CN110061747A - A kind of bit reversal interpretation method based on threshold value of polarization code - Google Patents

A kind of bit reversal interpretation method based on threshold value of polarization code Download PDF

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Publication number
CN110061747A
CN110061747A CN201910350491.5A CN201910350491A CN110061747A CN 110061747 A CN110061747 A CN 110061747A CN 201910350491 A CN201910350491 A CN 201910350491A CN 110061747 A CN110061747 A CN 110061747A
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threshold value
bit
polarization code
value
candidate
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CN201910350491.5A
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李世宝
邓云强
高迅
董振威
刘建航
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China University of Petroleum East China
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China University of Petroleum East China
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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
    • H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
    • 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
    • H03M13/11—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 using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105—Decoding
    • H03M13/1108—Hard decision decoding, e.g. bit flipping, modified or weighted bit flipping

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  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Error Detection And Correction (AREA)

Abstract

The invention proposes a kind of bit reversal interpretation methods based on threshold value of polarization code, when the CRC check failure of SC algorithm decoding result, are made decisions using pre-designed threshold value to the likelihood value in crucial collection, to filter out candidate inverted bit.Based on candidate inverted bit set, successively inverts candidate bit and re-start SC decoding from current, be empty until CRC check passes through or invert set remaining bits.The present invention makes full use of offline channel information, using Gaussian approximation theoretical calculation basic threshold, then uses monte carlo method Optimal Parameters k, can effectively promote the error-correcting performance of polarization code while reducing complexity.

