of increasing the decoding complexity, the error correction ability is stronger, and the transmission performance is significantly improved; it is especially suitable for practical engineering systems such as mobile communication, satellite communication, and underwater communication, and has a good prospect for promotion and application.

Description

Encoder Based on Repetition Coding and Channel Polarization and Its Coding and Decoding Method

technical field

The present invention relates to an encoder based on repetitive encoding and channel polarization and its encoding and decoding method, which is used to solve the problem of errors in transmitted data due to the interference of the channel on the communication process in a digital communication system, and belongs to the channel of digital communication coding technology field.

Background technique

Polar Codes (Polar Codes) is a constructive coding method proposed by E. Ar ₁ kan in 2009 that has been strictly proven to achieve channel capacity. Before polar encoding, it is first necessary to perform N=2 ⁿ independent binary input channels (or use the same channel for N consecutive times, that is, N available time slots of a channel), where n is a natural number, and the application diagram The basic unit of channel polarization shown in 1 repeatedly polarizes binary input discrete channels. The most basic channel polarization is a single-step polarization operation on two identical unpolarized channels W: X→Y, where X is the set of channel input symbols (for a binary input channel, X takes the value {0 ,1}), Y is the set of channel output symbols. The input bits marking the polarized channel are u ₀ and u ₁ respectively, these two input bits get x ₀ through a modulo two adder, on the other hand, u ₁ is directly assigned to x ₁ , namely x ₀ =u ₀ ⊕ u ₁ , x ₁ =u ₁ , ⊕ is a modulo two addition operation. Send x ₀ and x ₁ into the unpolarized channel W respectively, and the output is y ₀ and y ₁ . From the input of the channel polarization basic unit (u ₀ and u ₁ ) and the output of the two channels (y ₀ and y ₁ ), the originally independent two unpolarized channels W are combined into a two-input two The output vector channel W ₂ : X ² →Y ² , where X ² =X×X, and the operation X is a Cartesian product. This vector channel contains two sub-channels W ₂ ⁽⁰⁾ :X→Y×X (input is u _{0 and} output is y ₀ y ₁ ) and W ₂ ⁽¹⁾ :X→Y (input is u ₁ and output is y ₀ y ₁ u ₀ ), these two sub-channels are two polarized channels. After this single-step polarization process, from the perspective of channel capacity, I(W ₂ ⁽⁰⁾ )+I(W ₂ ⁽¹⁾ )=2×I(W), I(W ₂ ⁽⁰⁾ )≤I( W)≤I(W ₂ ⁽¹⁾ ), where I(·) represents a function for calculating channel capacity. That is to say: after single-step polarization, when the sum capacity remains unchanged, compared with the original unpolarized channel, the capacity of the polarized channel deviates: one increases and the other decreases. If a single-step polarization operation is performed on two sets of channels that have undergone one polarization operation, and then between two independent polarization channels with the same transition probability, the deviation will be more obvious, and this group of single-step polarization is called The polarization operation is the second layer polarization operation, and the previous group of single-step polarization operations is called the first layer polarization operation. For each additional layer of polarization operation, the number of channels required will be doubled. Therefore, to perform complete polarization on N=2 ⁿ channels, a total of n layers of polarization operations are required, and each layer of polarization operations includes N times of single-step polarization operations. Unless otherwise specified, "perform polarization operations on N channels" refers to complete polarization. Theoretically, it has been proved that after the polarization operation is performed on nearly infinite channels, there will be a phenomenon that the capacity of some channels is 1, and the capacity of the remaining channels is 0, and the proportion of channels with a capacity of 1 to all channels is exactly the original binary input Discrete channel capacity.

2的信道极化装置作递归操作来表示，递归过程中的最小单元（即当N=2时）即是图1所示的基本单元。图2中的信道极化装置中有一个长度为N的比特反转交织器，它的功能是：先将输入端的十进制序号i按二进制表示为b_n-1b_n-2...b₀，其中n=log₂N，再将该二进制序列反序，得到b₀b₁...b_n-1，最后重新按十进制表示成π(i)作为输入序号i对应的输出序号。比特反转交织器的用处是将输入端序号为i的比特映射到序号π(i)处。根据编码速率（R）对N个信道进行极化，并选取其中容量最大的K个信道（或者等价地，选取可靠性最高的K个信道，可靠性度量是采用密度进化（Density Evolution）工具或者计算巴塔恰里亚（Bhattacharyya）参数得到的），以承载用于传输消息的比特，称该部分比特为信息比特（其中

为向下取整运算），其余未被选中的信道则传输一个约定的比特序列，称其为固定比特序列（若信道对称则可简单地传输全零序列），从而形成一个从承载信息的K个比特到最终送入信道的N个比特的映射关系，这样的一种映射关系即为极化码，码长（编码后得到的二进制信号所包含的比特数）等于信道极化装置的长度N。Referring to Figure 2, a practical recursive structure of the channel polarization device is introduced. A channel polarization device with a length of N (to polarize N channels) can be used with a length of

The channel polarization device of 2 is represented by a recursive operation, and the smallest unit in the recursive process (that is, when N=2) is the basic unit shown in Fig. 1 . In the channel polarization device in Fig. 2, there is a bit inversion interleaver with a length of N, its function is: first, the decimal number i at the input end is expressed in binary as b _n-1 b _n-2 ...b ₀ , where n=log ₂ N, and then reverse the binary sequence to obtain b ₀ b ₁ ...b _n-1 , and finally re-express it in decimal as π(i) as the output number corresponding to the input number i. The purpose of the bit-reversed interleaver is to map the bit with the sequence number i at the input end to the sequence number π(i). The N channels are polarized according to the coding rate (R), and the K channels with the largest capacity are selected (or equivalently, the K channels with the highest reliability are selected. The reliability measurement is based on the Density Evolution tool. Or calculated Bhattacharyya (Bhattacharyya) parameters), to carry the bits used to transmit the message, and call this part of the bits information bits (wherein

is a downward rounding operation), and the rest of the unselected channels transmit an agreed bit sequence, which is called a fixed bit sequence (if the channel is symmetrical, it can simply transmit an all-zero sequence), thus forming a K The mapping relationship between bits to N bits that are finally sent to the channel, such a mapping relationship is a polar code, and the code length (the number of bits contained in the binary signal obtained after encoding) is equal to the length N of the channel polarization device .

，其中序号i为0到N-1的正整数，

表示将N个信道W极化后得到的序号为i的极化信道）。编码码块经过信道极化装置得到的x₀...x_N-1，通过N个独立信道W，接收到的信号序列为y₀...y_N-1。译码器的任务就是根据接收信号序列y₀...y_N-1得到发送信号序列u₀...u_N-1的一组估计值 The binary signal sequence u ₀ ... u _N-1 composed of information bits and fixed bits and sent to the channel polarization device is the code block (the order is consistent with the serial number of the polarized channel sent in, that is, u _i is sent to

, where the serial number i is a positive integer from 0 to N-1,

Indicates the polarized channel with sequence number i obtained after polarizing N channels W). The x ₀ ... x _N-1 obtained by the encoded code block through the channel polarization device passes through N independent channels W, and the received signal sequence is y ₀ ... y _N-1 . The task of the decoder is to obtain a set of estimated values of the transmitted signal sequence u ₀ ... u _N-1 according to the received signal sequence y ₀ ... y _N-1

The polar code can use the serial cancellation SC (successive cancellation) algorithm to decode each bit in the encoded code block sequentially from 0 to N-1 according to the following formula:

其中，信息比特的判决函数为：式中， $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|x)$ 为信道转移概率函数，即发送信号x通过信道

得到输出y₀...y_N-1和的概率。

Among them, the decision function of the information bit is: In the formula, $W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|x)$ is the channel transition probability function, that is, the sending signal x passes through the channel

to get output y ₀ ... y _N-1 and The probability.

