CN110336640A - A kind of long system LT code interpretation method of short code - Google Patents
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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
- H03M13/37—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35
- H03M13/3761—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35 using code combining, i.e. using combining of codeword portions which may have been transmitted separately, e.g. Digital Fountain codes, Raptor codes or Luby Transform [LT] codes
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- 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
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- 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
- H04L1/0047—Decoding adapted to other signal detection operation
- H04L1/005—Iterative decoding, including iteration between signal detection and decoding operation
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- 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
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- 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
Abstract
A kind of long system LT code interpretation method of short code is using the improvement interpretation method based on belief propagation (Belief Propagation, BP) algorithm.Its process are as follows: source bits information sequence carries out system LT code coding and uses binary phase shift keying (Binary Phase Shift Keying, BPSK it) modulates, modulation symbol sequence is wirelessly transmitted to receiver, receiver demodulator obtains the channel log-likelihood ratio information of system LT code coded-bit using traditional demodulation method, receiver LT decoder is decoded using BP decoding algorithm, after the completion of BP algorithm, the Soft Inform ation of receiver calculation code bit, receiver re-starts sequence to Soft Inform ation and adjudicates, bit reversal is carried out by the bit sequence obtained to judgement, find out minimum weight Hamming distance, to obtain last received information sequence.Compared to traditional BP decoding algorithm, improvement interpretation method provided by the invention, so as to further decrease frame error rate (Frame Error Rate, FER), achievees the purpose that reliable transmission due to taking full advantage of the Soft Inform ation of coded-bit.
Description
Technical field
The present invention relates to the long system LT codes of a kind of short code being suitable under radio noise channel in a wireless communication system to translate
Code method, belongs to communication code technical field.
Background technique
Fountain codes are a kind of novel error-correcting code techniques of no rate, and typical case includes multimedia broadcast/multicast service, distribution
Formula network storage etc..LT (Luby Transform) code and Raptor code are current most important two classes fountain codes, wherein
Raptor code is made of high code rate precoding and the cascade of LT code.Fountain codes are initially applied to be used to resist to lose in erasure channel
Packet, academia was proved fountain codes in radio noise channel (such as awgn channel, fading channel) equally with excellent in recent years
Performance, (see " Fixed-Rate Raptor Codes Over Rician Fading Channels ", IEEE
Transactions on Vehicular Technology, Vol.56, No.6, November 2008).
When transmitter sends signal using LT code, it is that realization can that high performance decoding algorithm how is designed at receiver
By one of received key technology.Traditional interpretation method is to obtain the channel logarithm of LT code coded-bit using demodulator first
Likelihood ratio (Log-likelihood Ratio, LLR) information is (see " Bitwise Log-likelihood Ratios For
Quadrature Amplitude Modulations ", IEEE Communications Letters, Vol.19, No.6,
June 2015), then fountain code decoder restores transmitting information using soft decoding algorithm.Traditional belief propagation (Belief
Propagation, BP) for decoding algorithm when LT code code length is longer, performance is close to maximum-likelihood decoding performance and has and can connect
The decoding algorithm complexity received.But when code length shorter (such as code word size is less than 500), decoding performance degradation is serious, because
This studies the more excellent decoding algorithm of performance when short code is long and is necessary.
Summary of the invention
The invention proposes a kind of improved system LT code interpretation methods, compared to traditional BP interpretation method, side of the present invention
Method has more excellent decoding performance.
The purpose of the present invention is what is be achieved through the following technical solutions:
A kind of long system LT code interpretation method of short code is a kind of based on belief propagation, i.e. Belief Propagation, BP
The improvement interpretation method of algorithm realizes that step is specific as follows:
Step 1: transmitter is to length K1Original bit information sequence use cyclic redundancy check, i.e. Cyclic first
Redundancy check, CRC code encode to obtain the source bits sequence of length K, then to the source bits sequence of length K into
It row system LT coding and modulates to obtain length using binary phase shift keying, that is, Binary Phase Shift Keying, BPSK
For the modulation symbol sequence of N；Generator matrix G known to receiver, G are the binary matrixs of a K × N.
Step 2: modulation symbol sequence is transferred to receiver by wireless channel.
Step 3: receiver demodulator obtains the channel logarithm of system LT code coded-bit seemingly using traditional demodulation method
So ratio, i.e. Log-likelihood Ratio, LLR information.
