CN104158549A - Efficient decoding method and decoding device for polar code - Google Patents

Abstract

The invention discloses an efficient decoding method and decoding device for a polar code, provides a decoding manner based on a 4 input 4 output basic operation module, which is different from a conventional polar code BP algorithm based on a 2 input 2 output basic operation module, and a corresponding decoding factor graph, and further provides a calculation method transferring information between adjacent nodes through the 4 input 4 output basic operation module to obtain a novel polar code BP decoding method. The method integrates two layers of nodes in conventional algorithm into one layer, and enables the number of the total layers of the decoding to be reduced by half; the invention provides the corresponding decoding device; compared with the conventional manners, information storage requirements are reduced by half effectively; half storage access operation is reduced correspondingly; the power consumption is reduced; the clock number required by decoding processing is reduced by half; the decoding rate is accelerated.

Description

A kind of polar code interpretation method and code translator

Technical field

The invention belongs to the channel coding technology field in digital communication system, relate to and using polar code (polar code) as the digital communication system of error correction coding, more specifically, relate to interpretation method and the code translator of polar code.

Background technology

The polar code being proposed by Ar1kan is an important breakthrough of coding theory.Polar code be at present unique a kind of have definite make can at binary system discrete memoryless channel(DMC), be issued to the channel coding method of Shannon capacity, meanwhile, it has lower encoding and decoding complexity.Polar code is conventionally by parameter (N, K, A) definition, wherein N=2 ⁿfor code length, K represents information bit u _alength, the set of A representative information bit position for freezing bit (frozen bits), is fixed as 0 except information bit, uses u _acrepresentative.

The cataloged procedure of polar code can be by represent, wherein u ₁ ⁿfor N bit before coding, comprising information bit with freeze bit u _a+ u _ac, x ₁ ⁿfor N the bit obtaining after coding. for generator matrix, B _nfor bit reversal matrix, represent Kronecker product, F matrix is $\left(\begin{array}{cc}1& 0\\ 1& 1\end{array}\right).$

Then, code word x ₁ ⁿvia noisy communication channel W ⁿtransmission, at channel output, we will receive y ₁ ⁿ.

Confidence spread BP (Belief Propagation) algorithm is the main decoding algorithm of polar code.BP algorithm carries out message according to the structure factor graph of polar code (factor graph) and calculates propagation and iterative decoding.Fig. 1 is the polar code factor graph schematic diagram of a N=8.This type polar code factor graph can be divided into n+1 layer, and every layer has N node, amounts to the individual node of N (n+1), and each is parameter (i, j) expression for node, and wherein 1≤i≤n+1 represents the number of plies, and 1≤j≤N represents node location.Far Left one deck represents is information bit and freezes bit-level, and rightmost one deck represents that the information receiving from channel is y ₁ ⁿ.

Each 2x2 basic processing unit in Fig. 1 (BCB, basic computational blocks) represents the computing module of one 2 input 2 outputs.Fig. 2 is the concrete structure of this computing module.

When decoding starts, the message R on factor graph Far Left one node layer _{1, j}according to j position, whether be that information bit is initialized as:

$R_{1,j}=\left\{\begin{array}{cc}0& \mathrm{if\; j}\∈A\\ \∞& \mathrm{if\; j}\∈A^c\end{array}\right.---\left(1\right)$

Message L on factor graph rightmost one node layer _{n+1, j}be initialized as the log-likelihood ratio (LLR) of each node of channel output:

$L_{n+1,j}=\ln \frac{P\left(y_j\right|x_j=0)}{P\left(y_j\right|x_j=1)}---\left(2\right)$

In decode procedure, calculate from left to right and upgrade confidence level message R _i,jand be transmitted to rightmost to the right, then from the right side, turn left to calculate and upgrade confidence level message L _i,jand being transmitted to Far Left left, the compute mode (3) of BCB BAM is followed in the message computing between adjacent node.Propagating one is an iterative process back and forth.

