WO2018133217A1 - 一种利用巴哈塔切亚参数构造极化码的方法及系统 - Google Patents

一种利用巴哈塔切亚参数构造极化码的方法及系统 Download PDF

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WO2018133217A1
WO2018133217A1 PCT/CN2017/079968 CN2017079968W WO2018133217A1 WO 2018133217 A1 WO2018133217 A1 WO 2018133217A1 CN 2017079968 W CN2017079968 W CN 2017079968W WO 2018133217 A1 WO2018133217 A1 WO 2018133217A1
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parameter
channel
bit
polarization
channels
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French (fr)
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何业军
张威
盖宝宏
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深圳大学
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/033—Theoretical methods to calculate these checking codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit

Definitions

  • the present invention relates to the field of channel coding technologies, and in particular, to a method and system for constructing a polarization code using Baha Tazzia parameters.
  • N 2 n
  • Linear merging and splitting operations are performed on the N virtual "bit channels".
  • Such a linear operation can be specifically described as a process in which a binary discrete memoryless channel is typically described by given W:X ⁇ Y, where W represents the channel and X and Y represent the input and output bit sets of the channel, respectively. And both sets are taken in ⁇ 0,1 ⁇ .
  • x), x ⁇ X, y ⁇ Y can be used to indicate the transition probability of this channel.
  • a channel vector composed of N W channels is represented by W N . Therefore, when a single channel W:X ⁇ Y is extended to the N channel, the mapping relationship of the N channel vector can be described as W N :X N ⁇ Y N , and the transition probability of the N channel can be expressed as The larger the value of N, the more times the linear operation needs to be performed.
  • N is large enough, after the polarization operation is performed on the N virtual "bit channels", the capacity of the channel will exhibit polarization, and the capacity of some channels will approach "1", while the other part will be “bit”. The capacity of the channel will approach "0".
  • the four symmetric binary channels (W, W, W, W) are subjected to two linear combining and splitting operations to obtain another four channels W 4 0 , W 4 1 , W 4 2 , W 4 3 .
  • the channel capacities obtained after the split were 0.0535, 0.5725, 0.4275, and 0.9465, respectively.
  • the capacity of more and more channels will approach "0" and approach "1", which shows a A phenomenon of polarization, referred to as polarization.
  • polarization A phenomenon of polarization
  • the original definition of the channel's Bahatetasian parameter (which can also be called the channel's polarization rate) is:
  • the Bahatta Chez parameter Z(W) can be regarded as the upper limit of the maximum likelihood decision error probability.
  • the channel satisfying the condition Z(W) ⁇ ⁇ can be regarded as a channel.
  • a noiseless channel, and a channel satisfying the condition Z(W) ⁇ 1- ⁇ is regarded as a pure noise channel, where the parameter ⁇ satisfies 0 ⁇ ⁇ ⁇ 1.
  • the Bahatta Chez parameter and the symmetric capacity of the channel in the binary discrete memoryless channel satisfy I(W)+Z(W) ⁇ 1, in the above inequality in the BEC channel. The equal sign is established.
  • the most important part of constructing a polarization code is to know how to accurately select the information bits. If you want to transmit the required information bits on a bit channel with a symmetric capacity of "1", you must first find a way to select these ideal bit channels. Out, and these methods of selecting ideal information bits are called encoding coding algorithms for polarization codes.
  • the Bahatachian parameter Z(W) is a particularly important criterion for measuring channel reliability. From the definition of the Bahat Tachia parameter, it can be analyzed that the value of the parameter Z(W) is smaller. The more reliable the performance of the channel, It is also known that the ultimate goal of the polarization code encoding construction algorithm is to pick out these channels with very small Z(W) values in the most accurate way.
  • an object of the present invention is to provide a method and system for constructing a polarization code using Baha Tazzia parameters, aiming at solving the high computational complexity and channel pole of the coding structure technology in the prior art.
  • the problem of slow speed is to provide a method and system for constructing a polarization code using Baha Tazzia parameters, aiming at solving the high computational complexity and channel pole of the coding structure technology in the prior art. The problem of slow speed.
  • a method of constructing a polarization code using a Bahatetas parameter comprising the following steps:
  • the linked list corresponding to the five types of parameter expressions is decoded, and the parameter expression with the lowest bit error rate and the block error rate is obtained as the coding structure parameter.
  • the method for constructing a polarization code using a Bahatetas parameter wherein the step A Specifically include:
  • pre-set the code length is N, where N is a positive integer greater than 0;
  • the method for constructing a polarization code by using a Bahat Tachia parameter wherein the step B is performed by performing polarization operations on N mutually associated bit channels to obtain a Bata Tacit parameter of an even-numbered channel.
  • Bahat Tachia parameters of odd-numbered channels among them i is a positive integer less than or equal to N/2.
  • step C specifically includes:
  • the method for constructing a polarization code by using a Baha Tazza parameter wherein in the step E, the linked list corresponding to the five types of parameter expressions is decoded according to the SCL-CRC algorithm, and the five types of parameter expressions are corresponding to
  • the bit error rate and the block error rate of the polarization code in the BSC channel and the Gaussian channel respectively obtain a parameter expression with a bit error rate and a minimum block error rate as coding structure parameters.
  • a system for constructing a polarization code using Bahatetas parameters including:
  • a linear processing module configured to linearly combine and split bit information of a preset encoding length to obtain a bit channel associated with each other;
  • a polarization operation module configured to perform a polarization operation on the bit channel, to obtain a Bahatta Chez parameter of the odd-numbered channel and a Bahata Chea parameter of the even-numbered channel;
  • a sampling module configured to extract five types of parameter expressions according to the set sampling corresponding to the Bahatetas parameter of the odd-numbered channel;
  • the polarization code construction module is configured to perform polarization code construction on the five types of parameter expressions, and obtain a linked list corresponding to the five types of parameter expressions respectively;
  • the decoding and obtaining module is configured to decode the linked list corresponding to the five types of parameter expressions according to the SCL-CRC algorithm, and obtain a parameter expression with the lowest bit error rate and the wrong block rate as the coding structure parameter.
  • the system for constructing a polarization code by using a Bahatachian parameter wherein the linear processing module specifically includes:
  • a code length preset unit configured to preset a code length of N, where N is a positive integer greater than 0;
  • a virtualization unit for virtualizing N-bit information bits into N independent messages Road
  • An association unit is configured to linearly combine and split the N channels to obtain N mutually associated bit channels.
  • the system for constructing a polarization code by using a Bahat Tachia parameter wherein the polarization operation module performs polarization operations on N interrelated bit channels to obtain a Bata Tachia parameter of an even-numbered channel.
  • Bahat Tachia parameters of odd-numbered channels among them i is a positive integer less than or equal to N/2.
  • sampling module specifically includes:
  • the system for constructing a polarization code by using a Bata Tazza parameter wherein the decoding and acquisition module enters a linked list corresponding to five types of parameter expressions according to the SCL-CRC algorithm
  • the bit error rate and the block error rate of the polarization codes corresponding to the five types of parameter expressions in the BSC channel and the Gaussian channel are respectively obtained, and the parameter expressions with the bit error rate and the block error rate are obtained as the coding structure parameters.
  • the method and system for constructing a polarization code by using a Baha Tazai parameter provided by the present invention include: linearly combining and splitting bit information of a preset code length to obtain a bit channel associated with each other;
  • the polarization operation obtains the Bahatta Chez parameter of the odd-numbered channel and the Bahatta-Cha parameter of the even-numbered channel; and extracts five kinds of parameter expressions according to the set sampling corresponding to the Bahattachian parameter of the odd-numbered channel;
  • the five types of parameter expressions are constructed by polarization code, and the linked list corresponding to the five types of parameter expressions is obtained.
  • the linked list corresponding to the five types of parameter expressions is decoded to obtain the bit error rate and the block error rate.
  • the lowest parameter expression is used as the encoding constructor.
  • the invention achieves a very low bit error rate and a block error rate, while also having the lowest computational complexity.