Step 4: receiver LT decoder is decoded using BP decoding algorithm, after iteration several times, information source is calculated
Soft Inform ation L={ the l of bit sequence1,l2,...,lK, and source bits sequence X is obtained to Soft Inform ation L hard decision；If information source ratio
Special sequence X is verified correctly by CRC code, and receiver terminates entire decoding process；Otherwise, following step is carried out.
Step 5: receiver calculates the Soft Inform ation L of coded-bit at this time after BP is decoded1, to L1Hard decision is carried out to obtain
To sequence C1, and by Soft Inform ation L1It arranges to obtain Soft Inform ation L according to sequence from big to small2, column change correspondingly is carried out to matrix G
Get matrix G in return1；Judgment matrix G1Whether preceding K column are Maximal linearly independent groups, if it is not, then again to matrix G1Carry out column change
Get matrix G in return2, so that matrix G2Preceding K it is linear unrelated, Soft Inform ation L2Also correspondingly replacement puts in order to obtain soft letter
Cease L3。
Step 6: receiver is first to Soft Inform ation L3Preceding K progress hard decisions, obtain new source bits sequence X1；Then
To matrix G2The front part unit matrix is set to obtain matrix G using Gaussian elimination method3, last X1With matrix G3Multiplication obtains
New sequences of code bits C2。
Step 7: according to the inverse process of step 5 sequence to sequence C2Rearrangement obtains sequence C3。
Step 8: sequence of calculation C1And sequence C3Weighting Hamming distance, i.e. the Weighted Hamming
Distance, WHD are denoted as WHD1。
Step 9: overturning source bits sequence X1I-th of bit obtain sequence With matrix
G3Multiplication obtains sequenceIt repeats step 7 and obtains sequenceThe sequence of calculationWith sequence C1Weighting Hamming distance WHDi,
Enable WHDopt=min (WHD1,WHD2,...,WHDK,WHD1), it obtains at the same time and WHDoptCorresponding coded-bit
Wherein min function representation is minimized function.
Step 10: choosing sequences of code bitsPreceding K1Position is used as original bit information sequence.
Improvement interpretation method provided by the invention is than traditional BP interpretation method in identical signal-to-noise ratio (Signal to
Noise Ratio, SNR) under have lower frame error rate (Frame Error Rate, FER).
Detailed description of the invention
Fig. 1 is the original bit information sequence length K under awgn channel1=240, when code rate R=0.5, traditional BP decoding
With the simulation result proposed by the present invention for improving decoding at different SNR；
Fig. 2 is the original bit information sequence length K under awgn channel1=240, noise variance σ2=0.5, the number of iterations
It is 20 times, traditional BP decoding and the simulation result proposed by the present invention for improving decoding under different modulating symbol lengths.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
A kind of long system LT code interpretation method of short code, the specific implementation steps are as follows:
Step 1: transmitter is to length K1Original bit information sequence use CRC code to encode to obtain the letter of length K first
Source bit sequence, the system LT for then carrying out code rate R to the source bits information sequence of length K encode to obtain coded-bit sequence
Column, sequences of code bits use BPSK to modulate the modulation symbol sequence for obtaining length as N, the set S=of S expression modulation symbol-
1,+1}。
Step 2: it is σ that modulation symbol sequence, which is 0 variance by mean value,2Awgn channel be transferred to receiver.
Step 3: receiver demodulator utilizes reception sequence rjThe channel of (j=1L N) computing system LT code coded-bit
LLR information, i.e.,
Step 4: receiver LT code decoder calculates the Soft Inform ation of source bits sequence using BP decoding algorithm, and adjudicate.
Its specific formula for calculation is as follows:
The message transmitted in a decoder is indicated with m, and l indicates the number of iterations.From i-th of coded-bit ciBelieve to j-th
Source bit djLLR message be expressed as It indicates from source bits diTo coded-bit cjLLR message.So,
When l iteration,For
Wherein, NiIndicate the indexed set for the source bits connecting with i-th of coded-bit, L (ci) indicate to be obtained by step 3
The channel LLR information of i-th of the coded-bit arrived.LLR messageIt is solely dependent upon and is transmitted to source bits diInformation.Cause
This, when the l times iteration,It is expressed as
Wherein, εiIndicate the indexed set for the coded-bit being connected with i-th of source bits.Finally calculate l iteration
The Soft Inform ation of i-th of source bits transmitting afterwards
It is rightHard decision is carried out, specific formula for calculation is as follows,
Obtain sequence X={ d1,d2,...,di,...,dK, if X is verified correctly by CRC code, can restore completely at this time
Source bits sequence then terminates decoding process；Otherwise continue below step.