$\begin{array}{c}{L}_{i,j}=g(L_{i+\mathrm{1,2}j-1},L_{i+\mathrm{1,2}j}+R_{i,j+N/2})\\ L_{i,j+N/2}=g(R_{i,j},L_{i+\mathrm{1,2}j-1})+L_{i+\mathrm{1,2}j}\\ R_{i+\mathrm{1,2}j-1}=g(R_{i,j},L_{i+\mathrm{1,2}j}+R_{i,j+N/2})\\ R_{i+\mathrm{1,2}j}=g(R_{i,j},L_{i+\mathrm{1,2}j-1})+R_{i,j+N/2}\end{array}---\left(3\right)$

G (x wherein, y)=log (cosh ((x+y)/2))-log (cosh ((x-y)/2)), realizes for the ease of hardware, is g (x conventionally by its approximate calculation, y) ≈ 0.9sign (x) sign (y) min (| x|, | y|).

After reaching certain iterations t, obtain the final node confidence level of layer 1, if j ∈ is A ^c, this node is for freezing node otherwise judge each node and obtain decode results according to (4).

${\hat{u}}_j=\left\{\begin{array}{cc}0& \mathrm{if}{R}_{1,j}\≥0\\ 1& \mathrm{else}\end{array}\right.---\left(4\right)$

Fig. 3 has represented N=2 ⁿthe schematic diagram of polar code iterative process in traditional BP decoding, message is first turned right and is reached n layer from the 1st layer, then by n+1 layer, is turned left and is reached the 2nd layer, the individual clock-unit of whole process need 2 (n-1).

The required memory capacity of this algorithm is the sum of transmission, updating message between node, amounts to the individual confidence level message of N (n-1), has the defect that message stores demand is high, critical path is short.

Summary of the invention

Goal of the invention: the feature high for conventional polar code BP code translator message stores demand, critical path is short, the invention provides a kind of new polar code BP interpretation method and corresponding code translator thereof, can guarantee under the condition that polar code decoding performance is constant, effectively reduce the message number that the required calculating of 1/2 polar code decoding is transmitted, also reduce the required message stores space of decoder; Reduce the operation of 1/2 access information, reduce decoder power consumption; Reduce by 1/2 decoding and process needed clock number, accelerate decoding speed.

Technical scheme: a kind of polar code interpretation method, four 2 original input 2 output elementary cells are merged into the BAM of one 4 input 4 outputs, in factor graph corresponding to polar code BP decoding, by the two-layer one deck of merging in traditional BP algorithm, make required total calculating number of plies in decode procedure reduce half.

1. the BAMs of 4 input 4 outputs are expressed as left node, 2., 3., 4. successively, right side node respectively be node 1. 2. 3. 4., 2. 4., 3. XOR value 4., 4.; As the same by the known relation of turning left from the right side of symmetry.

By factor graph, get four, left side node in the BAM of 4 inputs 4 outputs and be followed successively by from top to bottom (i, j), (i, j+N/4), (i, j+N/2), (i, j+3N/4), four nodes on the right are followed successively by (i+1,4j-3), (i+1,4j-2), (i+1 from top to bottom, 4j-1), (i+1,4j), the mathematical algorithm of output confidence level message is: while propagating to the right

$\begin{array}{c}{R}_{i+\mathrm{1,4}j-3}=g(R_{i,j},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ R_{i+\mathrm{1,4}j-2}=g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/2}+g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j-1}=g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/4}+g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j}=R_{i,j+3N/4}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}$

From symmetry, this algorithm to the right and left formula of pass-along message has identical form.

While propagating left,

$\begin{array}{c}{L}_{i,j}=g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ L_{i,j+N/4}=g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-1}+g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+N/2}=g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-2}+g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+3N/4}=L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(L_{i+1,4j-3},g(R_{i,j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}.$

The BAM of 4 input 4 outputs is applied in the factor graph of traditional BP algorithm, obtains new factor graph.For code length N=2 ⁿpolar code, the factor graph under decoding algorithm proposed by the invention comprises n/2+1 layer, and factor graph under traditional BP decoding algorithm comprises n+1 layer, the number of plies of the required calculating of decoding algorithm provided by the present invention reduces 1/2.

For code length N=2 ⁿpolar code, in decoding algorithm proposed by the invention, a required clock-unit of iterative process is n-2, and a required clock-unit of iterative process is that 2 (n-1) are individual in traditional decoding algorithm, the required clock-unit of decoding algorithm provided by the present invention reduces approximately half.

The BAM that comprises N/4 4 input 4 outputs in factor graph between adjacent layer.

Polar code code translator, comprises computing module and memory module.The feature of its memory module is: for code length N=2 ⁿpolar code, the memory space that code translator provided by the present invention is required, be that message number is (n/2-1) * N, and the required memory space of traditional polar code BP code translator is N message of (n-1) *, in the situation that each message quantizing bit number is identical, the required memory space of code translator provided by the invention reduces approximately half.