Description

A kind of bit reversal interpretation method based on threshold value of polarization code
Technical field
The invention belongs to fields of communication technology, and in particular to the successive elimination decoding in a kind of polarization code based on bit reversal The innovatory algorithm of algorithm.
Background technique
Polarization code (Polar Codes) is discussed in international information in 2008 by Turkey scientist and is put forward for the first time in conference, because It theoretically proves to reach the channel capacity of binary system Discrete Symmetry channel and be concerned.2015, in 3GPP meeting Polarization code is set to the encoding scheme of control channel under the 5th third-generation mobile communication eMBB scene in view.
Polarization code puts forward derived from channel-polarization phenomenon, after carrying out polarization conversion to N number of channel, a part of polaron The channel capacity of channel tends to 1, and the channel capacity of another part polarization subchannel tends to 0.Therefore, can tend in channel capacity Transmission information bit in 1 subchannel, corresponding position are known as non-freezing position；It is transmitted in the subchannel that channel capacity tends to 0 Fixed bit (generally zero), corresponding position is known as freezing position.
The basic decoding algorithm of polarization code is successive elimination (Successive Cancellation-SC) decoding algorithm.But It is that the algorithm is when middle short code is long with poor error code correction performance.In order to further increase polarization code under SC algorithm Error code correction performance, the SC decoding algorithm (SC-Flip) based on bit reversal are suggested.
First error bit when the basic thought of SC-Flip algorithm is by reversion SC decoding failure misses frame to improve Rate (Frame Error Rate-FER).CRC check bit is added in coding side, when the CRC check failure of SC decoding result, SC-Flip algorithm generates the set of candidate inverted bit, and carries out SC from the bit again according to each candidate inverted bit Decoding.After the completion of CRC check passes through or candidate inverted bit is all attempted, after SC-Flip algorithm exits and exports update SC decode result.
The ascending selection of the absolute value of the corresponding likelihood value in non-freezing position is waited during SC-Flip algorithm is decoded according to SC Inverted bit is selected, therefore SC-Flip algorithm needs to be ranked up likelihood value and selection operation, the calculating that this will increase algorithm is multiple Miscellaneous degree.Additionally, there are likelihood value very little but corresponding first bit error probability also very little the case where, this causes according to seemingly Right value size sequencing selection candidate's inverted bit has error.In view of the above problems, the invention proposes a kind of polarization code based on The bit reversal interpretation method of threshold value.
Summary of the invention
The invention proposes a kind of bit reversal (T-SC-Flip) interpretation method based on threshold value of polarization code, the algorithms The error code correction performance of polarization code can be effectively improved while reducing polarization code decoding complexity.
T-SC-Flip algorithm only considers the non-freezing position bit in crucial collection, and the calculating of key collection uses Oracle- The characteristics of assisted SC decoder, the decoder is the information that can obtain transmitting terminal transmission in advance, and the calculating of key collection is suitable With following steps:
Step 1, it is 1,000,000 times that setting, which emulates maximum frame number, and encoder generates K information bit and C CRC check every time Bit is sent into Gaussian channel after encoded；
Step 2, Oracle-assisted SC decoder receives information and carries out SC decoding, if current code word only has One error bit, then record the position of the error bit；
Step 3, statistics non-freezing position occur first error bit frequency: set occur an error bit frame number as E, i-th of non-freezing position are that the frame number of first error bit is Ei, then corresponding first error bit occurs probability fiIt can To be approximately fi=Ei/E；
Step 4, to non-freezing position position according to fiDescending sequence, the bit of s position collects as crucial before taking, and S meets
T-SC-Flip algorithm is sieved by being judged within crucial collect using reliability of the threshold value to decoding bit Candidate inverted bit is selected, the calculating of threshold value is theoretical by Gaussian approximation and optimizes using the method for Monte Carlo.
The calculating of threshold value is applicable in following steps in T-SC-Flip algorithm:
Step 1, if the noise variance of Gaussian channel is σ2, channel output information is yi, i=1,2 ... N are sent out in encoder In the case where sending code word to be all zero, initial likelihood value
Step 2, the corresponding likelihood value mean value of N number of polarization subchannel is calculated according to Gaussian approximation iterative formula
Step 3, according to formulaCalculate the error probability p of every sub-channelsi, i=1,2 ... N；
Step 4, if pi' for practical decoding when error probability, piFor the error probability estimated by Gaussian approximation, in order to Guarantee is correctly decoded with biggish probability as a result, then needing to meet pi′<pi, according to the available likelihood of the definition of likelihood value Value should be greater than log (1-pi/pi), therefore basic threshold T can be seti=log (1-pi/pi) screen error bit；
Step 5, the threshold value T of final optimization pass is calculatedi'=klog (1-pi/pi), k is optimized by monte carlo method.
According to crucial collection and the threshold value calculated, T-SC-Flip algorithm is applicable in following steps:
Step 1, decoder is according to reception informationGather with non-freezing positionSC decoding is carried out, Obtain decoding result
Step 2, to decoding resultCRC check is carried out, exports decoding result if if verifyingOtherwise enter step Rapid 3；
Step 3, it initializes candidate inverted bit set: it is corresponding seemingly according to ascending sequence to set critical bit position So value is α={ α1,α2,…,αs, corresponding serial number index={ c in the codeword1,c2,…,csAnd c1<c2<,…,< cs, then candidate inverted bit collection is combined into Flip_set={ ci|αi<Ti′,Ti'=klog (1-pi/pi)}；
Step 4, according to candidate inverted bit set correct first error bit: set the size of Flip_set as Tmax, successively inversed F lip_set [t], t ∈ { 1,2 ..., Tmax }, then continue SC decoding from current location, and tie to decoding Fruit carries out CRC check；
Step 5, when CRC check passes through or reaches maximum reversion number Tmax, decoding terminates.
Subchannel error probability p is estimated by Gaussian approximation in the calculating step 4 of threshold value in T-SC-Flip algorithmi, the mistake Accidentally probability is error probability on an average, it can be used as a restrictive condition come when limiting practical successfully decoded Probability (real-time conditional probability), i.e., practical successfully decoded conditional probability 1-pi' successful the condition less less than estimation is general Rate 1-pi, i.e. 1-pi′≥1-pi, so there is pi′<pi, further according to the definition of likelihood value it can be concluded that likelihood value should be greater than log (1-pi/pi), therefore, likelihood value is less than log (1-pi/pi) corresponding bit is insecure when can consider.
It is because Gaussian approximation has error, together that the calculating step 5 of threshold value, which optimizes likelihood value, in T-SC-Flip algorithm When also for the range for further reducing candidate inverted bit, should compared to directly monte carlo method being used to search threshold value Method can quickly locate threshold value.
Beneficial effect
The present invention, which compares prior art, has following innovative point:
This method calculates threshold value by Gaussian approximation theory and monte carlo method, makes full use of channel information, Ke Yitong It crosses off-line calculation and carrys out given threshold, advantage is had more in the scenes such as edge calculations.
This method makes decisions the corresponding likelihood value in non-freezing position using threshold value, according to code word serial number from small to being sentenced It is disconnected, when current likelihood value is less than the threshold value of setting, then candidate inverted bit set is added in the bit and inverted, effectively kept away Exempt from sequence and selection operation, improves reversion with regard to wrong performance.
Detailed description of the invention
Fig. 1 is that subchannel error probability calculates schematic diagram.
Fig. 2 is that T-SC-Flip decodes flow diagram.
Specific embodiment
Below in conjunction with Figure of description and embodiment, the present invention will be further described.
Illustrate the calculating process of threshold value first, if polarization code code length N=8, according to Gaussian approximation theory, then 8 polarons The error probability calculating process of channel is as shown in Figure 1.InputWherein σ2For noise variance, then And so on, it can calculate Then final error probability isThis is arrived, basic threshold Ti= log(1-pi/pi), i=1,2 ..., 8.Finally, taking k=1, FER is emulated with 0.1 interval scan, finds out optimal klog (1-pi/ pi)。
T-SC-Flip decoding is as shown in Figure 2: the crucial collection Crtical and threshold value Threshold of initialization first, then root Information is received according to decoderWith non-freezing position positionSC decoding is carried out, decoding result isIt is rightCRC check is carried out, such as Fruit verification passes through, then directly exportsOtherwise by using threshold value (Threshold) to the likelihood in crucial collection (Critical) Value (α) makes decisions to obtain candidate inverted bit set (Flip_set)；If Flip_set is not sky, Flip_ is taken out Set [t] a bit is inverted, and from this continue SC decoding, until CRC check pass through or Flip_set in ratio to be reversed Specially for sky, finally export
The above description is merely a specific embodiment, but the scope of protection of the present invention is not limited thereto, any ripe Those skilled in the art are known in technical scope proposed by the present invention, the variation or replacement that can be readily occurred in all are answered This is included within the scope of the present invention.