  • Figure 1 is a schematic diagram of polarization of a 2-channel.
  • Fig. 2 is a diagram showing the capacity change after polarization of 4 channels.
  • FIG. 3 is a schematic diagram of polarization of an N channel after expansion.
  • FIG. 4 is a schematic diagram of a polarization process of combining and splitting 8 channels in which bit flip is performed first.
  • Figure 5 is a schematic diagram of the polarization process of the natural sequence of 8 channels of merging and splitting.
  • Figure 6 is a diagram illustrating a coded code encoding with a code length of 8.
  • Channel index profile
  • Figure 10 is a basic schematic diagram of the linked list elimination decoding algorithm.
  • Figure 13 is a graph comparing the performance of the bit error rate of the polarization code constructed by the polarization code constructed by the type 5 parameter and the Gaussian approximation estimation method in the AGWN channel.
  • FIG. 14 is a flow chart of a preferred embodiment of a method for constructing a polarization code using Bahattacia parameters according to the present invention.
  • Figure 15 is a block diagram showing the construction of a preferred embodiment of the system for constructing a polarization code using the Bahattachian parameters of the present invention.
  • the present invention provides a method and system for constructing a polarization code using Bahattacia parameters. To further clarify and clarify the objects, technical solutions and effects of the present invention, the present invention will be further described in detail below. It is understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
  • a flow chart of a preferred embodiment of a method for constructing a polarization code using a Bahattacia parameter according to the present invention includes the following steps:
  • Step S100 linearly combining and splitting bit information of a preset encoding length to obtain a bit channel associated with each other.
  • step S100 specifically includes the following steps:
  • Step S101 Pre-set the code length to be N, where N is a positive integer greater than 0;
  • Step S102 virtualizing the N-bit information bits into N mutually independent channels
  • Step S103 linearly combining and splitting N channels to obtain N mutually associated bit channels.
  • the preset coding length is N
  • the N information bits are first virtualized into N independent channels, and then the N channels are linearly combined.
  • the split operation so that the original N independent discrete memoryless channels become N interrelated bit channels.
  • Shannon's information theory it can be known that the total capacity of the channel does not change, and the total cutoff frequency of the channel is improved. Therefore, each split bit channel can be made after this split operation. The cutoff frequency has changed.
  • Step S200 Perform a polarization operation on the bit channel to obtain a Bach of an odd-numbered channel. Tabahya parameters for the Tabea parameter and the even term channel.
  • the Bahattachian parameters of the odd-numbered channel and the Bahatascha parameters of the even-numbered channel can be obtained respectively.
  • Bahatetas parameters of even-numbered channels Is an equation expression that is easy to iteratively calculate
  • the Bahat Tachia parameter of the odd-numbered channel Is an inequality with upper and lower limits. In this way, it is necessary to deduct and deduct the inequality corresponding to the Bahattachian parameters of the odd-numbered channels on the basis of the original theory, and then derive the correct and reasonable Bahatta Cheya parameter equation in the range of the inequality.
  • Step S300 Extract five types of parameter expressions according to the set samples corresponding to the Bahatetas parameters of the odd-numbered channel.
  • Step S400 Perform a polarization code structure on the five types of parameter expressions to obtain a linked list corresponding to the five types of parameter expressions.
  • Step S500 Decode the linked list corresponding to the five types of parameter expressions according to the SCL-CRC algorithm, and obtain a parameter expression with the lowest bit error rate and the block error rate as the coding structure parameter.
  • the SCL-CRC algorithm is used at the decoding end for decoding.
  • BER bit error rate
  • FER block error rate
  • One is used as the final coding construct parameter, and finally to verify the performance of this parameter, then A method of Gaussian approximation estimation is used to compare performance.
  • FIG. 4 and FIG. 5 also specifically describe the virtualization of 8 bits of u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 before the merge and split operations. Become 8 independent symmetric channels W.
  • the polarization operation after the virtual is also regular. What is specifically mentioned here is that the channel combination refers to the merging between symmetric channels (channels with the same performance), instead of arbitrarily and arbitrarily merging the channels.
  • Figures 4 and 5 show the two correct channel merging and splitting methods selected for a large number of experiments on 8 channels.
  • the merge rule of FIG. 4 and FIG. 5 also follows the principle of merging between symmetric channels, wherein FIG. 4 performs channel merging in a natural order, so the index order of the finally obtained codewords is 1, 5 , 3, 7, 2, 6, 4, 8. 5 is a bit inversion operation before channel combining, so that the order of the finally obtained code words is the natural order 1, 2, 3, 4, 5, 6, 7, 8.
  • the combination of these two methods is correct. From the above, it can be known that when the coded codewords are in natural order, the workload of the decoder is relatively low, and the performance of the polarization code is greatly improved.
  • the merge splitting method presented in FIG. 5 is more inclined to perform polarization operation on the channel.
  • the channel polarization process demonstrated in FIG. 5 it can be seen that eight original independent channels W can obtain four pairs of related channels W 2 1 and W 2 2 after the merge and split operation of the first stage stage1;
  • the channel merge split operation of stage 2 is an operation between four channels W 2 1 and an operation between the other four channels W 2 2 , and two pairs of higher correlations can be obtained after the operation at this stage.
  • the third stage stage3 again merge the symmetric channel and then split it to get the final 8 related channels W 8 1 , W 8 2 , W 8 3 , W 8 4 , W 8 5 , W 8 6 , W 8 7 , W 8 8 .
  • the process of channel polarization calculation is analyzed and elaborated in detail above.
  • the key of the present invention is that it can accurately estimate the value of the Bahattachian parameter and the channel capacity after the completion of the channel polarization operation, and then accurately select from it.
  • the Bahattachian parameter (Bahata Chea parameter) is Z(W 0 ), and after the polarization of the first stage stage1, four pairs of symmetry are obtained.
  • Z(W 8 8 ) Z(W 4 4 ) 2 , Z(W 4 4 ) ⁇ Z(W 8 7 ) ⁇ 2Z(W 4 4 )-Z(W 4 4 ) 2
  • Z(W 8 6 ) Z(W 4 3 ) 2 , Z(W 4 3 ) ⁇ Z(W 8 5 ) ⁇ 2Z(W 4 3 )-Z(W 4 3 ) 2
  • Z(W 8 4 ) Z(W 4 2 ) 2 , Z(W 4 2 ) ⁇ Z(W 8 3 ) ⁇ 2Z(W 4 2 )-Z(W 4 2 ) 2
  • Z(W 8 2 ) Z(W 4 1 ) 2 , Z(W 4 1 ) ⁇ Z(W 8 1 ) ⁇ 2Z(W 4 1 )-Z(W 4 1 ) 2
  • the expression of the Bahattachian parameter of each bit channel after the polarization operation can be iterated as Even channel for BEC channel (Binary Erasure Channel), BSC channel (Binary Symmetric Channel), AWGN channel (Additive White Gaussian Noise)
  • BEC channel Binary Erasure Channel
  • BSC channel Binary Symmetric Channel
  • AWGN channel Additional White Gaussian Noise
  • the value of the Bahat Tachya parameter is easily calculated by the iterative equation, but it is limited by the decoding algorithm of the time. Arikan can only get the odd-numbered Bahata Cheya parameter values only under the BEC channel. Simplified directly to For other channels, the inequality of the Bahat Tached parameters of this odd number is not well handled.
  • the N mutually associated bit channels are subjected to polarization operation to obtain a Bata Tachia parameter of the even-numbered channel.
  • Bahat Tachia parameters of odd-numbered channels among them i is a positive integer less than or equal to N/2.
  • the step S300 specifically includes:
  • Step S301 the Bahattacia parameter of the odd-numbered channel Recorded as
  • the linked list corresponding to the five types of parameter expressions is decoded according to the SCL-CRC algorithm, and the five types of parameters are expressed.
  • the bit error rate and the block error rate of the polarization code corresponding to the equation are respectively in the BSC channel and the Gaussian channel, and the parameter expression with the bit error rate and the block error rate is obtained as the coding structure parameter.