Polar codes have a Tanner graph structure, so they can be decoded using the belief propagation (BP) algorithm that has been widely used in Low Density Parity-Check (LDPC) codes. Figure 3 shows a Tainer diagram of a polar code with a code length N (N=2 ⁿ ), and the circles and squares with crosses represent the variable nodes and check nodes of the Tainer diagram respectively. In the figure, there are n+1 layers, N variable nodes in each layer, and n layers, N check nodes in each layer. The variable node layer serial numbers from right to left are from 0 to n, and the check node layer serial numbers are from 0 to n-1. The serial numbers of the N variables (check nodes) in each layer are from 0 to N-1 from top to bottom. Layer 0 variable nodes get messages directly from the channel (distinguished by solid circles). Variable nodes in the nth layer correspond to information bits and fixed bits, and are sent to the i-th bit in the sequence u ₀ ... u _N-1 of the channel polarization device, which corresponds to the i-th variable node in the nth layer, i ranges from 0 to The positive integer serial number of N-1. Before the decoding starts, the variable nodes of layer 0 are first initialized with the signal received from the channel, and the corresponding part of the variable nodes of layer n is initialized with a known fixed bit sequence. After the initialization is completed, the belief propagation decoding algorithm is carried out on the Tener graph. After reaching a certain number of iterations, the decoding process is stopped, and the decoding sequence is obtained according to the message of the variable node corresponding to the information bit in the nth layer. The complexity of belief propagation decoding based on Taina graph is O(NlogN). The belief propagation decoding algorithm needs a certain number of iterations. The complexity is slightly higher than that of the serial offset decoding algorithm, but it can obtain very good performance. .

For polar codes with a small code length, it is also possible to calculate the posterior probability of each codeword by taking all possible codeword situations, and then select the codeword with the largest posterior probability as the decoding result. This method is called the maximum A Posteriori Probabilistic Decoding Algorithm. This method can obtain the most ideal decoding performance, but the complexity is extremely high, reaching O(2 ^N ), and it is difficult to be practical for larger code lengths.

Therefore, the disadvantages of the above-mentioned prior art are: the code length of the practical coding system cannot be infinitely long, and after the polarization operation is performed on a limited number of channels, there will still be some channels whose transmission performance is neither particularly good nor particularly poor , the present invention refers to this channel as a gray channel. According to the construction method of the polar code, information will inevitably be carried on those gray channels, so that the anti-noise performance of the coding scheme will be greatly affected by those bits.

Contents of the invention

In view of this, the object of the present invention is to provide a coder based on repetitive coding and channel polarization and its corresponding encoding and decoding method. Compared with polar codes, the present invention hardly pays for encoding and decoding complexity. The reliability is greatly improved, and the utility model has a good application prospect.

In order to achieve the above-mentioned purpose of the invention, the present invention provides an encoder based on repetition coding and channel polarization, which is used to encode binary transmission signals and output binary coded sequences; it is characterized in that: the encoder includes two Each encoding module is composed of a repeated encoder group whose output port number is m×L, a bit position mapper with a length of N, and a channel polarization device with a length of N, m× L is also called the repetition length, wherein the repetition encoder group is composed of L repetition encoders arranged in sequence with the number of repetitions m, and the two encoding modules are located between the repetition encoder and the bit position mapper. The mode selector is connected as a whole; each coding module is provided with two sets of input ports: input ports I(0), I(1),..., I(K-1) are used to receive the signal source output length K Binary signal sequence, the input ports F(0), F(1), ..., F(NKm·L-1) are used to configure the preset fixed binary signal sequence, and the two groups of input ports are also directly connected to the The input port of the bit position mapper, where N=2 ⁿ , n is a natural number, K, L, and m are all integers, and satisfy 0≤L≤K, 0<K≤N, m≥1 and m×L≤NK ; The input ports of the repeated encoder groups of the two encoding modules are respectively connected to the input ports I(KL), I(K-L+1),...,I(K-1) of the respective encoding modules one by one, and their sequential numbers are The output ports of R(0), R(1), ..., R(m·L-1) are respectively connected to the bit position mapper via the input end of the coding mode selector; The working mode outputs signals via the output ports X(0), X(1), . . . , X(N-1) of the length-N bit position mapper and the length-N channel polarizer.

In order to achieve the purpose of the above invention, the present invention also provides an encoding method using the encoder based on repetition encoding and channel polarization of the present invention, which is characterized in that: the method is to embed repetition encoding into the channel polarization process for encoding , the method includes the following steps:

(1) Determine the encoding parameters: the input signal sequence length K of each encoding module, the output sequence length N=2 ⁿ , n is a natural number, where 0<K≤N, the code rate is The number of repetitive encoders in each encoding module is L, and the number of repetitions of each repetitive encoder is m, where m≥1, 0≤L≤K, and m L≤NK;

(2) Calculate the reliability of each polarized channel:

简记为式中，下标N表示信道极化装置的长度，上标i表示极化信道的序号，0≤i≤N-1；First define N polarized channels according to the following method: the signal sequence sent to the channel polarization device is u ₀ u ₁ ...u _N-1 , and the signal sequence received by the receiver decoder from the channel is y ₀ y ₁ ... y _N-1 , the polarized channel with sequence number i takes u _i as input, y ₀ y ₁ ... y _N-1 and u ₀ u ₁ ... u _i-1 as output, and its transfer The probability function is

Abbreviated as In the formula, the subscript N represents the length of the channel polarization device, and the superscript i represents the serial number of the polarized channel, 0≤i≤N-1;

Then calculate the reliability value of each polarized channel, that is, the Bhattacharyya parameter of Bhattacharya: the calculation formula of the Bhattacharyya parameter of the binary input channel whose transition probability function is W(y|u) is: In the formula, Y is the possible value output by all channels; the channel with larger Bhattacharyya value has lower reliability; the channel with smaller Bhattacharyya value has higher reliability;

(3) Classify and determine four types of channel positions and quantities: According to the number L of repeated encoders, the number of repetitions m, and the length K of the input signal sequence of each encoding module, the following four types of channel positions and quantities are determined respectively: non-repetitive Information channels (K-L), repeated information channels L, repeated channels (m L) and fixed channels (N-K-m L); then the N polarized channels generated in step (2) are ranked in order of reliability Arrangement, that is, according to the order of Bhattacharyya parameters from small to large, select and mark them as four types: non-repeated information channel, repeated information channel, repeated channel and fixed channel;

(4) Determine the corresponding relationship between repeated information channels and repeated channels: arrange the repeated channels in the order of reliability, each L is a group, a total of m groups; and then reversely arrange the repeated information channels in the order of reliability , that is, according to the order of Bhattacharyya parameters from large to small; according to the principle of "the relatively unreliable channels in the repeated information channels work with the relatively reliable channels in the repeated channels", the repeated information channels are selected one by one, and the m groups of repeated channels In each group, select a channel that has not yet been marked and has the highest reliability in the group, and these m+1 channels form a repeated relationship, record and mark; the bit position mapper with a length of N in the encoder is based on The sequence numbers of the non-repeated information channel, repeated information channel, repeated channel and fixed channel generated by the above method generate an interleaving pattern to ensure that various bits are sent to the corresponding type of channel;

(5) If the selected encoding mode is "single code block encoding mode", execute steps (6) and (7) in sequence to complete an encoding operation; if the selected encoding mode is "dual code block encoding mode", then Jump to execute steps (8), (9) and (10) to complete an encoding operation;