The feature of computing module is: processing unit adopts the computing module of 4 basic input 4 outputs, and the algorithm of its execution is the computational methods described in claim 3.In the simultaneously treated situation of all nodes of individual layer, the quantity of computing module is N/4; Also can do time-division processing with computing unit still less.

For code length N=2 ⁿpolar code, in the situation that each confidence level message quantizing bit number is q, the capacity of memory cell is (n/2-1) * q*N bit, stores respectively the data in n/2-1 layer in decode procedure, wherein the shared memory capacity size of every one deck is q*N bit.

Beneficial effect: compared with prior art, polar code interpretation method of the present invention, the adjacent two-stage of traditional BP algorithm 2 input 2 output BAMs are merged, with the BAM of one-level 4 input 4 outputs, replace it, the message propagation compute mode based on these 4 input, 4 output basic modules is also one of core content of the present invention.The BAM of these 4 input, 4 outputs is applied to, in the factor graph of polar code BP decoding, can obtain new factor graph, based on this new factor graph, obtains the novel polar code BP decoding algorithm that the present invention proposes.Due to the introducing of novel BAM, the two-layer one deck that is merged in former BP algorithm factor figure, in new BP algorithm, the number of plies of factor graph is reduced to n/2+1 layer by traditional n+1 layer.It is substantially constant that simulation result shows that new decoding algorithm provided by the present invention and traditional BP algorithm are compared error-correcting performance.

On above polar code BP decoding algorithm basis, the invention provides a kind of corresponding polar code code translator.Each layer data in polar code BP decode procedure all needs storage, so the required memory space of polar code BP decoder is directly proportional to the number of plies in factor graph.The number of plies in new decoding algorithm factor graph reduces half with respect to traditional algorithm, so polar code code translator provided by the present invention can effectively reduce the memory space of half; Each iteration will once be read and write renewal to each message stores, therefore correspondingly, reduce by 1/2 storage operation, reduce decoder power consumption; The data that decoding device provided by the invention is processed within a clock cycle are in addition two-layer corresponding to former factor graph, therefore needed clock number is processed in decoding, can reduce 1/2, accelerated decoding speed.

Accompanying drawing explanation

Fig. 1 is the factor graph of traditional BP algorithm, wherein code length N=8;

Fig. 2 is the input of 2 in traditional BP algorithm 2 output BAMs;

Fig. 3 is N=2 ⁿthe schematic diagram of polar code iterative process in traditional BP decoding;

Fig. 4 is the BAM that 4 inputs 4 proposed by the invention are exported;

Fig. 5 is the factor graph of the polar code of N=16 proposed by the invention;

Fig. 6 is N=2 ⁿthe schematic diagram of polar code iterative process in the BP decoding algorithm that the present invention proposes;

Fig. 7 is traditional BP decoding algorithm and the performance comparison diagram of decoding algorithm provided by the present invention, wherein code length N=1024;

Fig. 8 is the decoder device schematic diagram of the polar code of N=1024 provided by the present invention.

Embodiment

Below in conjunction with specific embodiment, further illustrate the present invention, should understand these embodiment is only not used in and limits the scope of the invention for the present invention is described, after having read the present invention, those skilled in the art all fall within the application's claims limited range to the modification of the various equivalent form of values of the present invention.

The BP decoding of polar code is according to the process of the factor graph iteration pass-along message of Fig. 1.After formula (1) (2) initialization, carry out iterative decoding: as shown in Figure 2, the account form of message is provided by formula (3) 2x2 BAM wherein.What Fig. 3 showed is an iteration cycle, by Far Left layer 1 (i=1), started, R message calculating from left to right and transmission need n-1 clock cycle, and upgrading from right to left L message needs n-1 clock cycle equally, therefore complete a required clock cycle of iteration, is that 2 (n-1) are individual.Wherein each clock cycle calculates N message needs storage, and message stores demand amounts to the individual message of N (n-1), and each the memory cell read-write of each iteration once.