  • the most important part of the polarization code coding structure is that the first K bit channels with excellent channel capacity are accurately selected as the transmission information bits in a given N bit channels, and the remaining NKs are used.
  • the bit channels are used to transmit fixed bits (these fixed bits can take 0 or 1, which are known at both the transmitting and receiving ends).
  • the polarization code is a channel-specific code, so the proper coding structure can be selected more accurately for different channels, which can greatly improve the performance of the polarization code. Since the Baha Tazzya parameter is one of the most important indicators for measuring channel reliability in constructing the polarization code, step S200 and step S300 are two very critical steps in the process of bit channel selection.
  • step S200 and step S300 we give the initial Bahattachian parameter for each bit channel as Z(W 0 ). Therefore, for a bit channel with a code length of N, after the polarization operation, the equation of the Bahattachian parameter of the even-numbered channel can be obtained as The expression of the Bahat Tachia parameter of the odd-numbered channel is After the polarization operation, the Bahattachian parameters of all even-numbered channels can be obtained by the iterative operation by the above equation expression, and the calculation of the Bahat-Tac parameters of the odd-numbered channels is subject to mathematics. In the processing of the operation, in order to accurately select the required channel index, it is also necessary to accurately calculate the Bahattachian parameters of the odd-numbered channels.
  • the present invention also focuses on the calculation of the Bahattachian parameters of the odd-numbered channels as follows: it can be easily obtained from the above inequalities. Yes Lower limit, Yes The upper limit, and then the inequalities corresponding to the Bahata Cheya parameters of the odd-numbered channel are deduced and derived, and two parameters m and n are obtained, and m and n are non-negative numbers, where 0 ⁇ m ⁇ 1,0 ⁇ n ⁇ 1. By using the parameters m and n, the equation can be made It is absolutely true in the range of the inequality of the Bahattacia parameter of the above odd-numbered channel.
  • the Bahattachia parameter of the even-numbered channel can be directly obtained, it is only necessary to synthesize the equations of the Bahat Tachya parameter of the odd-numbered channel and the Bahatta Cheya parameter of the even-numbered channel. Then, it is easy to calculate the value of the Bahattachian parameter after each bit channel is subjected to the polarization operation. After obtaining the Bahata Chea parameter value of each channel, the N values are sorted in order from smallest to largest (or from large to small), and finally the first K values are selected as the transmission information bits. The channel index value used.
  • the BSC channel and the AWGN channel are selected as experimental channels.
  • the channel index distribution maps of the two are basically similar in rules, so the law of specifically presenting the channel index distribution map is selected.
  • a more representative AGWN channel is used for analysis and research.
  • FIG. 7 to FIG. 9 are five types of parameters: type one, type two, type three, type four, and type five, and the code length is 512.
  • bit channel index (i) represents the index value of the bit channel
  • the ordinate is the Bahat Tachia representing the bit channel.
  • the parameter value (which can also be called the polarization rate of the channel, ie Z(i)).
  • polarization rate of the channel ie Z(i)
  • some rules can be derived from the three index profiles, from type five to the class. Type one, the channel's Bahatacea parameters are increasingly concentrated to the bottom, which is usually considered a good trend in this case.
  • the polarization code constructed by the parameter of type 5 is the best among the five types of parameters. One kind.
  • the channel index generated for these five types of parameters should be selected among the former K.
  • the index value of each channel is then used to transmit information bits using the channel corresponding to the K index values (the complete information sequence contains information bits and fixed bits), and then the polarization code can be encoded.
  • the polarization code is also a linear block code. Similar to other channel coding techniques, the generated codeword of the polarization code is also multiplied by the information matrix by the information bits, and the obvious difference from other linear block codes is the polarization.
  • the code performs special processing in the process of selecting the transmission information bit (the coding structure of the polarization code), and it is this processing that can greatly improve the channel capacity even close to the Shannon limit capacity, when the code length N Reach When infinitely long, the symmetrical capacity of the channel is almost equal to the limit capacity of Shannon.
  • the encoding process of the polarization code is also relatively simple. In order to visually illustrate the encoding process of the polarization code, the binary input codeword is given here:
  • B N is an operation matrix of bit sequence inversion, that is, a bit flip operation, which is specifically presented in FIGS. 4 and 5.
  • N represents the code length
  • K is the number of information bits
  • f is a fixed-bit channel index, which is a subset of (1, 2...N)
  • the complement of f can be expressed as f c
  • u f is represented as a fixed bit vector
  • K/N is called the code rate of the code.
  • the above output codeword can be transformed into: In order to make the process of polarization code encoding more specific, given a parameter vector (8, 4, ⁇ 1, 3, 5, 6 ⁇ , (1, 0, 1, 0)), you can get The corresponding code is:
  • the coding demonstration diagram corresponding to the above encoding process is as shown in FIG. 6.
  • the encoded codeword is obtained.
  • the coding process with a code length of 8 is specifically demonstrated here, and a similar method can be used to extend the coding scenario to length N.
  • the next task is to transmit the generated codeword from the physical channel to the communication receiving end.
  • the most mature decoding technique used today is a cyclic redundancy auxiliary linked list splicing elimination decoding algorithm (CRC-SCL) to assist the coding structure.
  • This decoding algorithm is in SCL (linked list elimination decoding algorithm).
  • SCL linked list elimination decoding algorithm
  • SC continuous elimination decoding algorithm
  • SC continuous elimination decoding algorithm
  • the introduction of the cyclic redundancy check bit on the basis of the CRC-SCL algorithm can greatly improve the performance of the polarization code, and can also eliminate the problem of high computational complexity caused by the extended path in the SCL algorithm.
  • the tree diagram of the SCL decoding algorithm is used for description.
  • a binary tree can be used for analysis and description.
  • an improved version of SCL is used.
  • the code algorithm, CRC-SCL algorithm adds 24-bit cyclic redundancy bits to the information codeword. Only the path that passes this cyclic redundancy check is used as the decoding candidate sequence, which can eliminate the path expansion before. The impact is also improved by the performance of the polarization code. After the experiment, the performance results of the error rate (bit error rate, ie bit error rate) and block error rate of the five kinds of polarization codes corresponding to the above five parameters in the BSC channel and the Gaussian channel are obtained.
  • mold 1 - mold 5 represents type 1 to type 5, respectively, the abscissa Error probability BSC channel of Fig. 11 represents the error probability of the BCS channel, and the abscissa of Fig. 12 represents the signal noise.
  • Ratio ie SNR
  • left side of Figure 12 The ordinate of the slice represents the bit error rate
  • the ordinate of the right picture in FIG. 12 represents the block error rate (ie, Block Error Rate)
  • the abscissa of FIG. 13 represents the signal to noise ratio (ie, SNR)
  • FIG. 13 The ordinate indicates the bit error rate (abbreviated as BER).
  • the performance of the polarization code designed by using the parameter of type 5 and then combined with the CRC-SCL algorithm is almost close to the performance of the polarization code constructed by the Gaussian approximation estimation method, and there is no Gaussian approximation.
  • the estimation method is low in the polarization rate and the performance of the polarization code is greatly reduced due to error propagation, and the computational complexity can be kept at the lowest state, so the constructed method is used for the BEC channel, the BSC channel, The AWGN channel is still ideal.
  • the present invention also provides a system for constructing a polarization code using Bahattacia parameters.
  • the system for constructing a polarization code using the Bahatetas parameter includes:
  • the linear processing module 100 is configured to linearly combine and split the bit information of the preset encoding length to obtain a bit channel associated with each other;
  • the polarization operation module 200 is configured to perform a polarization operation on the bit channel to obtain a Bahatta Chez parameter of the odd-numbered channel and a Bahatta Cheya parameter of the even-numbered channel;
  • the sampling module 300 is configured to extract five types of parameter expressions according to the set samples corresponding to the Bahattachian parameters of the odd-numbered channel;
  • the polarization code construction module 400 is configured to perform polarization code construction on the five types of parameter expressions to obtain a linked list corresponding to the five types of parameter expressions respectively;
  • the decoding and obtaining module 500 is configured to decode the linked list corresponding to the five types of parameter expressions according to the SCL-CRC algorithm, and obtain a parameter table with the lowest bit error rate and the wrong block rate. As a coding construct parameter.
