CN105846827B - Iterative joint message source and channel interpretation method based on arithmetic code and low density parity check code - Google Patents

Iterative joint message source and channel interpretation method based on arithmetic code and low density parity check code Download PDF

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CN105846827B
CN105846827B CN201610152971.7A CN201610152971A CN105846827B CN 105846827 B CN105846827 B CN 105846827B CN 201610152971 A CN201610152971 A CN 201610152971A CN 105846827 B CN105846827 B CN 105846827B
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sequence
decoder
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code
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CN105846827A (en
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薛睿
孙岩博
李超
赵旦峰
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Harbin Engineering University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/40—Conversion to or from variable length codes, e.g. Shannon-Fano code, Huffman code, Morse code
    • H03M7/4006—Conversion to or from arithmetic code
    • 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
    • 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
    • H03M13/1148—Structural properties of the code parity-check or generator matrix

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  • Error Detection And Correction (AREA)

Abstract

The iterative joint message source and channel interpretation method based on arithmetic code and low density parity check code that the present invention is to provide a kind of.Source symbol sequence shCoded sequence b is obtained after AC encoderh, D coded sequence bhThe input message sequence b of LDPC encoder is obtained after parallel-to-serial converter, b forms codeword sequence x after passing through LDPC encoder, x is sent to awgn channel after BPSK is modulated, reception sequence r is input in the closed loop of ldpc decoder and Chase-SISO AC decoder composition and is iterated decoding, and ldpc decoder exports coding sequence after iteration several timesSequence is converted to through deserializerBy obtaining decoding symbol sebolic addressing after AC decoderThe present invention combines the very high AC of lossless compression efficiency with the very strong LDPC code of anti-error capability, so that the validity and reliability of system is all very high, while further improving reliability in the case where guaranteeing validity using IJSCD method.