Step 5: the Soft Inform ation of receiver i-th of coded-bit of calculating, i=1,2 ..., N,
First to L1It carries out hard decision and obtains sequence C1,
Then by L1It arranges to obtain L according to sequence from big to small2, rank transformation correspondingly is carried out to matrix G and obtains G1；Sentence
Disconnected matrix G1Whether preceding K column are Maximal linearly independent groups, if it is not, then again to matrix G1It carries out rank transformation and obtains G2, so that square
Battle array G2Preceding K it is linear unrelated, while L2Also correspondingly replacement puts in order to obtain L3。
Step 6: first to L3Preceding K progress hard decision, i=1,2 ..., K,
Then to matrix G2It carries out Gaussian elimination and obtains G3, so that matrix G3The submatrix that preceding K column are constituted is unit battle array, most
X afterwards1With matrix G3Multiplication obtains new sequences of code bits C2。
Step 7: step 5 is to L1Continuous two minor sort is carried out, according to its inverse process to sequence C2Rearrangement obtains
Sequence C3。
Step 8: sequence of calculation C1And sequence C3Weighting Hamming distance, j=1,2 ..., N,
Step 9: overturning X1I-th of bit obtain sequence With matrix G3Multiplication obtains
SequenceIt repeats step 7 and obtains sequenceIt calculatesWith C1Weighting Hamming distance WHDi,
It enables
WHDopt=min (WHD1,WHD2,...,WHDK,WHD1),
It obtains and WHDoptCorresponding sequences of code bits
Step 10: choosing sequences of code bitsPreceding K1Position is used as original bit information sequence.
The present invention is further illustrated below by specific embodiment.
Embodiment 1, a kind of long system LT code interpretation method of short code, the specific implementation steps are as follows:
Step 1: transmitter is to length K1=240 original bit information sequence uses CRC-16 code coding to obtain first
The source bits sequence of length K=256, the system LT for then carrying out code rate R=1/2 to source bits information sequence encode to obtain
Sequences of code bits, system LT code use document " Optimization Design and Asymptotic Analysis of
Systematic Luby Transform Codes Over BIAWGN Channels”(IEEE Transactions on
Communications, Vol.64, No.8, August 2016) degree distribution function be
Sequences of code bits uses BPSK to modulate the modulation symbol sequence for obtaining length as N=256/R again.
Step 2: it is σ that modulation symbol sequence, which is 0 variance by mean value,2Awgn channel be transferred to receiver.
Step 3: receiver demodulator utilizes reception sequence rjThe channel of (j=1L N) computing system LT code coded-bit
LLR information.
Step 4: receiver LT code decoder uses BP decoding algorithm, after iteration several times, source bits sequence is calculated
The Soft Inform ation L of column, and source bits sequence X is obtained to Soft Inform ation L hard decision.If X is correct by CRC-16 code check, receiver
Terminate entire decoding process and otherwise carries out following step.
Step 5: receiver calculates the Soft Inform ation L of sequences of code bits at this time after BP is decoded1, to L1Sentenced firmly
Certainly obtain sequence C1, and by L1It arranges to obtain L according to sequence from big to small2, rank transformation correspondingly is carried out to matrix G and obtains G1；
Judgment matrix G1Whether preceding K column are Maximal linearly independent groups, if it is not, then again to matrix G1It carries out rank transformation and obtains G2, so that
Matrix G2Preceding K it is linear unrelated, L2Also correspondingly replacement puts in order to obtain L3。
Step 6: receiver is first to Soft Inform ation L3Preceding K progress hard decisions, obtain new source bits sequence X1；Then
To G2The front part unit matrix is set to obtain matrix G using Gaussian elimination method3, last X1With matrix G3Multiplication retrieves
New sequences of code bits C2。
Step 7: according to the inverse process of step 5 sequence to sequence C2Rearrangement obtains sequence C3。
Step 8: sequence of calculation C1And sequence C3Weighting Hamming distance, be denoted as WHD1；
Step 9: overturning X1I-th of bit obtain sequence With matrix G3Multiplication obtains sequence
ColumnIt repeats step 7 and obtains sequenceIt calculatesWith C1Weighting Hamming distance WHDi, enable WHDopt=min (WHD1,
WHD2,...,WHDK,WHD1), it obtains at the same time and WHDoptCorresponding sequences of code bits
Step 10: choosing sequences of code bitsPreceding K1Position is used as original bit information sequence.