  • the linear processing module 100 specifically includes:
  • a code length preset unit configured to preset a code length of N, where N is a positive integer greater than 0;
  • a virtualization unit configured to virtualize N bits of information bits into N mutually independent channels
  • An association unit is configured to linearly combine and split the N channels to obtain N mutually associated bit channels.
  • the polarization operation module 200 performs polarization operations on the N interrelated bit channels to obtain an even-numbered channel of the Bahat Tower.
  • Chea parameter And Bahat Tachia parameters of odd-numbered channels among them i is a positive integer less than or equal to N/2.
  • the sampling module 300 specifically includes:
  • the decoding and obtaining module 500 decodes the linked list corresponding to the five types of parameter expressions according to the SCL-CRC algorithm, and class 5
  • the bit error rate corresponding to the parameter expression is the bit error rate and the block error rate under the BSC channel and the Gaussian channel, respectively, and the parameter expression with the bit error rate and the block error rate is obtained as the coding structure parameter.
  • the present invention provides a method and system for constructing a polarization code by using a Bahattacia parameter, the method comprising: linearly combining and splitting bit information of a preset code length to obtain an associated bit channel. Performing a polarization operation on the bit channel to obtain a Bahatta Chez parameter of the odd-numbered channel and a Bahatta Cheya parameter of the even-numbered channel; and extracting 5 classes according to the set sampling corresponding to the Bahattachian parameter of the odd-numbered channel Parameter expression; constructing the polarization code of the five types of parameter expressions to obtain a linked list corresponding to the five types of parameter expressions; decoding the linked list corresponding to the five types of parameter expressions according to the SCL-CRC algorithm to obtain the bit error
  • the parameter expression with the lowest rate and block error rate is used as the coding construction parameter.
  • the invention achieves a very low bit error rate and a block error rate, while also having the lowest computational complexity.

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Abstract

本发明公开了一种利用巴哈塔切亚参数构造极化码的方法及系统，方法包括：将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道；将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。本发明实现了极低的误比特率以及误块率，同时还具有最低的计算复杂度。

Description

一种利用巴哈塔切亚参数构造极化码的方法及系统 技术领域
本发明涉及信道编码技术领域，尤其涉及的是一种利用巴哈塔切亚参数构造极化码的方法及系统。
背景技术
在信道编码技术领域，达到香农极限容量是最优方案。之前提出的Turbo码以及LDPC码，在性能上已经十分的接近于香农极限容量，而且这两种编码技术也现代通信领域中得到了广泛的推广和应用。然而到目前为止仍然没有可靠的理论能够证明这两种编码技术可以达到香农极限，而且Turbo码和LDPC码还存在编解码复杂度高的问题。
Arikan终于在2009年使用了信道极化的概念提出了一种前所未有的编码技术--极化码，这种编码可分析性极强，最重要的是其拥有编解码复杂度低的特质。信道极化的特点可以描述为以下：在给定的信息序列被发送到信道之前，先将给定的这N(N＝2n)个比特序列位虚拟成N个“比特信道”，然后再对这N个虚拟的“比特信道”进行线性合并和拆分运算。这种线性运算操作可以具体描述为以下过程：通常情况下，给定W:X→Y来描述二进制离散无记忆信道，其中W表示信道，X和Y分别表示信道的输入以及输出的比特集合，而且这两个集合都是在{0,1}中进行取值。W(y|x),x∈X,y∈Y可以用来表示这个 信道的转移概率。这里为了方便表达，用WN来表示由N个W信道所构成的信道向量。因此由单个信道W:X→Y拓展到N信道时，这N信道向量的映射关系可以描述为WN:XN→YN，同时N信道的转移概率可以表示为
Figure PCTCN2017079968-appb-000001
N的取值越大，需要进行的线性运算的次数就越多。当N足够大时，这N个虚拟的“比特信道”在进行极化运算之后，信道的容量会呈现出两极分化的现象，一部分信道的容量会趋近于“1”，而另一部分“比特信道”的容量会趋近于“0”。容量为“1”的这部分信道称之为无噪信道，容量为“0”的信道就称为纯噪声信道。上述提到的极化运算过程可以由图1，图2，图3来具体呈现。
给定原始信道的初始对称容量为I(W)＝0.5，4个对称的二进制信道(W,W,W,W)经过两次线性合并与拆分运算之后就得到另外4个信道W4 0,W4 1,W4 2,W4 3。拆分之后所得到的信道容量分别为0.0535，0.5725，0.4275，0.9465。在给定的编码长度N不断的增大的过程中，很明显的可以发现越来越多的信道的容量会趋近于“0”和趋近于“1”，这样也就呈现出了一种两极分化的现象，简称为极化现象。，当然极化要呈现出两极均匀的状态才是合理的。
提到信道极化的概念，在这里必须重视两个十分重要的参数，信道的对称容量I(W)和信道的巴哈塔切亚参数Z(W)。信道的对称容量I(W)的定义式为：
Figure PCTCN2017079968-appb-000002
信道的巴哈塔切亚参数(也可以称之为信道的极化速率)的原始定义式为：
Figure PCTCN2017079968-appb-000003
结合信息序列的互信息链法则以及上面所描述的4信道的极化过程可以得到：
I(W4 0)+I(W4 1)+I(W4 2)+I(W4 3)＝4I(W)，
Z(W4 0)+Z(W4 1)+Z(W4 2)+Z(W4 3)≤4Z(W)。
当将其推广到N信道的场景时，即可得到：
Figure PCTCN2017079968-appb-000004
当信道为二进制离散无记忆信道时，巴哈塔切亚参数Z(W)可以被视作最大似然判决错误概率的上限，换句话说可以将满足条件Z(W)≤ξ的信道视为无噪信道，而将满足条件Z(W)≥1-ξ的信道看作是纯噪信道，这里的参数ξ满足0≤ξ≤1。而在Arikan的文章中已经给出在二进制离散无记忆信道下巴哈塔切亚参数和信道的对称容量是满足I(W)+Z(W)≥1的，在BEC信道中上面的不等式中的等号是成立的。