Description

It is decoded based on the iterative joint message source and channel of arithmetic code and low density parity check code Method
Technical field
The present invention relates to a kind of Joint Source-Channel Decoding methods in wireless communication system, specifically a kind of Iterative joint message source and channel interpretation method based on arithmetic code and low density parity check code.
Background technique
Source coding and channel coding is the indispensable two parts of communication system, and the purpose of message sink coding is removal information source Redundancy improves the validity of communication, and the purpose of channel coding is the reliability added redundancy and improve communication.Traditional receiver knot Usually source decoding and channel decoding separation are considered in structure design, do not utilize information source information fully.Combined signal source channel Decoding (Joint Source Channel Decoding, JSCD) method integrally considers information source and channel, obtains information source information To make full use of, under the premise of guaranteeing validity, reliability can further improve.
Arithmetic code (Arithmetic Coding, AC) is a kind of higher lossless source volume of compression efficiency ratio Huffman code Code, the symbol sebolic addressing global mapping that it will be encoded are a code word, introduce the thought of small number encoder, can infinite approach theory The upper limit of compression ratio is widely used in a variety of compression standards such as image, video.Low density parity check code (Low- Density Parity-check, LDPC) it is a kind of channel coding schemes that can be compared favourably with Turbo code, decoding performance can It limits close to Shannon, was adopted in 2003 by European new-generation digital satellite broadcast standard (DVB-S2).Therefore, arithmetic code It has broad application prospects and practical value, JSCD method can mention on the basis of guaranteeing validity with combining for LDPC code High anti-jamming capacity realizes the reliability requirement of communication.
With the proposition of Turbo iterative decoding thought, soft-output coding (Soft-input Soft-output, SISO) Decoding algorithm has obtained the extensive concern of domestic and foreign scholars.In order to realize the joint decoding of message source and channel, based on SISO algorithm Source decoder structure is suggested, and the source decoder combination information source prior information and channel information are obtained using related algorithm Soft Inform ation, and pass it to channel decoder.Present multimedia Digital Transmission has become the mainstream of communication service, transmission Data volume is very huge and faces channel circumstance complicated and changeable, proposes to the validity and reliability of communication system higher It is required that.If Joint Source-Channel Decoding technology is applied in multimedia communications system, it can guarantee the same of data efficient transmission The reliability of Shi Tigao system.
2007, M.Grangetto et al. was on magazine " IEEE Transactions on Image Processing " Deliver entitled " Iterative decoding of serially concatenated arithmetic and channel A codes with JPEG 2000applications " text, proposes a kind of iteration based on arithmetic code and systematic convolutional code Joint Source-Channel Decoding (Iterative Joint Source Channel Decoding, IJSCD) method, this method exist Forbidden symbol is added in arithmetic encoder to increase the error detecing capability of arithmetic code, AC-SISO decoder utilizes BCJR (Bahl Cocke Jelinek Raviv) algorithm calculates the posterior probability of information bit, and passes it to Convolutional Decoder Assembly, simultaneously The external information that Convolutional Decoder Assembly is obtained passes to AC-SISO decoder, is finally completed decoding by successive ignition.But it should The shortcoming of method is to have lost the partial shrinkage efficiency of arithmetic code, computationally intensive, and implementation complexity is high.
2008, beautiful leaf is met to mention in its Ph.D. Dissertation's " combined signal source channel encoding and decoding research based on arithmetic code " Gone out a kind of adaptive IJSCD method based on arithmetic code and systematic convolutional code, this method according to the quality of channel condition from The quantity of the decoding node of the adjusting bcjr algorithm of adaptation, the IJSCD method calculation amount mentioned compared to M.Grangetto et al. Declined, but when information bit length is larger, the operand of this method is still very huge, is not easy to realize.
Summary of the invention
The purpose of the present invention is to provide a kind of reliability that can be further improved system while guaranteeing validity, And operand is smaller, the lower iterative joint message source and channel based on arithmetic code and low density parity check code of implementation complexity Interpretation method.
The object of the present invention is achieved like this:
Source symbol sequence shCoded sequence b is obtained after AC encoder 1h, D coded sequence bhAfter parallel-to-serial converter 2 The input message sequence b, b for obtaining LDPC encoder 3 form codeword sequence x after passing through LDPC encoder 3, and x is after BPSK is modulated It is sent to awgn channel 4, sequence r is received and is input in the closed loop that ldpc decoder 5 and Chase-SISO AC decoder 6 form It is iterated decoding, ldpc decoder 5 exports coding sequence after iteration several times Sequence is converted to through deserializer 7 By obtaining decoding symbol sebolic addressing after AC decoder 8