The present invention merges into one deck by the adjacent two layers in former BP algorithm, can obtain the computing module of one 4 input 4 outputs as shown in Figure 4, the required number of plies of whole decode procedure reduces, 1. left node is expressed as, 2., 3., 4. successively, right side node respectively be node 1. 2. 3. 4., 2. 4., 3. XOR value 4., 4.; As the same by the known relation of turning left from the right side of symmetry.This module connects 8 nodes, and wherein 4, left side node is respectively j, j+N/4, j+N/2, a j+3N/4 node of i layer, 4j-3,4j-2,4j-1, a 4j node that 4 nodes on the right are i+1 layer.According to each internodal logical relation in Fig. 4, it is as follows that the present invention proposes between the adjacent node of these 4 input, 4 output modules message Transfer Formula: turn right while propagating,

$\begin{array}{c}{R}_{i+\mathrm{1,4}j-3}=g(R_{i,j},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ R_{i+\mathrm{1,4}j-2}=g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/2}+g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j-1}=g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/4}+g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j}=R_{i,j+3N/4}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}---\left(5\right)$

Because Fig. 4 has symmetry, so the formula of the formula of turning left while propagating when turning right propagation has identical form,

$\begin{array}{c}{L}_{i,j}=g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ L_{i,j+N/4}=g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-1}+g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+N/2}=g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-2}+g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+3N/4}=L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(L_{i+1,4j-3},g(R_{i,j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}---\left(6\right)$

The account form of above confidence spread (5) (6) is calculated and is drawn by factor graph; owing to there being a large amount of rings in figure; cannot draw the exact value of confidence level; must adopt certain being similar to; the above approximate calculation method that the present invention provides is not unique, and other similar approximation method is also in protection range of the present invention.

Fig. 5 is that to take N=16 (n=4) be example, and the code encoding/decoding mode of polar code is formed with the BAMs (4x4BCB) of 4 input 4 outputs.The present invention it should be noted that, when n is even number, with the alternative 2x2BCB reverse of polarity code factor graph of 4x4BCB, is directly and clearly, and obtaining new factor graph is n/2+1 layer; When n is odd number, will be converted to (n+1)/2 layer 4x4BCB by n+1 layer 2x2BCB and add 1 layer of 2x2BCB, the decoding algorithm of 4x4BCB part and the design of decoding device afterwards, the present invention is applicable equally.

Fig. 6 is the schematic diagram of an iterative process in the decoding algorithm that proposes of the present invention.Comparison diagram 3 is known, the polar code that is N for length, in traditional BP algorithm, a required clock-unit of iterative process is that 2 (n-1) are individual, and in decoding algorithm proposed by the invention, a required clock-unit of iterative process is n-2, and the required clock-unit of decoding reduces half.

Fig. 7 is traditional BP decoding algorithm and the performance comparison diagram of decoding algorithm provided by the present invention.Here adopting code length is that 1024 code checks are that 1/2 polar code is example, and maximum iteration time is set to 15, and for the polar code of other code length and code check, emulation has widely shown can obtain similar result.As shown in Figure 7, the error-correcting performance of decoding algorithm provided by the present invention is compared substantially and is remained unchanged with traditional BP algorithm.

Fig. 8 is the polar code code translator schematic diagram for N=1024 provided by the present invention, and this device comprises computing module and memory module; Computing module has adopted the BAM of 256 4 input 4 outputs to carry out the computing of the every one deck of executed in parallel.The factor graph of the polar code of N=1024 is 6 layers under decoding algorithm provided by the present invention, and 4 layers of middle message need to be calculated and upgrade and reading and writing memory data.

The feature of its memory module is: for code length N=2 ⁿpolar code, the memory space that code translator provided by the present invention is required, be that message number is (n/2-1) * N, and the required memory space of traditional polar code BP code translator is N message of (n-1) *, in the situation that each message quantizing bit number is identical, the required memory space of code translator provided by the invention reduces approximately half.

Claims (7)

1. a polar code interpretation method, it is characterized in that: the BAM of 42 inputs of adjacent two inter-stages in traditional BP algorithm, 2 output BAMs being merged into one 4 input 4 outputs, in factor graph corresponding to polar code BP decoding, by the two-layer one deck of merging in BP algorithm, make required total calculating number of plies in decode procedure reduce half;

1. the BAMs of 4 input 4 outputs, be expressed as left node, 2., 3., 4. successively, right side node respectively be node 1. 2. 3. 4., 2. 4., 3. XOR value 4., 4.; As the same by the known relation of turning left from the right side of symmetry.