构造极化码最重要的环节就是要知道如何准确的选取信息位，想要在对称容量为“1”的比特信道上传送所需要的信息位，首先得想办法将这些理想的比特信道给挑选出来，而这些选择理想信息位的方法称为极化码的编码构造算法。前面已经提到巴哈塔切亚参数Z(W)是衡量信道可靠性的一个特别重要的标准，从巴哈塔切亚参数的定义式可以分析得知参数Z(W)的值越小比特信道的性能也就越可靠，既 而也可以得知极化码编码构造算法的最终目标就是以最精确的方式来挑选出这些Z(W)值极小的信道。
因此，现有技术还有待改进和发展。
发明内容
鉴于上述现有技术的不足，本发明的目的在于提供一种利用巴哈塔切亚参数构造极化码的方法及系统，旨在解决现有技术中编码构造技术的计算复杂度高以及信道极化速度慢的问题。
本发明的技术方案如下：
一种利用巴哈塔切亚参数构造极化码的方法，其中，所述方法包括以下步骤：
A、将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道；
B、将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；
C、根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；
D、将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；
E、根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。
所述利用巴哈塔切亚参数构造极化码的方法，其中，所述步骤A 具体包括：
A1、预先设编码长度为N，其中N为大于0的正整数；
A2、将N位比特信息位虚拟为N个相互独立的信道；
A3、将N个信道进行线性合并和拆分，得到N个相互关联的比特信道。
所述利用巴哈塔切亚参数构造极化码的方法，其中，所述步骤B中将N个相互关联的比特信道进行极化运算，得到偶数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000005
和奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000006
其中
Figure PCTCN2017079968-appb-000007
i为小于或等于N/2的正整数。
所述利用巴哈塔切亚参数构造极化码的方法，其中，所述步骤C中具体包括：
C1、将奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000008
记为
Figure PCTCN2017079968-appb-000009
C2、取m1＝0.1、n1＝0.9时，得到第一类参数表达式记为
Figure PCTCN2017079968-appb-000010
取m2＝0.3、n2＝0.7时，得到第二类参数表达式记为取m3＝0.5、n3＝0.5时，得到第三类参数表达式记为
Figure PCTCN2017079968-appb-000012
取m4＝0.7、n4＝0.3时，得到第四类参数表达式记为
Figure PCTCN2017079968-appb-000013
取m5＝0.9、n5＝0.1时，得到第五类参数表达式记为
Figure PCTCN2017079968-appb-000014
所述利用巴哈塔切亚参数构造极化码的方法，其中，所述步骤E中根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，将5类参数表达式所对应的极化码分别在BSC信道以及高斯信道下的误比特率以及误块率，得到误比特率以及误块率最小的参数表达式作为编码构造参数。
一种利用巴哈塔切亚参数构造极化码的系统，其中，包括：
线性处理模块，用于将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道；
极化运算模块，用于将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；
抽样模块，用于根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；
极化码构造模块，用于将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；
解码及获取模块，用于根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。
所述利用巴哈塔切亚参数构造极化码的系统，其中，所述线性处理模块具体包括：
编码长度预设单元，用于预先设编码长度为N，其中N为大于0的正整数；
虚拟化单元，用于将N位比特信息位虚拟为N个相互独立的信 道；
关联单元，用于将N个信道进行线性合并和拆分，得到N个相互关联的比特信道。
所述利用巴哈塔切亚参数构造极化码的系统，其中，所述极化运算模块中将N个相互关联的比特信道进行极化运算，得到偶数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000015
和奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000016
其中
Figure PCTCN2017079968-appb-000017
i为小于或等于N/2的正整数。
所述利用巴哈塔切亚参数构造极化码的系统，其中，所述抽样模块具体包括：
推导单元，用于将奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000018
记为
Figure PCTCN2017079968-appb-000019
计算单元，用于取m1＝0.1、n1＝0.9时，得到第一类参数表达式记为
Figure PCTCN2017079968-appb-000020
取m2＝0.3、n2＝0.7时，得到第二类参数表达式记为
Figure PCTCN2017079968-appb-000021
取m3＝0.5、n3＝0.5时，得到第三类参数表达式记为
Figure PCTCN2017079968-appb-000022
取m4＝0.7、n4＝0.3时，得到第四类参数表达式记为
Figure PCTCN2017079968-appb-000023
取m5＝0.9、n5＝0.1时，得到第五类参数表达式记为
Figure PCTCN2017079968-appb-000024
所述利用巴哈塔切亚参数构造极化码的系统，其中，所述解码及获取模块根据SCL-CRC算法对与5类参数表达式分别对应的链表进 行解码，将5类参数表达式所对应的极化码分别在BSC信道以及高斯信道下的误比特率以及误块率，得到误比特率以及误块率最小的参数表达式作为编码构造参数。
本发明所提供的利用巴哈塔切亚参数构造极化码的方法及系统，方法包括：将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道；将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。本发明实现了极低的误比特率以及误块率，同时还具有最低的计算复杂度。
附图说明
图1是2信道的极化示意图。
图2是4信道的极化之后的容量变化图。
图3是经过拓展之后的N信道的极化示意图。
图4是先进行了比特翻转的8信道的合并与拆分的极化过程示意图。
图5是自然顺序的8信道的合并与拆分的极化过程示意图。
图6是编码长度为8的极化码编码演示图。
图7是在信噪比为SNR＝3dB,编码长度N＝512，码率为R＝1/2条 件下高斯信道中的第一种和第二种类型的巴哈塔切亚参数所对应的信道索引分布图。
图8是在信噪比为SNR＝3dB,编码长度N＝512，码率为R＝1/2条件下高斯信道中的第三种和第四种类型的巴哈塔切亚参数所对应的信道索引分布图。
图9是在信噪比为SNR＝3dB,编码长度N＝512，码率为R＝1/2条件下高斯信道中第五种类型的巴哈塔切亚参数所对应的信道索引分布图。
图10是链表接续消除译码算法的基本原理图。
图11是在编码长度N＝512，码率为R＝1/2条件下这五种类型的设计参数所构造的五种类型的极化码在BSC信道中的误码率以及误块率的对比图。
图12是在编码长度N＝512，码率为R＝1/2条件下这五种类型的设计参数所构造的五种类型的极化码在AGWN信道中的误码率及误块率的对比图。
图13是用类型五的参数构造的极化码与高斯近似估计方法构造的极化码在AGWN信道中误比特率的性能对比图。
图14是本发明所述利用巴哈塔切亚参数构造极化码的方法较佳实施例的流程图。
图15是本发明所述利用巴哈塔切亚参数构造极化码的系统较佳实施例的结构框图。
具体实施方式
本发明提供一种利用巴哈塔切亚参数构造极化码的方法及系统，为使本发明的目的、技术方案及效果更加清楚、明确，以下对本发明进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
如图14所示，为本发明利用巴哈塔切亚参数构造极化码的方法较佳实施例的流程图，所述方法包括以下步骤：
步骤S100、将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道。
本发明的实施例中，步骤S100具体包括以下步骤：
步骤S101、预先设编码长度为N，其中N为大于0的正整数；
步骤S102、将N位比特信息位虚拟为N个相互独立的信道；
步骤S103、将N个信道进行线性合并和拆分，得到N个相互关联的比特信道。
即，将预设编码长度为N，在这N个比特的信息被送到实际的物理信道之前，先将这N个信息位虚拟为N个独立的信道，然后对这N个信道进行线性合并和拆分运算，这样一来原先的N个独立的离散无记忆信道也就变成了N个相互关联的比特信道。根据香农信息论中的互信息的链式法则可以得知信道总的容量没有发生变化，而信道的总的截至频率会得到提升，因此通过这种拆分运算之后可以使得每个独立的比特信道的截止频率发生了变化。