中的前（K-L）个比特和剩余的L个比特分别标记为非重复信息比特序列和重复信息比特序列；再将重复信息比特序列

送入重复编码器组进行重复编码后，得到重复比特序列

；如果没有特殊设置，将固定比特序列

赋值为一个长度为（N-K-m·L）的全零序列；(6) A binary input signal sequence of length K

The first (KL) bits and the remaining L bits in are marked as non-repetitive information bit sequence and repeated information bit sequence ; Then repeat the information bit sequence

After being sent to the repeated encoder group for repeated encoding, the repeated bit sequence is obtained

; If not specified, the bit sequence will be fixed

The assignment is an all-zero sequence of length (NKm L);

按照下述方式分别送入信道极化装置中的非重复信息信道和重复信息信道：其中的重复信息比特序列

送入重复信息信道，重复比特序列

送入重复信道，固定比特序列

则送入固定信道；上述比特序列送入信道极化装置经过一系列交织及模二加运算后，得到最终将被送入极化前信道W的N个比特，即输出信号序列；至此，“单码块模式”的编码操作全部完成，流程结束；(7) According to the channel classification in steps (3) and (4) and the repetition relationship of the corresponding channels, the binary input signal sequence of length K

The non-repetitive information channel and the repeated information channel respectively sent to the channel polarization device in the following manner: the repeated information bit sequence

Send to repeat information channel, repeat bit sequence

Send to repeated channel, fixed bit sequence

Then send it to the fixed channel; the above bit sequence is sent to the channel polarization device and after a series of interleaving and modulo two addition operations, the N bits that will finally be sent to the channel W before polarization are obtained, that is, the output signal sequence ; So far, the encoding operations of the "single code block mode" are all completed, and the process ends;

(8) Perform steps (2), (3), and (4) again for another encoding module with the same structure to complete the marking of polarized channels and the construction of repetition relations. Each encoding process uses two encoding modules to pair two Operates on binary signal sequences of length K;

中，将前（K-L）个比特和剩余的L个比特分别标记为非重复信息比特序列和重复信息比特序列

再将重复信息比特序列

送入重复编码器进行重复编码后，得到长度为（m×L）的重复比特序列

同时，如果没有特殊设置，就将固定比特序列

赋值为一个长度为（N-K-m·L）的全零序列；再对第二个长度为K的信号序列按照上述同样方法标记出重复信息比特序列

并进行重复编码后，产生重复比特序列

和固定比特序列

(9) From the first signal sequence of length K

, mark the first (KL) bits and the remaining L bits as non-repetitive information bit sequences and repeated information bit sequences

repeating information bit sequence

After being sent to the repetition encoder for repeated encoding, a repeated bit sequence with a length of (m×L) is obtained

At the same time, if there is no special setting, the bit sequence will be fixed

The assignment is an all-zero sequence with a length of (NKm L); then the second signal sequence with a length of K Mark the repeated information bit sequence in the same way as above

And after repeated encoding, a repeated bit sequence is generated

and a fixed bit sequence

送入第一个编码模块的极化信道中的非重复信息信道和重复信息信道，其中的重复信息比特序列

送入第一个编码模块的极化信道中的重复信息信道，固定比特序列

送入第一个编码模块的极化信道中的固定信道；再将第二个长度为K的信号序列

送入第二个编码模块的极化信道中的非重复信息信道和重复信息信道，其中的重复信息比特序列

送入第二个编码模块的极化信道中的重复信息信道，固定比特序列

送入第二个编码模块的极化信道中的固定信道；(10) According to the channel classification in steps (3) and (4) and the repetition relationship of the corresponding channels, the first signal sequence of length K

The non-repetitive information channel and the repeated information channel in the polarized channel sent to the first encoding module, where the repeated information bit sequence

Repeated information channel in the polarized channel fed to the first encoding module, fixed bit sequence

Send to the fixed channel in the polarization channel of the first encoding module; then the second signal sequence with length K

The non-repetitive information channel and the repeated information channel in the polarized channel sent to the second encoding module, where the repeated information bit sequence

Repeated information channel in the polarized channel fed to the second encoding module, fixed bit sequence

A fixed channel among the polarized channels fed to the second encoding module;

送入第二个编码模块的极化信道中的重复信道，第二个编码模块的重复比特序列

送入第一个编码模块的极化信道中的重复信道；上述比特序列送入该两个信道极化装置经过一系列交织及模二加运算后，得到最终将被送入极化前信道W的两组N个比特，即输出信号序列

和；至此，完成“双码块模式”的编码操作，流程结束。Different from the single code block coding mode, the repeated bit sequence of the first coding module in the double code block coding mode

The repeated channel in the polarized channel fed to the second coding module, the repeated bit sequence of the second coding module

The repeated channel in the polarization channel sent to the first encoding module; the above bit sequence is sent to the two channel polarization devices and undergoes a series of interleaving and modulo two addition operations to obtain the final channel W that will be sent to the polarization channel The two sets of N bits, that is, the output signal sequence

and ; So far, the encoding operation of the "dual code block mode" is completed, and the process ends.

The key innovation technology of the encoder and its encoding and decoding method based on repetitive encoding and channel polarization in the present invention is: an encoder with an innovative structure and its encoding and decoding method are proposed, which divides the polarized channel into four categories: non-repetitive channel, Repeated information channel, repeated channel and fixed channel, and correspondingly proposed two encoding methods for establishing a repeated relationship between repeated information channel and repeated channel in single code block mode and double code block mode, and correspondingly in double code block mode The serial cancellation algorithm and the Teiner graph structure in single code block mode.

The innovative advantage of the present invention is: it is the first time to propose a specific method for channel coding and decoding by embedding repetition codes in the process of channel polarization on the basis of a new structure encoder. The method of the invention has stronger error correction capability under the premise of almost no increase in decoding complexity. If the "dual code block coding" mode of the present invention is adopted, although it is necessary to pay the price of an average decoding delay of 0.5 times, the transmission performance can be greatly improved, and it can even exceed the extreme decoding complexity of polar codes. High maximum a posteriori probability decoding performance. In a word, the codec of the present invention has linear codec complexity and excellent error correction capability, and is especially suitable for practical engineering systems such as mobile communication, satellite communication, and underwater communication, and has a good prospect for popularization and application.

Description of drawings

FIG. 1 is a schematic diagram of a basic unit structure of channel polarization.

FIG. 2 is a schematic diagram of a recursive structure of a channel polarization device with a length of N, where the minimum unit of recursion (ie when N=2) is the basic unit shown in FIG. 1 .

Fig. 3 is a Tainer diagram of a polar code with code length N.

Fig. 4 is a schematic diagram of the structural composition of the encoder based on repetition coding and channel polarization in the present invention.

Fig. 5 is a flow chart of the decoding operation steps of the serial cancellation algorithm when the present invention is in the dual code block encoding mode, the channel is a binary erasure channel and the repetition number m=1 of repeated encoding.

FIG. 6 is a schematic structural diagram of a Tanner graph in the single code block coding mode of the present invention.

FIG. 7 is a schematic structural diagram of a Tanner graph in the double code block coding mode of the present invention.

Fig. 8 is a schematic diagram of the performance comparison of the embodiment of the present invention under the confidence propagation decoding algorithm of the single-code block repeated polar code with different code rates and different repetition lengths with a code length of 1024 (100 iterations, the repetition length is 0, which is the general polar code) code).

Fig. 9 is a schematic diagram of the performance comparison of the embodiment of the present invention under the serial cancellation algorithm of the dual code block repeated polar code with a code length of 1024.

Fig. 10 is a schematic diagram of the performance comparison of the embodiment of the present invention between the belief propagation decoding algorithm and the general polar code of the dual code block repetition polar code with a code rate of 0.36, different code lengths and different repetition lengths (100 iterations).

