CN108768411A - Polarization code low complex degree segment decoder design based on SCL - Google Patents

Polarization code low complex degree segment decoder design based on SCL Download PDF

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Publication number
CN108768411A
CN108768411A CN201810744371.9A CN201810744371A CN108768411A CN 108768411 A CN108768411 A CN 108768411A CN 201810744371 A CN201810744371 A CN 201810744371A CN 108768411 A CN108768411 A CN 108768411A
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scl
decoding
error
decodings
waypoint
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王秀敏
吴卓铤
汪晓锋
李君�
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China Jiliang University
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China Jiliang University
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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
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0052—Realisations of complexity reduction techniques, e.g. pipelining or use of look-up tables
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0061—Error detection codes

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Theoretical Computer Science (AREA)
  • Error Detection And Correction (AREA)

Abstract

The invention discloses a kind of polarization code low complex degree segment decoder design scheme based on SCL.The shortcomings that SC decoding algorithms are simple in structure but there are error propagations, and the improvement that SCL is decoded as SC, solve the disadvantage that error propagation, but it considerably increases the complexity of decoder well.Whether the present invention combines the advantages of two kinds of decoding algorithms, and SC decoding algorithms are selected first in decoding, correct by CRC check decoding, according to the distribution situation of mistake if decoding error, suitable breakpoint is selected to carry out SCL decodings.The design of encoder is while ensureing that bit error rate performance approaches SCL again so that the complexity of the decoder is significantly less than SCL decoders.