The reception sequence r is input in the closed loop that ldpc decoder 5 and Chase-SISO AC decoder 6 form and carries out Iterative decoding specifically includes: the initial value that setting Chase-SISO AC decoder 6 feeds back to ldpc decoder 5 is " 0 ", demodulation Device obtains sending the posterior probability of sequence according to channel information r, and passes it to ldpc decoder 5, then carries out for the first time Iterative joint decodes process；The first time iterative joint decoding process includes: that ldpc decoder 5 is exported using LLR-BP algorithm Coding sequenceAnd Soft Inform ation qi, the coding sequenceAnd Soft Inform ation qiPass to Chase-SISO AC decoder 6, Chase- SISO AC decoder 6 is according to sequenceWith Soft Inform ation qiNew Soft Inform ation w is obtained with Chase-type algorithmi, and will be new Soft Inform ation wiIt feeds back to ldpc decoder 5 and completes the decoding of first time iterative joint.
The iteration several times be according to the identical method of first time iterative joint decoding process continue to complete second, For the third time ..., iv-th iteration, until reach maximum outer iteration number or
Iterative joint message source and channel based on arithmetic code (AC) and low-density checksum (LDPC) code of the invention decodes (IJSCD) method, by AC encoder 1, parallel-to-serial converter (P/S) 2, LDPC encoder 3, awgn channel 4, ldpc decoder 5, AC soft-output coding (Chase-SISO AC) decoder 6, deserializer (S/P) 7 based on Chase-type algorithm and It is completed in the system that AC decoder 8 is constituted.Source symbol sequence shCoded sequence b is obtained after AC encoder 1h, D code sequence Arrange bhThe input message sequence b, b that LDPC encoder 3 is obtained after parallel-to-serial converter 2 form code word after passing through LDPC encoder 3 Sequence x, x are sent to awgn channel 4 after BPSK is modulated, and receive sequence r and are input to ldpc decoder 5 and Chase-SISO AC It is iterated decoding in the closed loop that decoder 6 forms, ldpc decoder 5 exports coding sequence after iteration several times Through going here and there simultaneously Converter 7 is converted to sequence By obtaining decoding symbol sebolic addressing after AC decoder 8Main feature of the invention exists In:
(1) ldpc decoder 5 and Chase-SISO AC decoder 6 form one and handle closed loop based on SISO algorithm iteration, It is " 0 " that Chase-SISO AC decoder 6, which is arranged, to feed back to the initial value of ldpc decoder 5.Demodulator is obtained according to channel information r To the posterior probability of transmission sequence, and ldpc decoder 5 is passed it to, then carries out first time iterative joint and decode process, I.e. ldpc decoder 5 exports coding sequence using LLR-BP algorithmAnd Soft Inform ation qi, the sequence and Soft Inform ation pass to Chase-SISO AC decoder 6, Chase-SISO AC decoder 6 is according to sequenceWith confidence level qiIt is calculated with Chase-type Method obtains Soft Inform ation wi, and it is fed back to ldpc decoder 5.So far, the decoding of first time iterative joint is completed, according to the method Continue to complete second, third time ..., iv-th iteration, until reach maximum outer iteration number or
(2) constitute one of ldpc decoder 5 and Chase-SISO AC decoder 6 is closed based on the processing of SISO algorithm iteration Ring intercourses channel decoder and source decoder and transmits Soft Inform ation, makes full use of information source information by iterator mechanism With channel information.
(3) in AC decoder 6 the Chase-type algorithm of low complex degree introducing and application.
The present invention realizes the SISO structure of arithmetic code using a kind of Chase-type algorithm of low complex degree, and by arithmetic Code is iterated joint decoding with LDPC code, and the complexity realized has been taken into account while improving system reliability.
Present invention has an advantage that
In view of the realization of the AC-SISO decoder based on bcjr algorithm is to sacrifice AC code efficiency as cost, therefore The present invention designs AC-SISO decoder using Chase-type algorithm.It is not necessarily to concentrate in information source with Chase-type algorithm Forbidden symbol is added, and the code efficiency of AC is not influenced.
For the problem that the operand of the AC-SISO decoder based on bcjr algorithm is big and implementation complexity is high, the present invention The Chase-type algorithm of use can effectively reduce the calculation amount of AC-SISO decoder.AC- based on Chase-type algorithm SISO decoder is only in Q=2αThe sequence for meeting following condition is selected in (α generally takes 6) a candidate sequence as coding sequence:
1) length for decoding symbol sebolic addressing is equal to source symbol sequence length；
2) there is maximum a posteriori probability.
Since decoding process does not have more multiplying, and operand only has with the bit number α for selecting confidence level minimum It closes, it is unrelated with the length of sequence.Therefore the AC-SISO decoder based on Chase-type algorithm has lower operand, easily In realization.
The present invention combines the current very high AC of lossless compression efficiency with the very strong LDPC code of anti-error capability, makes The validity and reliability for the system of obtaining is all very high, while using IJSCD method, can be in the case where guaranteeing validity, further Raising system reliability.