Fig. 11 is a schematic diagram of the performance comparison of the embodiment of the present invention under different decoding algorithms between a single/double code block repetition polar code with a code length of 1024 and a general polar code.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

Referring to Fig. 1, introduce the structural composition of the coder based on repetitive coding and channel polarization of the present invention: comprise two coding modules with identical structure: coding module 0 and coding module 1, each coding module is connected by an output port of sequence The number of repeated encoder groups is m×L (m×L is also called the repetition length), a bit position mapper with a length of N and a channel polarization device with a length of N, where the repeated encoder group is It is composed of L sequentially arranged repetition encoders whose number of repetition encoding is m, and the two encoding modules are connected as a whole through an encoding mode selector located between the repetition encoder and the bit position mapper. Each encoding module has two sets of input ports: input ports I(0), I(1),..., I(K-1) are used to receive the binary signal sequence of length K output by the source, and input port F (0), F(1), ..., F(NKL-1) are used to configure the preset fixed binary signal sequence, and the two sets of input ports are directly connected to the bit position mapper with length N, where N=2 ⁿ , n is a natural number, K, L, and m are all integers, and satisfy 0≤L≤K, 0<K≤N, m≥1 and m×L≤NK.

The input ports of the repeated encoder groups between the two encoding modules are respectively connected to the input ports of the respective encoding modules one by one $I(K-\frac{L}{m}),I(K-\frac{L}{m}+1),...,I(K-1),$ The output ports are sequentially numbered as R(0), R(1), . According to the working mode selected by the coding mode selector, the output ports X(0), X(1), ..., X(N-1) of the length-N bit position mapper and the length-N channel polarizer output signal.

The encoding mode selector has the following two working modes:

When the encoding mode selector is in the state of "double code block encoding", the output ports R(0), R(1), ..., R(L-1) of the repeated encoder group of each encoding module are respectively connected to another encoding Bit position mapper for modules.

When the encoding mode selector is in the "single code block encoding" state, the output ports R(0), R(1), ..., R(L-1) of the repetitive encoder groups of the two encoding modules are directly connected to their respective Bit position mapper, at this time, the two encoding modules work independently. Therefore, the encoding mode selector is an optional component. If the "dual code block encoding" mode is not planned to be selected, the encoder can omit the encoding mode selector and configure only one encoding module.

According to the working mode selected by the encoding mode selector, the output ports X(0), X(1), ..., X(N-1) of the bit position mapper with a length of N and the channel polarizer with a length of N are output Signal.

The essence of the N-length bit position mapper provided in each encoding module is an interleaver, whose function is to combine two input port groups I(0), I(1),..., I(K-1 ) and F(0), F(1), ..., F(N-K-L-1) and the respective signals of the output port groups R(0), R(1), ..., R(L-1) of the repetitive encoder, According to the preset rules, it is mapped to the input port groups U(0), U(1), ..., U(N-1) of a channel polarization device with length N, so that after polarization processing, the output port group X (0), X(1), . . . , X(N-1) output signal sequences.

The coding method of the encoder based on repetitive coding and channel polarization in the present invention is to embed repetitive coding into the channel polarization process for coding, and the method includes the following steps:

每个编码模块中的重复编码器数量为L，每个重复编码器的重复次数为m，其中m≥1，0≤L≤K，且m·L≤N-K。(1) Determine the encoding parameters: the input signal sequence length K of each encoding module, the output sequence length N=2 ⁿ , n is a natural number, where 0<K≤N, the code rate is

The number of repetitive encoders in each encoding module is L, and the number of repetitions of each repetitive encoder is m, where m≥1, 0≤L≤K, and m·L≤NK.

(2) Calculate the reliability of each polarized channel:

简记为

式中，下标N表示信道极化装置的长度，上标i表示极化信道的序号，0≤i≤N-1；First define N polarized channels according to the following method: the signal sequence sent to the channel polarization device is u ₀ u ₁ ...u _N-1 , and the signal sequence received by the receiver decoder from the channel is y ₀ y ₁ ... y _N-1 , the polarized channel with sequence number i takes u _i as input, y ₀ y ₁ ... y _N-1 and u ₀ u ₁ ... u _i-1 as output, and its transfer The probability function is

Abbreviated as

In the formula, the subscript N represents the length of the channel polarization device, and the superscript i represents the serial number of the polarized channel, 0≤i≤N-1;

式中，Y为所有信道输出的可能取值；Bhattacharyya数值越大的信道，可靠性越低；Bhattacharyya数值越小的信道，可靠性越高。Then calculate the reliability value of each polarization channel, that is, the Bhattacharyya parameter: the calculation formula of the Bhattacharyya parameter of the binary input channel whose transition probability function is W(y|u) is:

In the formula, Y is the possible output value of all channels; the channel with larger Bhattacharyya value has lower reliability; the channel with smaller Bhattacharyya value has higher reliability.

(3) Classify and determine four types of channel positions and quantities: According to the number L of repeated encoders, the number of repetitions m, and the length K of the input signal sequence of each encoding module, the following four types of channel positions and quantities are determined respectively: non-repetitive Information channels (K-L), repeated information channels L, repeated channels (m L) and fixed channels (N-K-m L); then the N polarized channels generated in step (2) are ranked in order of reliability Arrangement, that is, according to the order of Bhattacharyya parameters from small to large, select and mark four types: non-repetitive information channel, repeated information channel, repeated channel and fixed channel.

(4) Determine the corresponding relationship between repeated information channels and repeated channels: arrange the repeated channels in the order of reliability, each L is a group, a total of m groups; and then reversely arrange the repeated information channels in the order of reliability , that is, according to the order of Bhattacharyya parameters from large to small; according to the principle of "the relatively unreliable channels in the repeated information channels work with the relatively reliable channels in the repeated channels", the repeated information channels are selected one by one, and the m groups of repeated channels In each group, select a channel that has not yet been marked and has the highest reliability in the group, and these m+1 channels form a repeated relationship, record and mark; the bit position mapper with a length of N in the encoder is based on The sequence numbers of the non-repeated information channel, repeated information channel, repeated channel and fixed channel generated by the above method generate an interleaving pattern to ensure that various bits are sent to the corresponding type of channel;

(5) If the selected encoding mode is "single code block encoding mode", execute steps (6) and (7) in sequence to complete an encoding operation; if the selected encoding mode is "dual code block encoding mode", then Jump to steps (8), (9) and (10) to complete an encoding operation.

中的前

个比特和剩余的个比特分别标记为非重复信息比特序列和重复信息比特序列

再将重复信息比特序列

送入重复编码器组进行重复编码后，得到重复比特序列

；如果没有特殊设置，将固定比特序列

赋值为一个长度为（N-K-L）的全零序列。(6) A binary input signal sequence of length K

in the front

bits and the rest bits are marked as non-repetitive information bit sequence and repeated information bit sequence

repeating information bit sequence

After being sent to the repeated encoder group for repeated encoding, the repeated bit sequence is obtained

; If not specified, the bit sequence will be fixed

The assignment is an all-zero sequence of length (NKL).

按照下述方式分别送入信道极化装置中的非重复信息信道和重复信息信道：其中的重复信息比特序列

送入重复信息信道，重复比特序列

送入重复信道，固定比特序列则送入固定信道；上述比特序列送入信道极化装置经过一系列交织及模二加运算后，得到最终将被送入极化前信道W的N个比特，即为输出信号序列

；至此，“单码块模式”的编码操作全部完成，流程结束。(7) According to the channel classification in steps (3) and (4) and the repetition relationship of the corresponding channels, the binary input signal sequence of length K

The non-repetitive information channel and the repeated information channel respectively sent to the channel polarization device in the following manner: the repeated information bit sequence

Send to repeat information channel, repeat bit sequence

Send to repeated channel, fixed bit sequence Then send it to a fixed channel; the above bit sequence is sent to the channel polarization device and after a series of interleaving and modulo two addition operations, the N bits that will be sent to the channel W before polarization are finally obtained, which is the output signal sequence

; So far, the encoding operations of the "single code block mode" are all completed, and the process ends.