According to the process of embodiment 1, signal-to-noise ratio is defined as SNR=P/ σ2, P is normalized signal power.According to iteration time
Several differences, we are emulated for different signal-to-noise ratio, and Fig. 1 is simulation result.As seen from Figure 1, for traditional BP
For decoding algorithm, the number of iterations is respectively that 30 times and 50 times FER curves are almost overlapped, that is to say, that when the number of iterations increases
When arriving certain value greatly, the number of iterations is continued growing, only will increase decoding complexity, and FER performance cannot be improved.And this hair
The improvement interpretation method of bright proposition can then reduce FER on this basis.
Embodiment 2, one kind being based on the long LT code coding method of short code, and the specific implementation steps are as follows:
Transmitter is to length K1=240 original bit information sequence uses CRC-16 code coding to obtain length K=first
256 source bits sequence, the system LT for then carrying out code rate R to source bits information sequence encode to obtain coded-bit sequence
Column, for LT code using degree distribution function with embodiment 1, sequences of code bits uses BPSK to modulate to obtain length as N=256/R's again
Modulation symbol sequence.It is assumed that noise variance σ2=0.5, the number of iterations is 20 times.Remaining step is the same as embodiment 1.
According to the process of embodiment 2, we are emulated for different N/K, and Fig. 2 is simulation result.In identical N/K
Under, the FER proposed by the present invention for improving interpretation method is lower than the FER of traditional BP interpretation method, it can be seen that improved decoding
Method has lower FER.
Claims (8)
1. a kind of long system LT code interpretation method of short code, it is characterised in that: be a kind of based on belief propagation, i.e. Belief
Propagation, the improvement interpretation method of BP algorithm realize that step is specific as follows:
Step 1: transmitter is to length K1Original bit information sequence use cyclic redundancy check, i.e. Cyclic first
Redundancy check, CRC code encode to obtain the source bits sequence of length K, then to the source bits sequence of length K into
It row system LT coding and modulates to obtain length using binary phase shift keying, that is, Binary Phase Shift Keying, BPSK
For the modulation symbol sequence of N；Generator matrix G known to receiver, G are the binary matrixs of a K × N；
Step 2: modulation symbol sequence is transferred to receiver by wireless channel；
Step 3: receiver demodulator obtains the channel log-likelihood of system LT code coded-bit using traditional demodulation method
Than, i.e. Log-likelihood Ratio, LLR information；
Step 4: receiver LT decoder is decoded using BP decoding algorithm, after iteration several times, source bits are calculated
Soft Inform ation L={ the l of sequence1,l2,...,lK, and source bits sequence X is obtained to Soft Inform ation L hard decision；If source bits sequence
It arranges X to verify correctly by CRC code, receiver terminates entire decoding process；Otherwise, following step is carried out；
Step 5: receiver calculates the Soft Inform ation L of coded-bit at this time after BP is decoded1, to L1It carries out hard decision and obtains sequence
Arrange C1, and by Soft Inform ation L1It arranges to obtain Soft Inform ation L according to sequence from big to small2, rank transformation correspondingly is carried out to matrix G and is obtained
To matrix G1；Judgment matrix G1Whether preceding K column are Maximal linearly independent groups, if it is not, then again to matrix G1Rank transformation is carried out to obtain
To matrix G2, so that matrix G2Preceding K it is linear unrelated, Soft Inform ation L2Also correspondingly replacement puts in order to obtain Soft Inform ation L3；
Step 6: receiver is first to Soft Inform ation L3Preceding K progress hard decisions, obtain new source bits sequence X1；Then to square
Battle array G2The front part unit matrix is set to obtain matrix G using Gaussian elimination method3, last X1With matrix G3Multiplication obtains new
Sequences of code bits C2；
Step 7: according to the inverse process of step 5 sequence to sequence C2Rearrangement obtains sequence C3；
Step 8: sequence of calculation C1And sequence C3Weighting Hamming distance, i.e. the Weighted Hamming Distance,
WHD is denoted as WHD1；
Step 9: overturning source bits sequence X1I-th of bit obtain sequence With matrix G3Phase
It is multiplied to arrive sequenceIt repeats step 7 and obtains sequenceThe sequence of calculationWith sequence C1Weighting Hamming distance WHDi, enable
WHDopt=min (WHD1,WHD2,...,WHDK,WHD1), it obtains at the same time and WHDoptCorresponding coded-bitIts
Middle min function representation is minimized function；
Step 10: choosing sequences of code bitsPreceding K1Position is used as original bit information sequence.