Detailed description of the invention
Fig. 1 be and system block diagram corresponding to the present invention；
Fig. 2 be and AC corresponding to the present invention and LDPC code iterative joint decoding during message transmission schematic diagram；
Fig. 3 is the bit error rate curve with AC corresponding to the present invention and the decoding of LDPC code iterative joint；
Fig. 4 is the packet loss curve with AC corresponding to the present invention and the decoding of LDPC code iterative joint.
Specific embodiment
The invention will be further described for citing with reference to the accompanying drawing:
Fig. 1 is system block diagram corresponding with the present invention, and the system is by AC encoder 1, parallel-to-serial converter (P/S) 2, LDPC Encoder 3, awgn channel 4, ldpc decoder 5, the AC soft-output coding (Chase-SISO based on Chase-type algorithm AC) decoder 6, deserializer (S/P) 7 and AC decoder 8 are constituted.Each module definition is as follows in Fig. 1:
1 is arithmetic code coder；
2 be parallel-to-serial converter (P/S)；
3 be LDPC code encoder；
4 be additive white Gaussian noise (Additive White Gaussian Noise, AWGN) channel；
5 be ldpc decoder；
6 is using the AC-SISO decoders of Chase-type algorithm；
7 be deserializer (S/P), is acted on opposite with module 2；
8 be arithmetic code decoder.
For ease of description, each symbol definition in Fig. 1 is as follows:
sh[L]: the length of information source input is the symbol sebolic addressing of L, and 1≤h≤D, D indicate to be input to AC encoder 1 parallel The number of symbol sebolic addressing；
bh[kh]: the length that AC encoder 1 exports is khCodeword sequence；
B [K]: the length that parallel-to-serial converter 2 exports is the codeword sequence of K；
X [N]: the length that LDPC encoder 3 exports is the codeword sequence of N；
R [N]: the length that awgn channel 4 exports is the sequence of N；
Q [K]: the length that ldpc decoder 5 exports is the sequence of K；
qh[kh]: the length that deserializer 7 exports is khSequence；
wh[kh]: the length that Chase-SISO AC decoder 6 exports is khSequence；
W [K]: the sequence that the length of the output of parallel-to-serial converter 2 and feeding ldpc decoder 5 is K；
After row several times iteration, the length that ldpc decoder 5 exports is the coding sequence of K；
The length exported after deserializer 7 is khSequence；
The length that AC decoder 8 exports is the decoding symbol sebolic addressing of L.
In conjunction with Fig. 1, symbol sebolic addressing s to be senthObtaining length through AC encoder 1 is khCoded sequence bh, D bhIt is logical It crosses after parallel-to-serial converter 2 is converted and obtains length into K information sequence b, i.e.,The information bit length of LDPC code is K ', If K < K ', in order to guarantee LDPC code efficient coding, then polishing several " 0 " or " 1 " behind sequence b.B is compiled by LDPC Codeword sequence x is formed after code device 3, x is sent to awgn channel 4 after BPSK is modulated, and receives sequence r and is input to ldpc decoder 5 It is iterated decoding in the closed loop formed with Chase-SISO AC decoder 6, the output of ldpc decoder 5 is translated after iteration several times Code sequence Sequence is converted to through deserializer 7 By obtaining decoding symbol sebolic addressing after AC decoder 8
In conjunction with Fig. 2, Fig. 2 is the message transmission schematic diagram in AC and LDPC code iterative process, and the definition of each symbol is such as in Fig. 2 Under:
vj(1≤j≤M): j-th of check-node of LDPC code；
ci(1≤i≤N): i-th of variable node of LDPC code；
Lij: j-th of check-node vjPass to i-th of variable node ciMessage；
qi: i-th of variable node ciPass to the Soft Inform ation of Chase-SISO AC decoder 6；
wi: Chase-SISO AC decoder 6 passes to i-th of variable node ciSoft Inform ation；
Tji: i-th of variable node ciPass to j-th of check-node vjMessage.
Since the check bit that LDPC code coding generates does not contain any information source information, variable node ciOnly by information bit Message transmission to Chase-SISO AC decoder 6, i.e. qiMeet 1≤i≤K；Similarly, ciMeet 1≤i≤K.
Ldpc decoder receives channel information sequence r=(r1,r2,...,rN) after start to decode, decoding process it is as follows:
1) initializing variable node ciPass to check-node v connected to itjInformation:
Wherein, δ2For the mean square deviation of white Gaussian noise, wiInitial value be 0；
2) check-node v is calculatedjIt is transmitted to variable node c connected to itiInformation, and i ∈ C (j), C (j) indicate all With check-node vjThe set of the variable node of connection:
Wherein, C (j) i indicate remove variable node ciAll same check-node v in additionjThe set of the variable node of connection, t For LDPC decoding iteration number, referred to as the inner iteration number of joint decoding；
3) variable node c is calculatediIt is transmitted to check-node v connected to itjInformation, and j ∈ V (i), V (i) indicate all With variable node ciThe set of the check-node of connection:
Wherein, V (i) j indicate remove check-node vjAll same variable node c in additioniThe set of the check-node of connection；
4) the hard decision information of whole variable nodes is calculated:
IfThen coding sequenceI-th of code wordOtherwiseThe check matrix of LDPC code is H, such as FruitThen the iterative joint decoding of AC and LDPC terminates；IfAnd do not reach maximum inner iteration number, then Return step 2) continue to decode；IfAnd having reached maximum inner iteration number, then ldpc decoder is by coding sequence And its confidence level qi=Ti (t)Chase-SISO decoder is passed to as external information.