(8) Perform steps (2), (3), and (4) again for another encoding module with the same structure to complete the marking of polarized channels and the construction of repetition relations. Each encoding process uses two encoding modules to pair two Operates on sequences of binary signals of length K.

中，将前（K-L）个比特和剩余的L个比特分别标记为非重复信息比特序列和重复信息比特序列

，再将重复信息比特序列

送入重复编码器进行重复编码后，得到长度为（m×L）的重复比特序列

；同时，如果没有特殊设置，就将固定比特序列

赋值为一个长度为（N-K-m×L）的全零序列；再对第二个长度为K的信号序列按照上述同样方法标记出重复信息比特序列

，并进行重复编码后，产生重复比特序列和固定比特序列

。(9) From the first signal sequence of length K

, mark the first (KL) bits and the remaining L bits as non-repetitive information bit sequences and repeated information bit sequences

, and then repeat the information bit sequence

After being sent to the repetition encoder for repeated encoding, a repeated bit sequence with a length of (m×L) is obtained

; At the same time, if there is no special setting, the bit sequence will be fixed

The assignment is an all-zero sequence of length (NKm×L); then for the second signal sequence of length K Mark the repeated information bit sequence in the same way as above

, and after repeated encoding, a repeated bit sequence is generated and a fixed bit sequence

.

送入第一个编码模块的极化信道中的非重复信息信道和重复信息信道、其中的重复信息比特序列

送入第一个编码模块的极化信道中的重复信息信道，固定比特序列

送入第一个编码模块的极化信道中的固定信道；再将第二个长度为K的信号序列

送入第二个编码模块的极化信道中的非重复信息信道和重复信息信道、其中的重复信息比特序列

送入第二个编码模块的极化信道中的重复信息信道，固定比特序列

送入第二个编码模块的极化信道中的固定信道。不同于单码块编码模式，双码块编码模式下第一个编码模块的重复比特序列

送入第二个编码模块的极化信道中的重复信道，第二个编码模块的重复比特序列

送入第一个编码模块的极化信道中的重复信道；上述比特序列送入该两个信道极化装置经过一系列交织及模二加运算后，得到最终将被送入极化前信道W的两组N个比特，即输出信号序列

和

；至此，完成“双码块模式”的编码操作，流程结束。(10) According to the channel classification in steps (3) and (4) and the repetition relationship of the corresponding channels, the first signal sequence of length K

The non-repetitive information channel and the repeated information channel in the polarized channel sent to the first coding module, the repeated information bit sequence

Repeated information channel in the polarized channel fed to the first encoding module, fixed bit sequence

Send to the fixed channel in the polarization channel of the first encoding module; then the second signal sequence with length K

The non-repetitive information channel and the repeated information channel in the polarized channel sent to the second coding module, the repeated information bit sequence

Repeated information channel in the polarized channel fed to the second encoding module, fixed bit sequence

The fixed channel in the polarized channel fed to the second encoding module. Different from the single code block coding mode, the repeated bit sequence of the first coding module in the double code block coding mode

The repeated channel in the polarized channel fed to the second coding module, the repeated bit sequence of the second coding module

The repeated channel in the polarization channel sent to the first encoding module; the above bit sequence is sent to the two channel polarization devices and undergoes a series of interleaving and modulo two addition operations to obtain the final channel W that will be sent to the polarization channel The two sets of N bits, that is, the output signal sequence

and

; So far, the encoding operation of the "dual code block mode" is completed, and the process ends.

Corresponding to the above encoding method, the present invention also provides two decoding methods:

Referring first to Figure 5, the first method of decoding a code with a binary erasure channel in the "dual-code block coding" mode and a code with a repetition number m=1 of repeated codes using a simple and fast serial cancellation algorithm is introduced, which includes the following The above operation steps:

(1) Detect whether the decoder is in the "double code block encoding" mode, and whether the channel is a binary erasure channel BEC (Binary Erasure Channel) and the number of repeated encoding m=1; if both are satisfied, proceed to the step ( 2); otherwise, the decoding fails, and the decoding process ends.

(2) For two sets of signal sequences of length N received from the channel, perform serial offset decoding operations on each bit in the order of sequence numbers from 0 to N-1:

进行判决；若为非重复信息比特、重复信息比特或者重复比特时，根据序号为i的极化信道的转移概率函数，计算概率值 $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)$ 和 $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1)$ 并进行如下操作：When decoding the bit with sequence number i in the code block corresponding to each group of received sequences, if it is a fixed bit, directly follow

Make a judgment; if it is a non-repeated information bit, repeated information bit or repeated bit, calculate the probability value according to the transition probability function of the polarized channel with the sequence number i $W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)$ and $W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1)$ and proceed as follows:

if $W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)>W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1)$ Then the judgment is 0;

if $W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)<W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1)$ Then the judgment is 1;

if $W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)=W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA0000055589170000021.png,HDA0000055589170000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0...{\mathrm{the\; y}}_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1),$ Then do not judge the bit immediately, suspend the decoding operation corresponding to the code block, and immediately jump to step (3);

At this time, if the judgment of all bits of a certain code block has been completed, the corresponding decoding operation is ended; if both decoding operations are in the end state, perform step (5); otherwise, continue to perform the operation of step (2) , waiting for the end of another decoding operation.

(3) Determine whether the bit with the sequence number i is a repeated information bit or a repeated bit, if yes, perform step (4); otherwise, end the paused decoding operation process, and mark the corresponding code block with the sequence number in the bit Each bit after i cannot be judged, continue to perform the operation of step (2), and wait for the end of another decoding operation.

(4) Waiting for the judgment result of the repeated bit or repeated information bit j in another decoding operation that constitutes a repeated relationship with the bit i, if the bit j in another decoding process is successfully judged, the judgment result of bit j As the judgment result of bit i in the decoding operation that has been suspended in step (2), then return to step (2) to continue the decoding operation; if two decoding operations are in the suspended state, end the two Operation process, and execute step (5) in sequence.

(5) For the code blocks that have successfully judged all bits, take out the repeated information bits and non-repeated information bits from the corresponding decision sequence, and arrange them according to the sequence numbers from small to large, and then sort the repeated information bit sequence and The non-repetitive information bit sequences are combined to ensure that the non-repetitive information bits are in the front and the repeated information bits are in the rear, and the decoding results of the corresponding code blocks are obtained and output; for the code blocks that have not been completely judged, the decoding is declared to be failed and the decoding is terminated process.

Introduce the second kind of decoding method that adopts the encoder based on repetitive coding and channel polarization of the present invention again: the general decoding method that uses the belief degree propagation algorithm based on the Tener diagram of excellent performance to carry out, this method comprises the following operation steps :

(1) On the basis of the polar code Tainer diagram, according to the relationship between the repeated information bits and the repeated bits, the check nodes representing the repeated coding relationship are added; among them,

For the "single-code block coding" mode, based on the Tanner diagram of ordinary polar codes (see Figure 6), the n-th layer variable nodes corresponding to the repeated information bits and the repeated bits corresponding to the repeated bits The variable node of the nth layer is connected to a variable node with a degree of (m+1) through (m+1) check nodes with a degree of 2. The degree of a node is the number of edges associated with the node, where m is the number of repetitions of the repetition encoder; a total of L variable nodes and (m×L+L) check nodes need to be added, and L is the number of repetition encoders, so as to obtain the Tanner diagram in the "single code block encoding" mode.