2. the long system LT code interpretation method of a kind of short code according to claim 1, it is characterised in that: step 4 is specifically such as
Under: the message transmitted in a decoder is indicated with m, and l indicates the number of iterations；From i-th of coded-bit ciTo j-th of source bits
djLLR message be expressed asIt indicates from source bits diTo coded-bit cjLLR message；So, the l times
When iteration,For
Wherein, NiIndicate the indexed set for the source bits connecting with i-th of coded-bit, L (ci) indicate to be obtained by step 3
The channel LLR information of i-th of coded-bit；LLR messageIt is solely dependent upon and is transmitted to source bits diInformation；Therefore,
When l iteration,It is expressed as
Wherein, εiIndicate the indexed set for the coded-bit being connected with i-th of source bits；Finally i-th after l iteration of calculating
The Soft Inform ation of a coded-bit transmittingFor
It is rightHard decision is carried out, specific formula for calculation is as follows,
Obtain sequence X={ d1,d2,...,di,...,dK, if X is verified correctly by CRC code, information source can be restored completely at this time
Bit sequence then terminates decoding process；Otherwise continue below step.
3. the long system LT code interpretation method of a kind of short code according to claim 1, it is characterised in that: step 5 is specifically such as
Under: the Soft Inform ation of receiver i-th of coded-bit of calculating, i=1,2 ..., N,
First to L1It carries out hard decision and obtains C1,
Then by L1It arranges to obtain L according to sequence from big to small2, rank transformation correspondingly is carried out to matrix G and obtains G1；Judge square
Battle array G1Whether preceding K column are Maximal linearly independent groups, if it is not, then again to matrix G1It carries out rank transformation and obtains G2, so that matrix G2
Preceding K it is linear unrelated, while L2Also correspondingly replacement puts in order to obtain L3。
4. the long system LT code interpretation method of a kind of short code according to claim 1, it is characterised in that: step 6 is specifically such as
Under: first to Soft Inform ation L3Preceding K progress hard decision, i=1,2 ..., K,
Then to matrix G2It carries out Gaussian elimination and obtains matrix G3, so that matrix G3The submatrix that preceding K column are constituted is unit battle array, most
Source bits sequence X afterwards1With matrix G3Multiplication obtains new sequences of code bits C2。
5. the long system LT code interpretation method of a kind of short code according to claim 1, it is characterised in that: step 7 is specifically such as
Under: step 5 is to Soft Inform ation L1Continuous two minor sort is carried out, according to its inverse process to sequence C2Rearrangement obtains sequence
C3。
6. the long system LT code interpretation method of a kind of short code according to claim 1, it is characterised in that: step 8 is specifically such as
Under: sequence of calculation C1And sequence C3Weighting Hamming distance, j=1,2 ..., N,
7. the long system LT code interpretation method of a kind of short code according to claim 1, it is characterised in that: step 9 is specifically such as
Under: overturning source bits sequence X1I-th of bit obtain With matrix G3Multiplication obtains sequenceIt repeats step 7 and obtains sequenceThe sequence of calculationWith sequence C1Weighting Hamming distance WHDi, j=1,2 ..., N,
It enables
WHDopt=min (WHD1,WHD2,...,WHDK,WHD1),
It obtains and WHDoptCorresponding coded-bit
8. the long system LT code interpretation method of a kind of short code according to claim 1, it is characterised in that: step 10 is specifically such as
Under: choose sequences of code bitsPreceding K1Position is used as original bit information sequence.
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| CN111181691B (en) * | 2019-12-31 | 2022-08-16 | 上海微波技术研究所（中国电子科技集团公司第五十研究所） | Millimeter wave system high-speed Raptor coding and decoding method and system |
| CN113162731A (en) * | 2021-05-26 | 2021-07-23 | 中南大学 | Mixed digital-analog broadcasting communication method |
| CN113162731B (en) * | 2021-05-26 | 2022-09-16 | 中南大学 | Mixed digital-analog broadcasting communication method |
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