Claims (3)

1. a kind of bit reversal interpretation method based on threshold value of polarization code, which is characterized in that generating candidate inverted bit In the process, the likelihood value in crucial collection is screened using threshold value from small to large according to code word serial number, the threshold value is close by Gauss It is seemingly calculated, and is optimized by Monte Carlo method, when the absolute value of likelihood value is less than threshold value, then by the bit mark It is denoted as candidate inverted bit, when SC decoding result CRC check failure, then candidate inverted bit is successively inverted, until CRC check By or candidate inverted bit collection be combined into sky.
2. a kind of bit reversal interpretation method based on threshold value of polarization code according to claim 1, which is characterized in that use Pass through formula T in the threshold value of screeningi'=klog (1-pi/pi) calculate, wherein piIt is the error probability of i-th of polarization subchannel, It is calculated by Gaussian approximation.
3. a kind of bit reversal interpretation method based on threshold value of polarization code according to claim 1, which is characterized in that right In threshold value Ti'=klog (1-pi/pi) in k value optimization use monte carlo method, simulation times be 500,000.
CN201910350491.5A 2019-04-28 2019-04-28 A kind of bit reversal interpretation method based on threshold value of polarization code Pending CN110061747A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111082813A (en) * 2019-11-29 2020-04-28 中国地质大学（武汉） Multi-threshold-based Polar code SC-FLIP decoding method, equipment and storage equipment
CN113472361A (en) * 2021-05-25 2021-10-01 中国科学院微电子研究所 Method and system for acquiring polarization code

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CN107612560A (en) * 2017-09-14 2018-01-19 山东科技大学 Polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio
CN108494527A (en) * 2018-03-20 2018-09-04 清华大学 A kind of data transmission and reception method based on LoRa
CN109257148A (en) * 2018-11-26 2019-01-22 北京理工大学 A kind of polarization code BP interpretation method based on Gaussian approximation threshold decision
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CN106803759A (en) * 2016-12-27 2017-06-06 南京邮电大学 Polar yards of effective adaptive decoding method based on Gauss construction
CN107612560A (en) * 2017-09-14 2018-01-19 山东科技大学 Polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio
CN108494527A (en) * 2018-03-20 2018-09-04 清华大学 A kind of data transmission and reception method based on LoRa
CN109286405A (en) * 2018-09-10 2019-01-29 山东科技大学 A kind of progressive bit reversal SC interpretation method of the polarization code of low complex degree
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Publication number Priority date Publication date Assignee Title
CN111082813A (en) * 2019-11-29 2020-04-28 中国地质大学（武汉） Multi-threshold-based Polar code SC-FLIP decoding method, equipment and storage equipment
CN111082813B (en) * 2019-11-29 2021-07-27 中国地质大学（武汉） Multi-threshold-based Polar code SC-FLIP decoding method, equipment and storage equipment
CN113472361A (en) * 2021-05-25 2021-10-01 中国科学院微电子研究所 Method and system for acquiring polarization code

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Application publication date: 20190726