For the "dual code block coding" mode, based on two Tainer diagrams of ordinary polar codes (see Figure 7), each diagram corresponds to a coding code block, and the repeated information bits in each diagram correspond to the first The n-layer variable node and the n-th layer variable node corresponding to the repeated bit that constitutes a repeated relationship in another graph pass through (m+1) check nodes with a degree of 2 and a variable with a degree of (m+1) The nodes are connected, where m is the number of repetitions of the repeated encoder; a total of 2L variable nodes and (2m×L+2L) check nodes need to be added, and L is the number of repeated encoders in each encoding module. The 2L The check node and (2m×L+2L) check nodes are connected to the original two polar coded Tanner graphs to obtain the Tanner graph in the “dual code block coding” mode.

(2) Based on the Tanner graph established in step (1), use the belief propagation algorithm for iterative decoding: in the initial stage of decoding, initialize the variables of layer 0 with the signal received from the channel and the known fixed bit sequence respectively node and the corresponding part of the variable nodes in the variable nodes of the nth layer; after the initialization is completed, the iterative decoding of the belief propagation is performed; after the iterative decoding process stops, the corresponding bits are judged according to the message of the variable node of the nth layer to obtain the decision sequence , take out repeated information bits and non-repeated information bits from each decision sequence, arrange them in ascending order, and then merge the sorted repeated information bit sequences and non-repeated information bit sequences to ensure that the non-repeated information bits In the front, the repeated information bits are in the back, and the decoding result is obtained and output.

The present invention has carried out multiple implementation tests. In the description of the embodiments, for the convenience of narration, the method of encoding and decoding using the single-code block coding mode of the present invention is called single-code block repetitive polar code, and the dual-code code of the present invention is used to The method of encoding and decoding in block coding mode is called dual code block repetition polar code.

Taking the single/double code block repeated polar code with a repeated code rate of 0.5 as an example, in conjunction with accompanying drawings 8 to 11, the encoding and decoding method of the present invention and its performance analysis are introduced in detail:

表示向下取整运算。每个编码模块中的重复编码器数量L从{0,10,20,30,40,50,60}中选取，当L=0时，即为一般的极化码。信道采用删除概率为0.5的二进制删除信道。这里，因为m=1所以重复长度也取值为L。First calculate the parameters required for encoding: the code length N is 1024 or 512, the value range of the code rate R is: {0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.40}, the number of repetitions of repeated encoding m takes 1. Calculate the number of bits of the information sequence according to the code length N and the code rate R

Indicates the rounding down operation. The number L of repeated encoders in each encoding module is selected from {0, 10, 20, 30, 40, 50, 60}, and when L=0, it is a general polar code. The channel uses a binary erasure channel with an erasure probability of 0.5. Here, since m=1, the repetition length also takes a value of L.

First use the following two formulas to calculate the reliability of the channel after each polarization, that is, the Bhattacharyya parameter: $Z\left(W_{2N}^{\left(2i\right)}\right)\&le;2Z(W_N^{\left(i\right)}-Z{\left(W_N^{\left(i\right)}\right)}^2),$ in, $Z\left({W_1}^{\left(0\right)}\right)=0.5,$ 0≤i≤N-1.

Then, the polarized channels are arranged in descending order according to the Bhattacharyya parameters. Select the first K smallest Bhattacharyya parameters from the sorted channel numbers as the information channel: among them, the (K-L) ones with smaller Bhattacharyya parameters are marked as non-repetitive information channels, and the bit sequences sent to this part of the channel do not participate in repetitive coding, and the marked The L channels with larger Bhattacharyya parameters are repeated information channels, and the bit sequences sent to these channels will participate in repeated coding. Then, select L channels with the smallest Bhattacharyya parameter from the (N-K) polarized channels except the information channel as repeated channels. The last remaining (N-K-L) channels are marked as fixed channels.

The number of repetitions m=1 in the repetition encoding indicates that one repetition information channel corresponds to one repetition channel. Repeated information channels are sorted from large to small according to Bhattacharyya parameters, and repeated channels are sorted from small to large according to Bhattacharyya parameters, and are selected one by one to form a repeated relationship. The operation steps and their performance are introduced as follows:

1. Use single code block coding mode for coding and decoding:

Encoding is performed with the encoder of the present invention shown in FIG. 3 , and the single code block encoding mode is selected: firstly, the repetitive information bit sequence is passed through the repetitive encoder to obtain the repetitive bit sequence. The fixed bit sequence is assigned an all-zero sequence. Pass the encoded code block composed of non-repetitive information bit sequence, repeated information bit sequence, repeated bit sequence and fixed bit sequence through the bit position mapper, and then map the non-repeated information bit, repeated information bit, repeated bit and fixed bit to the corresponding polarized channel. Finally, the output signal of the encoder is obtained through the channel polarization device and sent to the transmission channel.

According to the signal received from the transmission channel, the decoder uses the belief propagation algorithm based on the Tener diagram to decode, iterates 100 times, and counts the error block rate.

Referring to Fig. 8, for each code rate, the coding performance will first improve as the repetition length increases, and when the repetition length increases to a certain extent, the transmission performance will deteriorate as it continues to increase. Corresponding to each code rate, there is an optimal repetition length.

2. Encoding and decoding using double code block mode

Use the encoder of the present invention shown in Figure 3 to encode every two uncoded binary signal sequences, and select the dual code block encoding mode: first, the repetition information bits of the two signal sequences are passed through the repetition encoder to obtain repetition bits. Then group each bit sequence, the first coding code block is composed of information bits (including repeated and non-repetitive) of the first signal sequence, repeated bits of the second signal sequence and the first group of fixed bits; the second A coding code block is composed of information bits of the second signal sequence, repetition bits of the first signal sequence and a second group of fixed bits. Wherein, the fixed bits of the two encoded code blocks are assigned as all zero bit sequences. Then, the two encoded code blocks are respectively sent to the two encoding modules in the encoder of the present invention, and the non-repeated information bits, repeated information bits, repeated bits and fixed bits are mapped to the corresponding polarized channel, respectively, through the channel polarization device to obtain two sets of encoder output signals, and send them into the transmission channel.

Referring to FIG. 9 , it introduces the performance comparison after the decoder of the present invention receives the message from the channel and performs decoding using the serial cancellation algorithm. In the area of low code rate, the performance of dual code block repetition polar code is obviously better than ordinary polar code.

The decoder uses the belief propagation algorithm to decode the signal received from the transmission channel, and iterates 100 times. Since the encoding and decoding of the double code block repetitive polar code are based on the code block pair (two coded code blocks that are encoded and decoded at the same time), in addition to the single code block error probability in general statistics, the statistics also need to be The error rate of the code block pair is counted, that is, the error probability of the double code block.

Referring to FIG. 10 , the comparison between double-code block repetition polar codes with code lengths 512 and 1024 with different repetition lengths and general polar codes with different code lengths at a code rate of 0.36 is introduced. Similar to the case of single code, the coding performance will firstly improve as the repeat length increases, and when the repeat length increases to a certain extent, the performance will deteriorate as it continues to increase. There is also an optimal repeat length. It can be observed from Fig. 10 that the error probability of the double code block of the double code block repetition polar code with a length of 512 codes can be better than that of the single code block of a common polar code with a code length of 1024 codes when the repetition length is better. Repeat probability. In this case, statistics are made on 1024 bit sequences fairly each time, and the average decoding delay of the double code block repetition polar code is slightly lower than that of the general polar code, but the performance is even better. No less.