Description

Polarization code low complex degree segment decoder design based on SCL
Technical field
The invention belongs to channel decoding field more particularly to a kind of polarization code low complex degree segment decoders based on SCL Design method.
Background technology
Polarization code was put forward for the first time by E.Arikan in 2007.Polarization code coding/decoding takes full advantage of channel-polarization phenomenon, After channel-polarization, user information is stored in the preferable information bit of channel capacity.Theoretical proof, when code length endless When, for channel capacity by perfact polarization, polarization code at this time can reach shannon limit.And due to polarization code compared to LDPC and Turbo code has lower complexity, this makes polarization code become an emerging research heat in channel error correction encoding field Point, and become the short code communication plan of 5G standards.
Currently, the polarization code decoding algorithm of mainstream has SC decoding algorithms, BP decoding algorithms and SCL decoding algorithms.SC is translated Code algorithm is proposed that the decoding algorithm is the inverse process of polarization code coding by E.Arikan.SC decodings have lower complexity, but Relevance before and after information sequence after being encoded due to polarization code between information bit is stronger, this makes SC decodings have serious mistake Code propagation characteristic.SCL can effectively solve the problem that the error propagation characteristic of SC decodings.SCL is decoded during decoding, retains L kinds Possibility is decoded, and calculates the confidence level (PM values) of this L kind decoding possibility.Confidence level is chosen when final output decodes Highest path is as output.Although the error propagation characteristic of SCL effective solutions SC decodings, it considerably increases system Calculation amount, reduce decoding speed.The present invention will propose a kind of point based on SCL on the basis of SC is decoded and decoded with SCL The low complex degree that SC is decoded is combined by section interpretation method, this method with the good error performances of SCL so that new decoding utensil There are low complex degree, high performance feature.
The technical solution used in the present invention is as follows：
(1) dual CRC codings.In polarization code cataloged procedure, a suitable breakpoint is taken to carry out CRC volumes at breakpoint Code, and it is reassembled into new information sequence, carry out a CRC coding again to this information sequence.24 CRC check error probabilities It is 1/224, and the bit error rate performance of polarization code about 1 × 10-5Left and right, therefore 24 CRC do not interfere with the error code of polarization code substantially Rate performance.
(2) SC and SCL segmented decodings.During decoding, first to information sequence carry out SC decodings and with CRC check its The correctness of decoding.The CRC check at breakpoint is enabled if decoding error, and the physical segment of information sequence is in the error code that misdeems It falls.If after error bit is distributed in waypoint, retaining the decoding before waypoint as a result, and being carried out to the information sequence after waypoint SCL is decoded.If before error bit is distributed in waypoint, a SCL decodings, finally output decoding knot are carried out to entire information sequence Fruit.The improved decoding algorithm is ensureing that performance is unabated, reduces the complexity integrally decoded.The innovatory algorithm It is as shown in Figure 1 with the bit error rate of SCL and the performance comparison analogous diagram of frame error rate.
(3) complexity is estimated.If the complexity of the polarization code segment decoder based on SCL is θ (NL1), the complexity of SC decodings Degree is θ (NA), the complexity of SCL decodings is θ (NAL).If under different signal-to-noise ratio, the frame error rate of SC decodings is P1, segmentation scales are t.P is the percent of pass of waypoint CRC, then the complexity of the segmentation algorithm is represented by formula (1).
θ(NL1)=(1-P1)θ(NA)+P1[tPθ(NAL)+(1-P)θ(NAL)] (1)
Wherein, tP θ (NAL)+(1-P)θ(NAL) can abbreviation be (1-tP) θ (NAL)。
The complexity of SC and SCL decodings can be separately disassembled into formula (2) and formula (3).
θ(NA)=(1-P1)θ(NA)+P1θ(NA) (2)
θ(NAL)=(1-P1)θ(NAL)+P1θ(NAL) (3)
It is analyzed and be can be calculated by formula (1), (2) and (3), the complexity of segmented decodings algorithm is significantly less than the complexity of SCL Degree, but the complexity more than SC, θ (NL1) and θ (NA) gap determined by P and t.When Pt is smaller, the complexity of the segmentation algorithm Degree more approaches the complexity of SC decoding algorithms.
(4) error probability distribution is calculated, determines best waypoint.The distribution of P and t can be determined by Monte Carlo Experiment Situation.The experimental design mainly designs a statistics SC decoding algorithm and is 1024 in code length, when code check is 1/2, different noises Than the Monte Carlo Experiment of lower error bit distribution situation, whether preceding 512 (t=1/2) deposit in 1000 erroneous frames of the experiment pair It is counted in error message, as shown in table 1.
1 incorrect bit distribution probability of table counts
In table 1, CRC table shows that preceding 512 numbers by CRC check, P are percent of pass in 1000 erroneous frames.It is special by covering Carlow experimental result is it is found that when code check is 1/2, and when code length is 1024, the incorrect bit under different signal-to-noise ratio is not present in information sequence The probability of the first half of row is about 0.4~0.56, and signal-to-noise ratio is higher, which shows gradual increased trend.By Many experiments, when t takes 1/2 under this code length code check, P is close to 1/2, and the value of Pt is minimum at this time.
Description of the drawings
Fig. 1 performance comparison analogous diagrams
Fig. 2 algorithm flow charts
Specific implementation mode
It is 1024 to use code length below, and the segment decoder that code check is 1/2 combines Fig. 1 to carry out the present invention as example The modulation system of detailed description, the decoder is modulated for BPSK, channel WAGN, specific implementation mode following steps：
Step 1：Best waypoint is selected, to the polarization code coding codeword that random code length is 1024, code check is 1/2, The Monte Carlo Experiment of SC decodings is carried out under different signal-to-noise ratio.Whenever there is decoding error, the error message sequence is counted Error bit distribution situation.Stop testing when there is 1000 frame mistake and observes whole error bit distribution situation.Finally When comprehensive analysis takes the waypoint i.e. P=1/2 of Pt minimums so that Pt obtains minimum value 1/4, as shown in table 1.In the code check code length Under, remove after freezing position, which falls at the 1/4 of noncoded information.
Step 2：Dual CRC codings, if information bit is u, size is 464, chooses and is used as waypoint at the 1/4 of u. 24 CRC are carried out at waypoint encodes to obtain u1, u at this time1It it is 488, and by u1It is added again as new information sequence CRC check obtains ucrc, u at this timecrcIt is 512.
Step 3：Polarization code encodes, by 512 ucrcPolarization code is carried out to encode to obtain 1024 bit-encoded informations and add X is obtained after white Gaussian noise, using x as the input of decoder.
Step 4：SC of x progress is decoded and is carried out whole CRC check by segmented decodings, if CRC check success, CRC decodings are carried out at waypoint and export final information bit.If CRC check mistake carries out the schools CRC at waypoint It tests, if the verification error at waypoint, illustrates that error bit is present in before waypoint, carried out again to entire sequence x at this time SCL decoding.If the CRC check at waypoint is correct, illustrate that error bit is not present before waypoint, at this time only to waypoint Information bit later carries out SCL decodings again.CRC decodings and output information position are carried out after the completion of decoding.