2. polar code interpretation method as claimed in claim 1, it is characterized in that: by factor graph, get four, left side node in the BAM of 4 inputs 4 outputs and be followed successively by from top to bottom (i, j), (i, j+N/4), (i, j+N/2), (i, j+3N/4), four of the right nodes are followed successively by (i+1,4j-3), (i+1 from top to bottom, 4j-2), (i+1,4j-1), (i+1,4j), the mathematical algorithm of output confidence level message is:

While propagating to the right,

$\begin{array}{c}{R}_{i+\mathrm{1,4}j-3}=g(R_{i,j},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ R_{i+\mathrm{1,4}j-2}=g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/2}+g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j-1}=g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/4}+g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j}=R_{i,j+3N/4}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}$

From symmetry, this algorithm to the right and left formula of pass-along message has identical form;

While propagating left,

$\begin{array}{c}{L}_{i,j}=g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ L_{i,j+N/4}=g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-1}+g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+N/2}=g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-2}+g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+3N/4}=L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(L_{i+1,4j-3},g(R_{i,j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}.$

3. polar code interpretation method as claimed in claim 1, is characterized in that: for code length N=2 ⁿpolar code, in factor graph, between adjacent layer, comprise the BAMs of N/4 4 input 4 outputs.

4. a polar code code translator, is characterized in that: comprise computing module and memory module; Computing module adopts the BAMs of 4 input 4 outputs, and 1. the BAMs of 4 input 4 outputs are expressed as left node, 2., 3., 4. successively, right side node respectively be node 1. 2. 3. 4., 2. 4., 3. XOR value 4., 4.; As the same by the known relation of turning left from the right side of symmetry;

The feature of memory module is: for code length N=2 ⁿpolar code, the required memory space of code translator is N message of (n/2-1) *.

5. polar code code translator according to claim 4, it is characterized in that: by factor graph, get four, left side node in the BAM of 4 inputs 4 outputs and be followed successively by from top to bottom (i, j), (i, j+N/4), (i, j+N/2), (i, j+3N/4), four of the right nodes are followed successively by (i+1,4j-3), (i+1 from top to bottom, 4j-2), (i+1,4j-1), (i+1,4j), the mathematical algorithm of output confidence level message is:

While propagating to the right,

$\begin{array}{c}{R}_{i+\mathrm{1,4}j-3}=g(R_{i,j},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ R_{i+\mathrm{1,4}j-2}=g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/2}+g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j-1}=g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},R_{i,j+N/4}+g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ R_{i+\mathrm{1,4}j}=R_{i,j+3N/4}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(R_{i,j},g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}$

From symmetry, this algorithm to the right and left formula of pass-along message has identical form;

While propagating left,

$\begin{array}{c}{L}_{i,j}=g(L_{i+\mathrm{1,4}j-3},g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-1})+g(L_{i+\mathrm{1,4}j-2},R_{i,j+N/2})\\ +g(R_{i,j+3N/4}+L_{i+\mathrm{1,4}j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},\left(L_{i+\mathrm{1,4}j-1}\right)))\\ L_{i,j+N/4}=g(L_{i+\mathrm{1,4}j-2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-1}+g(R_{i,j+N/2},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+N/2}=g(L_{i+\mathrm{1,4}j-1},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j}+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2}))\\ +g(L_{i+\mathrm{1,4}j-3},g(R_{i,j},L_{i+\mathrm{1,4}j-2}+g(R_{i,j+N/4},R_{i,j+3N/4}+L_{i+\mathrm{1,4}j})))\\ L_{i,j+3N/4}=L_{i+\mathrm{1,4}j}+g(R_{i,j+N/2},L_{i+\mathrm{1,4}j-1})+g(R_{i,j+N/4},L_{i+\mathrm{1,4}j-2})\\ +g(L_{i+1,4j-3},g(R_{i,j},g(R_{i,j+N/4},R_{i,j+N/2})+g(L_{i+\mathrm{1,4}j-2},L_{i+\mathrm{1,4}j-1})))\end{array}.$

6. polar code code translator according to claim 4, is characterized in that: in the simultaneously treated situation of all nodes of individual layer, the quantity of computing module is N/4; Also can do time-division processing with computing unit still less.

7. polar code code translator according to claim 4, is characterized in that: for code length N=2 ⁿpolar code, in the situation that each confidence level message quantizing bit number is q, the capacity of memory cell is (n/2-1) * q*N bit, stores respectively the data in n/2-1 layer in decode procedure, wherein the shared memory capacity size of every one deck is q*N bit.