Referring to Fig. 11, it introduces the single/double code block repetition polar code with the optimal repetition length obtained by the repetition length configuration of the embodiment of the present invention and the use of the BP (Belief Propagation) algorithm or the maximum a posterior probability MAP (maximum a posterior) The performance of different polar codes decoded by the algorithm is compared. The statistics are single code block error probability. It can be seen from the performance curve that the decoding performance of the belief propagation of the single code block repeated polar code is obviously better than the performance of the general polar code under the belief propagation decoding, and in the case of a low code rate, it can It is close to the performance of general polar codes under the condition of maximum a posteriori probability decoding with extremely high decoding complexity. If double code blocks are used to repeat polar codes, the performance will be further improved, and it can be significantly better than the performance of polar codes under the maximum a posteriori probability decoding when the code rate is low.

The above descriptions are only 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 principles of the present invention shall be included in the present invention. within the scope of protection.

Claims (7)

1. An encoder based on repetition coding and channel polarization for encoding a binary transmission signal to output a binary code sequence; the method is characterized in that: the encoder comprises two encoding modules with identical structure, each encoding module comprises a repetition encoder group with m × L output ports, a bit position mapper with length N and a channel polarization device with length N, which are connected in sequence, wherein the m × L is also called repetition length, the repetition encoder group comprises L repetition encoders with repetition times m arranged in sequence, and the two encoding modulesConnected as a whole by a coding mode selector between the repetition coder and the bit position mapper; each coding module is respectively provided with two groups of input ports: input ports I (0), I (1), …, I (K-1) are used for receiving binary signal sequence with length K output by source, input ports F (0), F (1), …, F (N-K-m.L-1) are used for configuring preset fixed binary signal sequence, and the two groups of input ports are also directly connected with input ports of bit position mapper with length N, wherein N =2ⁿN is a natural number, K, L, m are integers, and L is more than or equal to 0 and less than or equal to K, 0<K is less than or equal to N, m is more than or equal to 1, and mxL is less than or equal to N-K; the input ports of the repeated coder groups of the two coding modules are respectively connected with the input ports I (K-L), I (K-L +1), … and I (K-1) of the respective coding modules one by one, and the output ports with the serial numbers of R (0), R (1), … and R (m.L-1) are respectively connected to a bit position mapper through the input end of a coding mode selector; the signals are output via the bit position mapper of length N and the output ports X (0), X (1), …, X (N-1) of the channel polarization means of length N according to the operation mode selected by the coding mode selector.

2. The encoder of claim 1, wherein: the coding mode selector is provided with the following two working modes:

when the coding mode selector is in a 'double-code-block coding' state, the output ports R (0), R (1), …, R (m.L-1) of the repeated coder group of each coding module are respectively connected with the bit position mapper of the other coding module;

when the coding mode selector is in a 'single-code-block coding' state, output ports R (0), R (1), … and R (m.L-1) of the repeated coder groups of the two coding modules are respectively and directly connected with respective bit position mappers, and at the moment, the two coding modules respectively and independently work.

3. The encoder of claim 1, wherein: the coding mode selector is an optional component, and if the mode of 'double code block coding' is not designed to be selected, the coder omits the coding mode selector and only configures one coding module.

4. The encoder of claim 1, wherein: the bit position mapper with the length of N is essentially an interleaver, and functions to map the signals of the two input port groups I (0), I (1), …, I (K-1) and F (0), F (1), …, F (N-K-m.L-1) and the output port group R (0), R (1), …, R (m.L-1) of the repetition coder to the input port groups U (0), U (1), …, U (N-1) of a channel polarization device with the length of N according to a preset rule so as to perform polarization processing.

5. A coding method using the repetition coding and channel polarization based encoder according to claim 1, characterized in that: the method is to embed repeated codes into a channel polarization process for coding, and comprises the following operation steps:

(1) determining the encoding parameters: input signal sequence length K for each coding module, output sequence length N =2ⁿN is a natural number, wherein 0<K is less than or equal to N, then the code rate is(ii) a The number of the repeated encoders in each encoding module is L, the repetition frequency of each repeated encoder is m, wherein m is more than or equal to 1, L is more than or equal to 0 and less than or equal to K, and m.L is more than or equal to N-K;

(2) calculating the reliability of each polarization channel:

first, N polarized channels are defined according to the following method: the signal sequence fed to the channel polarization means is u₀u₁...u_N-1The signal sequence received by the receiving end decoder from the channel is y₀y₁...y_N-1Polarized channel with index i and u_iIs input, y₀y₁...y_N-1And u₀u₁...u_i-1To output, its transition probability function is

It is briefly described asIn the formula, subscript N represents the length of the channel polarization device, superscript i represents the serial number of the polarization channel, and i is more than or equal to 0 and less than or equal to N-1;

then, the reliability value of each polarization channel, namely the Bhattacharyya parameter of the Bartay-Chiia is calculated: the Bhattacharyya parameter of the binary input channel with the transition probability function of W (y | u) is calculated as

In the formula, Y is a possible value of all channel outputs; the larger the Bhattacharyya value is, the lower the reliability is; the smaller the Bhattacharyya value is, the higher the reliability is;

(3) four types of channel positions and numbers are determined by classification: according to the number L of repeated encoders, the repeated times m and the length K of the input signal sequence of each encoding module, the following four types of channel positions and numbers are respectively determined: non-repeating information channels (K-L), repeating information channels (L), repeating channels (m.L) and fixed channels (N-K-m.L); arranging the N polarized channels generated in the step (2) according to the sequence of the reliability, namely the sequence of the Bhattacharyya parameters from small to large, and sequentially selecting and marking the N polarized channels as: non-repeated information channel, repeated channel and fixed channel;

(4) determining the corresponding relation between the repeated information channel and the repeated channel: arranging repeated channels according to the sequence of the reliability, wherein each L is a group, and the groups are m; then, the repeated information channels are reversely arranged according to the sequence of the reliability, namely according to the sequence of the Bhattacharyya parameters from large to small; according to the principle that 'relatively unreliable channels in repeated information channels and relatively reliable channels in repeated channels work in a matched mode', repeated information channels are selected one by one, a channel which is not marked yet and has the highest reliability in a group is selected from each group of m groups of repeated channels, the m +1 channels form a repeated relation, and the repeated relation is recorded and marked; a bit position mapper with the length of N in the encoder generates an interleaving pattern according to the serial numbers of the non-repeated information channel, the repeated channel and the fixed channel generated by the method, and ensures that various bits are sent into the channels with corresponding types;

(5) if the selected coding mode is a single code block coding mode, sequentially executing the steps (6) and (7) to finish a coding operation; if the selected coding mode is a 'double-code-block coding mode', skipping to execute the steps (8), (9) and (10) to finish a coding operation;

(6) a binary input signal sequence with length KThe first (K-L) bits and the remaining L bits are labeled as a non-repeated information bit sequence and a repeated information bit sequence, respectively

(ii) a Repeating the information bit sequenceSending the data into a repetition coder group to carry out repetition coding to obtain a repetition bit sequence

(ii) a If no special setting exists, assigning the fixed bit sequence F as an all-zero sequence with the length of (N-K-m.L);

(7) according to the channel classification in the steps (3) and (4) and the repetitive relation of the corresponding channel, the binary input signal sequence with the length of K is classified and constructed

The non-repeated information channel and the repeated information channel which are respectively sent into the channel polarization device are as follows: in which a repetitive information bit sequence is presentFeeding into a repeated information channel, repeating a bit sequence

Feeding into a repetition channel, a fixed bit sequence

Sending the data to a fixed channel; the bit sequence is sent to a channel polarization device to obtain N bits which are finally sent to a channel W before polarization after a series of interweaving and modulo two addition operation, namely an output signal sequence(ii) a So far, the coding operation of the "single code block mode" is completely finished, and the process is finished;