Claims (3)

1. the polarization code low complex degree segment decoder design based on SCL, it is characterised in that the design includes the following steps：
(1) segmented decodings of SC and SCL；
(2) error probability distribution is calculated, determines best waypoint.
2. design of encoder according to claim 1, it is characterised in that the segmentation of step (1) SC the and SCL algorithms is translated Code, specifically：
During decoding, first to information sequence carry out SC decodings and with CRC check its decode correctness.If decoding error The CRC check at breakpoint is then enabled, the specific paragraph of information sequence is in the error code that misdeems.If error bit is distributed in waypoint Afterwards, then retain the decoding before waypoint as a result, and carrying out SCL decodings to the information sequence after waypoint.If error bit is distributed in Before waypoint, then a SCL decodings, finally output decoding result are carried out to entire information sequence.
3. design of encoder according to claim 1, it is characterised in that the step (2) calculates error probability distribution, really Fixed best waypoint, specifically：
If the complexity of SC decodings is θ (NA), the complexity of SCL decodings is θ (NAL).If under different signal-to-noise ratio, the mistake of SC decodings Frame per second is P1, segmentation scales t.P is the percent of pass of waypoint CRC, then the complexity of the algorithm is represented by formula (1).
θ(NL1)=(1-P1)θ(NA)+P1[tPθ(NAL)+(1-P)θ(NAL)] (1)
Wherein, tP θ (NAL)+(1-P)θ(NAL) can abbreviation be (1-tP) θ (NAL).Complexity of the different values of P and t to system There is prodigious influence.
The optimal selection of P and t are determined by Monte Carlo Experiment.Monte Carlo Experiment design is as follows, designs a statistics SC decoding algorithms are in code length 1024, code check 1/2, the Monte Carlo Experiment of error bit distribution situation, the reality under different signal-to-noise ratio It tests and first 512 in 1000 erroneous frames is counted with the presence or absence of error message, as shown in table 1.CRC table shows 1000 in table Preceding 512 numbers by CRC check, P are percent of pass in erroneous frame.
CN201810744371.9A 2018-07-09 2018-07-09 Polarization code low complex degree segment decoder design based on SCL Pending CN108768411A (en)

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Cited By (3)

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CN110808740A (en) * 2019-11-01 2020-02-18 北京航空航天大学 Low-complexity decoding method based on polarization code under abridged channel
CN111224680A (en) * 2019-11-29 2020-06-02 北京航空航天大学 Low-delay high-reliability quick decoding method and decoder for polarization code
CN113114274A (en) * 2021-04-16 2021-07-13 中国计量大学 Simplified polar code continuous elimination list decoder based on segmented key set

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CN111224680B (en) * 2019-11-29 2022-02-22 北京航空航天大学 Low-delay high-reliability quick decoding method and decoder for polarization code
CN113114274A (en) * 2021-04-16 2021-07-13 中国计量大学 Simplified polar code continuous elimination list decoder based on segmented key set

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Application publication date: 20181106