步骤S200、将比特信道进行极化运算，得到奇数项信道的巴哈 塔切亚参数及偶数项信道的巴哈塔切亚参数。
根据步骤S100中的运算操作，可以分别得到奇数项信道的巴哈塔切亚参数和偶数项信道的巴哈塔切亚参数。偶数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000025
是一个很容易迭代计算的等式表达式，而奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000026
是一个具有上下限的一个不等式。这样就需要在原先的理论基础之上对奇数项信道的巴哈塔切亚参数对应的不等式进行了推导和演绎，然后得出在这个不等式范围内正确合理的巴哈塔切亚参数的等式表达式的集合。
步骤S300、根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式。
对于步骤S200中所得到的奇数项信道的巴哈塔切亚参数的集合，紧接着对其运用概率论中的方法。通过使用抽样的方法从集合中选出五种具有代表性的等式表达式来作为分析和估计信道的参数。
步骤S400、将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表。
步骤S500、根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。
在解码端运用SCL-CRC算法来进行解码。通过对比分析这5种类型的极化码(即与5类参数表达式分别对应的链表)所对应的误比特率(BER)以及误块率(FER)，然后再从中选出性能最好的一种来作为最终的编码构造参数，最后为了验证这种参数的性能，再将其 与高斯近似估计的方法来进行性能对比。
在本发明中引入了虚拟信道的概念，而且在编码构造过程中所提到的信道并不是现实当中的物理信道，这种信道是为了实现极化运算而虚拟出来的一种现实不存在的比特信道。步骤S100也提到了这个虚拟的过程，图4和图5中也有具体描述到在合并和拆分运算之前先将u1 u2 u3 u4 u5 u6 u7 u8这8个比特虚拟成为8个独立对称的信道W。当然虚拟之后的极化运算也是有规律可循的，在这里要特别说明的是信道的合并指的是对称信道(性能一样的信道)之间的合并，而不是随意无规律的将信道进行合并，这一要求在信道极化的过程中十分的重要。图4和图5是针对于8信道通过大量的实验所挑选出的两种正确的信道合并以及拆分的方式。图4和图5的合并规则也正是遵循对称信道之间才合并的原则，其中图4是按照自然顺序来进行信道合并的，所以最后拆分所得到的码字的索引顺序是1、5、3、7、2、6、4、8。而图5是在信道合并之前先进行比特反转运算，这样最后得到的码字的顺序就是自然顺序1、2、3、4、5、6、7、8。这两种方式的合并都是正确的，从上可以知道当编码的码字为自然顺序的时候，解码端的工作量要相对低很多，而极化码的性能也会因此而得到很大的提升，所以在极化码的编码过程中更倾向于图5当中所呈现的合并拆分方式来对信道进行极化运算。根据图5中所演示的信道极化过程，可以看到8个原先独立的信道W经过第一阶段stage1的合并拆分运算之后即可得到4对相关的信道W2 1和W2 2；而在第二阶段stage2的信道合并拆分运算是4个信道W2 1之间的运算以及另4个信道 W2 2之间的运算，在这个阶段的运算之后可以得到两对相关度更高的信道W4 1，W4 2，W4 3，W4 4。同样的原理，在第三阶段stage3中再次合并对称信道然后再对其进行拆分后即可得到最终的8个相关的信道W8 1、W8 2、W8 3、W8 4、W8 5、W8 6、W8 7、W8 8。信道的合并和拆分运算是要运算到最后没有任何的对称信道为止，所以8比特信道需要进行三次拆分合并运算，当拓展到N＝2n的比特信道时则需要n次运算。
上面详细分析和阐述了信道极化运算的过程，本发明的关键就在于能够准确的估计信道极化运算完成之后的巴哈塔切亚参数值以及信道容量的变化，然后准确的从中挑选出能够作为传送信息位所需要的比特信道。正如图5所呈现那样，给定8个初始比特信道的巴哈塔切亚参数(巴哈塔切亚参数)为Z(W0)，经过第一阶段stage1的极化运算之后得到4对对称的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000027
和
Figure PCTCN2017079968-appb-000028
然后在第二阶段Stage2运算后得到两对对称的巴哈塔切亚参数Z(W4 1)，Z(W4 2)，Z(W4 3)，Z(W4 4)，最后再经过第三阶段的运算之后最终得到8比特信道最终的巴哈塔切亚参数为Z(W8 1)，Z(W8 2)、Z(W8 3)、Z(W8 4)、Z(W8 5)、Z(W8 6)、Z(W8 7)、Z(W8 8)。经过推导演绎可以得出：
Z(W8 8)＝Z(W4 4)2，Z(W4 4)≤Z(W8 7)≤2Z(W4 4)-Z(W4 4)2
Z(W8 6)＝Z(W4 3)2，Z(W4 3)≤Z(W8 5)≤2Z(W4 3)-Z(W4 3)2
Z(W8 4)＝Z(W4 2)2，Z(W4 2)≤Z(W8 3)≤2Z(W4 2)-Z(W4 2)2
Z(W8 2)＝Z(W4 1)2，Z(W4 1)≤Z(W8 1)≤2Z(W4 1)-Z(W4 1)2
而将其推广到N比特信道的时候，极化运算之后每个比特信道的巴哈塔切亚参数的表达式可以迭代为
Figure PCTCN2017079968-appb-000029
Figure PCTCN2017079968-appb-000030
对于BEC信道(Binary Erasure Channel，即二进制擦除信道)、BSC信道(Binary Symmetric Channel，即二进制对称信道)、AWGN信道(Additive White Gaussian Noise，即高斯加性白噪声信道)而言，偶数项信道的巴哈塔切亚参数的值很容易通过迭代的等式计算得出，然而受限于当时的译码算法Arikan只能得出奇数项的巴哈塔切亚参数值只是在BEC信道下可以直接简化为
Figure PCTCN2017079968-appb-000031
而对于其他的信道没能很好的处理这个奇数项的巴哈塔切亚参数的不等式。
优选的，在所述利用巴哈塔切亚参数构造极化码的方法中，所述步骤S200中将N个相互关联的比特信道进行极化运算，得到偶数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000032
和奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000033
其中
Figure PCTCN2017079968-appb-000034
i为小于或等于N/2的正整数。
优选的，在所述利用巴哈塔切亚参数构造极化码的方法中，所述步骤S300中具体包括：
步骤S301、将奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000035
记为
Figure PCTCN2017079968-appb-000036
步骤S302、取m1＝0.1、n1＝0.9时，得到第一类参数表达式记为
Figure PCTCN2017079968-appb-000037
取m2＝0.3、n2＝0.7时，得到第二类参数表达式记为
Figure PCTCN2017079968-appb-000038
取m3＝0.5、n3＝0.5时，得到第三类参数表达式记为
Figure PCTCN2017079968-appb-000039
取m4＝0.7、n4＝0.3时，得 到第四类参数表达式记为
Figure PCTCN2017079968-appb-000040
取m5＝0.9、n5＝0.1时，得到第五类参数表达式记为
Figure PCTCN2017079968-appb-000041
优选的，在所述利用巴哈塔切亚参数构造极化码的方法中，所述步骤S500中根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，将5类参数表达式所对应的极化码分别在BSC信道以及高斯信道下的误比特率以及误块率，得到误比特率以及误块率最小的参数表达式作为编码构造参数。
根据上面的分析可知极化码编码构造最重要的环节就是在给定的N个比特信道中准确的挑选出信道容量极佳的前K个比特信道作为传送信息位来使用，而剩下的N-K个比特信道则是用来传送固定比特位(这些固定位可以取0或者1，其在发送端和接收端都是已知的)。极化码是一种信道专属编码，所以针对不同的信道运用合适的编码构造方法可以更加准确的选出性能极佳的信道，从而能够极大的提高极化码的性能。由于在构造极化码的过程中，巴哈塔切亚参数是衡量信道可靠性的最重要的指标之一，所以在比特信道挑选的过程中步骤S200和步骤S300是两个十分关键的步骤。
在步骤S200和步骤S300中，我们给定每个比特信道的初始巴哈塔切亚参数为Z(W0)。从而对于编码长度为N的比特信道在经过极化运算之后直接就可以得到偶数项信道的巴哈塔切亚参数的等式表示为
Figure PCTCN2017079968-appb-000042
而奇数项信道的巴哈塔切亚参数的表达式为
Figure PCTCN2017079968-appb-000043
在经过极化运算之后，所有偶 数项信道的巴哈塔切亚参数可以由上面的等式表达式来通过迭代运算来得到，而奇数项信道的巴哈塔切亚参数的计算则要经过数学运算的处理，要想准确的选出所需要的信道索引，准确的计算出奇数项信道的巴哈塔切亚参数也是必不可少的。
本发明也重点对奇数项信道的巴哈塔切亚参数的计算进行了如下处理：根据上述不等式可以很容易得出
Figure PCTCN2017079968-appb-000044