(8) performing the steps (2), (3) and (4) again on another coding module with the same structure to complete the construction of the marking and repeating relation of the polarized channel, wherein two coding modules are used for operating two binary signal sequences with the length of K in the coding process each time;

(9) from a first signal sequence of length K

In the method, the first (K-L) bits and the remaining L bits are respectively marked as a non-repeated information bit sequence and a repeated information bit sequence

Then repeating the information bit sequence

Sending the data to a repetition coder for repetition coding to obtain a repetition bit sequence with the length of (m multiplied by L)

(ii) a Meanwhile, if no special setting is provided, the method will be usedFixed bit sequence

Assigning as an all-zero sequence of length (N-K-m.L); for a second signal sequence with length KMarking out repeated information bit sequence according to the same method

And after repetition coding, generating a repeated bit sequence

And a fixed bit sequence

；

(10) Classifying the first signal sequence with the length of K according to the channels in the steps (3) and (4) respectively and constructing the repetitive relation of the corresponding channels

A non-repeating information channel and a repeating information channel in the polarized channel fed to the first coding module, wherein the repeating information bit sequenceRepeated information channels, fixed bit sequences, in the polar channel fed to the first coding module

A fixed channel in the polarized channel fed to the first encoding module; then, the second signal sequence with length K is added

Into the pole of a second coding moduleNon-repeating information channels and repeating information channels in a channelization, in which a sequence of repeating information bits

Repeated information channel, fixed bit sequence, in a polar channel fed to a second coding module

A fixed channel in the polarized channel sent to the second coding module;

the sequence of repeated bits of the first coding module in the dual block coding mode, unlike the single block coding mode

Repeated channels in the polarization channel fed into a second coding module, repeated bit sequences of the second coding module

A repetition channel in the polarization channel fed into the first coding module; the bit sequence is sent to the two channel polarization devices to obtain two groups of N bits which are finally sent to the channel W before polarization after a series of interweaving and modulo two addition operation, namely an output signal sequence

And

(ii) a At this point, the encoding operation of the "dual block mode" is completed, and the process ends.

6. The encoding method of an encoder based on repetition coding and channel polarization according to claim 5, characterized in that: the decoding method corresponding to the coding method is to use a simple and quick serial cancellation algorithm to decode the code with the binary erasure channel of the 'double-code block coding' mode and the repetition times of repeated coding m =1, and the method comprises the following operation steps:

(1) detecting whether a decoder is in a 'double-code-block coding' mode, wherein a channel is a Binary Erasure Channel (BEC) and the number of times of repeated coding m = 1; if yes, continuing to execute the step (2); otherwise, decoding fails, and the decoding process is ended;

(2) for two groups of signal sequences with the length of N received from a channel, carrying out serial offset decoding operation on each bit according to the sequence of sequence numbers from 0 to N-1 respectively:

when decoding the bit with serial number i in the code block corresponding to each group of received sequences, if the bit is a fixed bit, directly decoding the code block according to the sequence number i

Judging; if the bit is a non-repeated information bit, a repeated information bit or a repeated bit, calculating a probability value according to a transition probability function of a polarized channel with a sequence number i $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)$ And $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1)$ and the following operations are carried out:

if it is not $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)>W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1)$ The decision is 0;

if it is not $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)<W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1)$ The decision is 1;

if it is not $W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|0)=W_N^{\left(i\right)}(y_0...y_{N-1},{\hat{u}}_0...{\hat{u}}_{i-1}|1),$ If not, pausing the decoding operation corresponding to the code block, and immediately skipping to execute the step (3);

at this time, if the judgment on all bits of a certain code block is finished, the corresponding decoding operation is ended; if both decoding operations are in the end state, executing the step (5); otherwise, continuing to execute the operation of the step (2) and waiting for the end of another decoding operation;

(3) judging whether the bit with the sequence number i is a repeated information bit or a repeated bit, if so, executing the step (4); otherwise, ending the suspended decoding operation process, marking that all bits with the serial numbers after the bit i in the corresponding code blocks can not be judged, continuing to execute the operation of the step (2), and waiting for the end of another decoding operation;

(4) waiting for the decision result of the repeated bit or the repeated information bit j forming a repeated relationship with the bit i in another decoding operation, if the bit j in another decoding process is successfully decided, taking the decision result of the bit j as the decision result of the bit i in the decoding operation which is already suspended in the step (2), and then returning to the step (2) to continue executing the decoding operation; if the two decoding operation processes are in the pause state, ending the two operation processes and sequentially executing the step (5);

(5) for the code blocks of which all bits are successfully judged, taking out repeated information bits and non-repeated information bits from the corresponding judgment sequences, respectively arranging the repeated information bits and the non-repeated information bits from small to large according to the serial numbers, merging the sequenced repeated information bit sequences and non-repeated information bit sequences, ensuring that the non-repeated information bits are in front and the repeated information bits are in back, and obtaining and outputting the decoding results of the corresponding code blocks; and for the code block which is not completely judged, declaring decoding failure and terminating the decoding process.

7. The encoding method of an encoder based on repetition coding and channel polarization according to claim 5, characterized in that: the decoding method corresponding to the coding method is general decoding which is carried out by using a confidence coefficient propagation algorithm based on a tanner graph with excellent performance, and comprises the following operation steps:

(1) on the basis of a polar code tanner graph, adding check nodes representing repeated coding relations according to the relations between repeated information bits and repeated bits; wherein,

for the single code block coding mode, based on a tanner graph of a common polarization code, connecting an nth layer variable node corresponding to a repeated information bit and an nth layer variable node corresponding to a repeated bit forming a repeated relation with the nth layer variable node one by one with a variable node with a degree of (m +1) through (m +1) check nodes with a degree of 2, wherein the degree of the node is the number of edges associated with the node, and m is the repetition number of a repeated coder; adding L variable nodes and (m multiplied by L + L) check nodes in total, wherein L is the number of repeated encoders, and obtaining a tanner graph in a single code block encoding mode;

for the 'double-code block coding' mode, on the basis of tanner graphs of two common polarization codes, each graph corresponds to one coding code block, and the variable nodes of the nth layer corresponding to the repeated information bits in each graph and the variable nodes of the nth layer corresponding to the repeated bits forming the repeated relation with the repeated information bits in the other graph are connected with the variable nodes of one degree (m +1) through the check nodes of (m +1) degrees 2, wherein m is the repeated times of the repeated coder; 2L variable nodes and (2 m.L + 2L) check nodes are added in total, L is the number of repeated encoders in each encoding module, and the 2L check nodes and the (2 m.L + 2L) check nodes are connected with the original two polar code tanner graphs to obtain the tanner graphs in the 'double-code block encoding' mode;

(2) based on the tanner graph established in the step (1), iterative decoding is carried out by using a confidence coefficient propagation algorithm: in the initial decoding stage, a variable node of the 0 th layer is initialized by using a signal received from a channel, a corresponding partial variable node in the variable node of the n th layer is initialized by using a known fixed bit sequence, and after the initialization is finished, confidence coefficient propagation iterative decoding is carried out; after the iterative decoding process is stopped, judging corresponding bits according to the information of the nth layer variable node to obtain a judgment sequence, respectively taking out repeated information bits and non-repeated information bits from each judgment sequence, respectively arranging the repeated information bits and the non-repeated information bits from small to large according to the sequence numbers, then combining the sequenced repeated information bit sequence and the non-repeated information bit sequence, ensuring that the non-repeated information bits are in front and the repeated information bits are in back, and obtaining and outputting a decoding result.

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