是
Figure PCTCN2017079968-appb-000045
的下限，
Figure PCTCN2017079968-appb-000046
是
Figure PCTCN2017079968-appb-000047
的上限，再将奇数项信道的巴哈塔切亚参数所对应的不等式进行演绎推导运算之后得出了两个参数m和n，并且m和n为非负数，其中0≤m≤1,0≤n≤1。通过运用参数m和n，可以使得等式
Figure PCTCN2017079968-appb-000048
在上述奇数项信道的巴哈塔切亚参数的不等式的范围内是绝对成立的。这个等式表达式的得出对于计算极化之后的奇数项信道的巴哈塔切亚参数尤为关键，可以更加方便分析和研究巴哈塔切亚参数对于极化码构造的影响。而且从这个表达式中可以很容易得出一个结论：
Figure PCTCN2017079968-appb-000049
的取值必然是一个集合。为了方便分析和研究，对于这个集合进行了简化处理。结合概率论中的抽样原理再将这个集合划分为五个范围，然后从这五个范围当中抽取五种具有代表性的等式表达式来进行了针对性的研究与分析。较佳的，对m和n选取了五对具有代表性的值，即(0.1,0.9)，(0.3,0.7)，(0.5，0.5)，(0.7,0.3)，(1,0)，当然此处是为了方便分析。在经过大量的仿真试验之后，只选取了其中的五种具有代表性的值，通过这五组值可以计算得出五种典型的
Figure PCTCN2017079968-appb-000050
参数表达式，这五种类型的等式表达式依次为：
类型一：
Figure PCTCN2017079968-appb-000051
类型二：
Figure PCTCN2017079968-appb-000052
类型三：
Figure PCTCN2017079968-appb-000053
类型四：
Figure PCTCN2017079968-appb-000054
类型五：
Figure PCTCN2017079968-appb-000055
由于偶数项信道的巴哈塔切亚参数是直接就能够得出来的，所以接下来只需要综合奇数项信道的巴哈塔切亚参数和偶数项信道的巴哈塔切亚参数的等式表达式，然后就能够很容易计算出每个比特信道在进行极化运算之后的巴哈塔切亚参数值。得到每个信道的巴哈塔切亚参数值之后，再将这N个值按从小到大的顺序进行排序(或者从大到小排序)，最后再选取其中的前K个值作为传送信息位所用到的信道索引值。
在本发明中，选择了BSC信道以及AWGN信道作为实验信道，对于BSC信道和AWGN信道，两者的信道索引分布图在规律上基本是相似的，所以在具体呈现信道索引分布图的规律上选择了更具代表性的AGWN信道来进行分析和研究，在本发明中图7-图9依次是类型一，类型二，类型三，类型四，类型五这五种参数，在编码长度为512，信噪比为3dB,以及码率为0.5的条件下所产生的信道索引分布图。图7-图9这三副图中的横坐标都是表示比特信道的索引值(即bit channel index(i)表示比特信道的索引值)，纵坐标都是表示比特信道的巴哈塔切亚参数值(也可以称之为信道的极化速率，即Z(i))，当然从这三幅索引分布图中可以得出一些规律，即从类型五一直到类 型一，信道的巴哈塔切亚参数越来越集中到底部，通常在这种情况可能会认为这是一种好的趋势。因为上面分析到在极化运算之后希望更多的信道的巴哈塔切亚参数的值趋向于0，但是在这里要注意一点，信道极化最理想状况是均匀的向两级分化，而不是单纯往某一个方向极化，因为不均匀的极化会导致信道的极化速率过快，导致过多的信道趋向于好信道，这样会造成有很多性能差的信道也混入到了好信道的行列。从而导致在选择信息位的时候必须在好的信道中再挑选出更好的信道，这种操作是相当有难度的，而且会使得对信道的性能估计产生巨大的误差，甚至会误选出很多本身性能较差的信道。当信道的极化呈现均匀的两级分化时，对于信道的估计才是最准确的，因此在这里可以初步得出用类型五的参数构造的极化码是这五种类型参数中性能最佳的一种。
在之前已经分析得出了一些结论，这些巴哈塔切亚参数的取值越小比特信道的性能也就越可靠，所以针对于这五种类型的参数所产生的信道索引应当选择其中前K个信道的索引值，然后用这K个索引值所对应的信道来传送信息位(完整的信息序列包含信息位和固定位)，然后就可以进行极化码的编码了。
极化码也是一种线性分组码，与其他的信道编码技术类似的是极化码的生成码字也是通过信息位与生成矩阵相乘，而与其他的线性分组码明显的差别就在于极化码在选取传送信息位(极化码的编码构造过程)的过程中进行了特殊的处理，也正是这样的处理可以使得信道容量得到极大的提高甚至接近于香农极限容量，当编码长度N达到 无限长时，信道的对称容量几乎就是等于香农极限容量。极化码的编码过程也比较简单，为了能够形象的说明极化码的编码过程，在这里给定二进制输入码字为：
Figure PCTCN2017079968-appb-000056
那么其输出码字
Figure PCTCN2017079968-appb-000057
这里的生成矩阵
Figure PCTCN2017079968-appb-000058
BN是一个比特序列反转的运算矩阵，即比特翻转运算，这个在图4和图5中得到了具体的呈现。矩阵
Figure PCTCN2017079968-appb-000059
Figure PCTCN2017079968-appb-000060
表示不同维数矩阵之间的Kronecker积。对于一个具体的极化码，可以表示为一个参数向量(N,K,f,uf)，其中N表示编码码长，K是信息位的个数，f是固定位的信道索引，其是(1,2...N)的一个子集，而f的补集可以表示为fc，uf则表示为固定位向量，K/N称为编码的码率，
Figure PCTCN2017079968-appb-000061
的准确选择也正是运用编码构造方法的结果。因此上述输出码字可以变换为：
Figure PCTCN2017079968-appb-000062
为了使得极化码编码的过程更加的形象具体，在这里给定了一个参数向量(8,4,{1,3,5,6},(1,0,1,0))，则可得到对应的编码为：
Figure PCTCN2017079968-appb-000063
上述编码过程所对应的编码演示图正如图6所示。给定一个源码块(u2,u4,u7,u8)＝(1,1,0,1)，即可得到编码后的码字为
Figure PCTCN2017079968-appb-000064
当然在这里仅仅只是对编码长度为8的编码过程进行了具体的演示， 用相似的方法可以将其拓展到长度为N的编码情景。得到编码的码字之后，接下来的任务就是将这个生成码字由物理信道传送到通信接收端，考虑到传送过程中的噪声，在通信接收端我们得到的信号可以表示为y＝(1-2x)+n，其中x为编码后的码字，n为高斯白噪声。
在本发明中运用了现今最成熟的译码技术即循环冗余辅助链表接续消除译码算法(CRC-SCL)来协助编码构造，这种译码算法是在SCL(链表接续消除译码算法)译码算法的基础之上再在信息位中加入了一定位数的循环冗余校验位，而SCL算法是在SC(接续消除译码算法)算法的基础之上通过拓展译码序列的路径来提升极化码的性能。在CRC-SCL算法的基础上再引入循环冗余校验位既可以大大的就提高极化码的性能，同时还可以消除SCL算法中由于拓展路径而所引起的计算复杂度高的问题。在这里就以SCL译码算法的树图来进行说明，依照图10中这种译码算法的大致原理可以使用一棵二叉树来进行分析和描述，在本发明中使用的是改进版的SCL译码算法，即CRC-SCL算法，在信息码字中加入了24位的循环冗余位，只有通过了这个循环冗余校验的路径才作为译码备选序列，这样可以消除之前以为路径拓展带来的影响，同时还提高了极化码的性能。通过实验之后，得到了上述五种参数所对应的五种极化码分别在BSC信道以及高斯信道下的误码率(误码率即误比特率)以及误块率等性能图，依次为图11-图13，其中图11-图13中，mold 1-mold 5分别代表类型一至类型五，图11的横坐标Error probability of BSC channel表示BCS信道的误差概率，图12的横坐标表示信噪比(即SNR)，图12中左侧图 片纵坐标表示误比特率(即Bit Error Rate)，图12中右侧图片纵坐标表示误块率(即Block Error Rate)，图13的横坐标表示信噪比(即SNR)，图13的纵坐标表示误比特率(即Bit Error Rate，简记为BER)。通过性能比较之后，可以发现利用类型五的参数然后再结合CRC-SCL算法所设计的极化的性能跟高斯近似估计方法所构造的极化码的性能几乎是接近的，而且其不存在高斯近似估计方法所面临的极化速率低以及因为错误传播而导致极化码性能大大降低的问题，同时其计算复杂度可以保持在最低的状态，所以这种构造的方法用于BEC信道、BSC信道、AWGN信道还是比较理想的。
基于上述方法实施例，本发明还提供一种利用巴哈塔切亚参数构造极化码的系统。如图15所示，所述利用巴哈塔切亚参数构造极化码的系统包括：
线性处理模块100，用于将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道；
极化运算模块200，用于将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；
抽样模块300，用于根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；
极化码构造模块400，用于将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；
解码及获取模块500，用于根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表 达式作为编码构造参数。
优选的，在所述利用巴哈塔切亚参数构造极化码的系统中，所述线性处理模块100具体包括：
编码长度预设单元，用于预先设编码长度为N，其中N为大于0的正整数；
虚拟化单元，用于将N位比特信息位虚拟为N个相互独立的信道；
关联单元，用于将N个信道进行线性合并和拆分，得到N个相互关联的比特信道。
优选的，在所述利用巴哈塔切亚参数构造极化码的系统中，所述极化运算模块200中将N个相互关联的比特信道进行极化运算，得到偶数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000065
和奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000066
其中
Figure PCTCN2017079968-appb-000067
Figure PCTCN2017079968-appb-000068
i为小于或等于N/2的正整数。
优选的，在所述利用巴哈塔切亚参数构造极化码的系统中，所述抽样模块300具体包括：
推导单元，用于将奇数项信道的巴哈塔切亚参数
Figure PCTCN2017079968-appb-000069
记为
Figure PCTCN2017079968-appb-000070
计算单元，用于取m1＝0.1、n1＝0.9时，得到第一类参数表达式记为
Figure PCTCN2017079968-appb-000071
取m2＝0.3、n2＝0.7时，得到第二类参数表达式记为
Figure PCTCN2017079968-appb-000072
取m3＝0.5、n3＝0.5时，得到第三类参数表达式记为 取m4＝0.7、n4＝0.3时，得到第四类参数表达式记为
Figure PCTCN2017079968-appb-000074
取m5＝0.9、n5＝0.1时，得到第五类参数表达式记为
Figure PCTCN2017079968-appb-000075
优选的，在所述利用巴哈塔切亚参数构造极化码的系统中，所述解码及获取模块500根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，将5类参数表达式所对应的极化码分别在BSC信道以及高斯信道下的误比特率以及误块率，得到误比特率以及误块率最小的参数表达式作为编码构造参数。
综上所述，本发明所提供的利用巴哈塔切亚参数构造极化码的方法及系统，方法包括：将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道；将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。本发明实现了极低的误比特率以及误块率，同时还具有最低的计算复杂度。
应当理解的是，本发明的应用不限于上述的举例，对本领域普通技术人员来说，可以根据上述说明加以改进或变换，所有这些改进和变换都应属于本发明所附权利要求的保护范围。

Claims (10)

  1. 一种利用巴哈塔切亚参数构造极化码的方法，其特征在于，所述方法包括以下步骤：
    A、将预设编码长度的比特信息进行线性合并和拆分，得到相互关联的比特信道；
    B、将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；
    C、根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；
    D、将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；
    E、根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。
  2. 根据权利要求1所述利用巴哈塔切亚参数构造极化码的方法，其特征在于，所述步骤A具体包括：
    A1、预先设编码长度为N，其中N为大于0的正整数；
    A2、将N位比特信息位虚拟为N个相互独立的信道；
    A3、将N个信道进行线性合并和拆分，得到N个相互关联的比特信道。
  3. 根据权利要求2所述利用巴哈塔切亚参数构造极化码的方法，其特征在于，所述步骤B中将N个相互关联的比特信道进行极化运算，得到偶数项信道的巴哈塔切亚参数
    Figure PCTCN2017079968-appb-100001
    和奇数项信道的巴哈塔 切亚参数
    Figure PCTCN2017079968-appb-100002
    其中
    Figure PCTCN2017079968-appb-100003
    Figure PCTCN2017079968-appb-100004
    i为小于或等于N/2的正整数。
  4. 根据权利要求3所述利用巴哈塔切亚参数构造极化码的方法，其特征在于，所述步骤C中具体包括：
    C1、将奇数项信道的巴哈塔切亚参数
    Figure PCTCN2017079968-appb-100005
    记为
    Figure PCTCN2017079968-appb-100006
    C2、取m1＝0.1、n1＝0.9时，得到第一类参数表达式记为
    Figure PCTCN2017079968-appb-100007
    取m2＝0.3、n2＝0.7时，得到第二类参数表达式记为
    Figure PCTCN2017079968-appb-100008
    取m3＝0.5、n3＝0.5时，得到第三类参数表达式记为
    Figure PCTCN2017079968-appb-100009
    取m4＝0.7、n4＝0.3时，得到第四类参数表达式记为
    Figure PCTCN2017079968-appb-100010
    取m5＝0.9、n5＝0.1时，得到第五类参数表达式记为
    Figure PCTCN2017079968-appb-100011
  5. 根据权利要求4所述利用巴哈塔切亚参数构造极化码的方法，其特征在于，所述步骤E中根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，将5类参数表达式所对应的极化码分别在BSC信道以及高斯信道下的误比特率以及误块率，得到误比特率以及误块率最小的参数表达式作为编码构造参数。
  6. 一种利用巴哈塔切亚参数构造极化码的系统，其特征在于，包括：
    线性处理模块，用于将预设编码长度的比特信息进行线性合并和 拆分，得到相互关联的比特信道；
    极化运算模块，用于将比特信道进行极化运算，得到奇数项信道的巴哈塔切亚参数及偶数项信道的巴哈塔切亚参数；
    抽样模块，用于根据奇数项信道的巴哈塔切亚参数对应的集合抽样提取5类参数表达式；
    极化码构造模块，用于将5类参数表达式进行极化码构造，得到与5类参数表达式分别对应的链表；
    解码及获取模块，用于根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，获取误比特率及误块率最低的参数表达式作为编码构造参数。
  7. 根据权利要求6所述利用巴哈塔切亚参数构造极化码的系统，其特征在于，所述线性处理模块具体包括：
    编码长度预设单元，用于预先设编码长度为N，其中N为大于0的正整数；
    虚拟化单元，用于将N位比特信息位虚拟为N个相互独立的信道；
    关联单元，用于将N个信道进行线性合并和拆分，得到N个相互关联的比特信道。
  8. 根据权利要求7所述利用巴哈塔切亚参数构造极化码的系统，其特征在于，所述极化运算模块中将N个相互关联的比特信道进行极化运算，得到偶数项信道的巴哈塔切亚参数
    Figure PCTCN2017079968-appb-100012
    和奇数项信道的巴哈塔切亚参数
    Figure PCTCN2017079968-appb-100013
    其中
    Figure PCTCN2017079968-appb-100014
    Figure PCTCN2017079968-appb-100015
    i为小于或等于N/2的正整数。
  9. 根据权利要求8所述利用巴哈塔切亚参数构造极化码的系统，其特征在于，所述抽样模块具体包括：
    推导单元，用于将奇数项信道的巴哈塔切亚参数
    Figure PCTCN2017079968-appb-100016
    记为
    Figure PCTCN2017079968-appb-100017
    计算单元，用于取m1＝0.1、n1＝0.9时，得到第一类参数表达式记为
    Figure PCTCN2017079968-appb-100018
    取m2＝0.3、n2＝0.7时，得到第二类参数表达式记为
    Figure PCTCN2017079968-appb-100019
    取m3＝0.5、n3＝0.5时，得到第三类参数表达式记为
    Figure PCTCN2017079968-appb-100020
    取m4＝0.7、n4＝0.3时，得到第四类参数表达式记为
    Figure PCTCN2017079968-appb-100021
    取m5＝0.9、n5＝0.1时，得到第五类参数表达式记为
    Figure PCTCN2017079968-appb-100022
  10. 根据权利要求9所述利用巴哈塔切亚参数构造极化码的系统，其特征在于，所述解码及获取模块根据SCL-CRC算法对与5类参数表达式分别对应的链表进行解码，将5类参数表达式所对应的极化码分别在BSC信道以及高斯信道下的误比特率以及误块率，得到误比特率以及误块率最小的参数表达式作为编码构造参数。
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