Coding sequenceAnd its confidence level qiD length is obtained after S/P7 is converted as khCoding sequenceAnd its it is corresponding Credible degree series qh, Chase-SISO AC decoder 6 is to this D sequence pairIt is decoded, decoding process is as follows:
1) according to qhDetermine sequenceThe position of α minimum bit of middle confidence level；
2) i-th of test vector is generatedWherein Q=2α；tiHaving traversed only allows can There is " 1 " in the corresponding position of α minimum bit of reliability, " 0 " occurs in remaining position and maximum code is no more than all the two of α again System sequence；
3) i-th of cycle tests is generatedWherein Indicate 2 He of mould, ykIt is coding sequenceK-th of hard-decision bits；
4) using the arithmetic decoder of standard to Q cycle tests ziIt is decoded, if sequence ziDecode obtained symbol Sequence length is equal to L, which is added in set Γ, otherwise by sequence ziGive up；
5) sequence z in set of computations ΓiCorresponding maximum a posteriori probability (Maximum a Posteriori, MAP):
Wherein,For sequence ziThe sequence modulated through BPSK, siFor sequence ziCalculation through standard The symbol sebolic addressing that art decodes, P (si) indicate symbol sebolic addressing siThe prior probability of appearance；
6) sequence of calculation pairThe external information w of outputh:
Wherein,To have the corresponding sequence of maximum MAP value in set Γ, J is sequence in set Γ Number, σ is experiment value, and E is the smallest bit of α confidence level in sequenceIn corresponding position.
7) D sequence pairD external information sequence w is obtained through the decoding of Chase-SISO AC decoder 6h, then through P/ Obtain passing to the information w of variable node after S2 conversion.If having reached maximum outer iteration number, decoding terminates；Otherwise it returns Continue to decode to ldpc decoder.
The IJSCD method based on AC and LDPC of present embodiment can be further under the premise of guaranteeing system effectiveness Its reliability is improved, and this method operand is small, implementation complexity is low.Main feature is as follows:
1) AC encoder 1 uses binary system adaptive arithmetic code, and the probability of source symbol is set as waiting general distribution before encoding, Encode initial section be [0,0XFFFF), using following bit method to be encoded；
2) LDPC encoder 3 uses system LDPC code, and check matrix constructs (PEG) method using edge density, and coding uses Near lower triangular matrix coder method；
3) ldpc decoder 5 uses likelihood ratio belief propagation (the Log-likelihood-rate based based on number field Belief Propagation, LLR-BP) algorithm；
4) Chase-SISO AC decoder 6 uses Chase-type algorithm.
By taking probability distribution is 0.9 and 0.1 binary system independence zero-memory information source as an example, the symbol sebolic addressing s of generationhLength It is the symbol sequence s of 110,49 inputs in parallelhForm a data packet；LDPC check matrix carries out structure using edge density method It makes, code length 3000, code rate 0.876, the average degree of variable node is 5, and the average degree of check-node is the best of 37.58, σ Value is 1, is modulated using BPSK, decodes (Separate based on AC and the separation message source and channel of LDPC code under awgn channel Source Channel Decoding, SSCD) and IJSCD bit error rate (Bit Error Rate, BER) curve and packet loss For rate (Packet Error Rate, PER) curve as shown in attached drawing 3 and Fig. 4, what is wherein selected when α expression AC-SISO decoding can The minimum bit number of reliability, β indicate that LDPC decodes inner iteration number, and ε indicates outer iteration number.
From figure 3, it can be seen that the bit error rate of the IJSCD method based on AC and LDPC code is small compared with SSCD method, explanation The decoding performance of IJSCD method is more preferable, and reliability is higher.For IJSCD method, in the case where β and ε certain, as α=6 Its performance improves about 0.1dB compared with α=4；In the case where α and ε certain, as β=50, its performance is obvious compared with β=20 more preferable； In the case where α and β certain, as ε=7, its performance has compared with ε=5 and slightly improves.Thus, the value of α is bigger, inner iteration and The number of outer iteration is more, and the decoding performance of the IJSCD method based on AC and LDPC code is better.When α=6, β=50, ε=5 When, IJSCD method can get the gain of about 0.2dB compared with SSCD.Equally as shown in Figure 4, it can get using IJSCD method and compare SSCD The lower packet loss of method, improves the reliability of communication.

Claims (1)

1. a kind of iterative joint message source and channel interpretation method based on arithmetic code and low density parity check code, it is characterized in that: letter Source symbol sebolic addressing shCoded sequence b is obtained after AC encoder (1)h, D coded sequence bhIt is obtained after parallel-to-serial converter (2) The input message sequence b, b of LDPC encoder (3) form codeword sequence x by LDPC encoder (3) afterwards, and x is after BPSK is modulated It is sent to awgn channel (4), receives sequence r and be input to what ldpc decoder (5) and Chase-SISO AC decoder (6) formed Decoding is iterated in closed loop, ldpc decoder (5) exports coding sequence after iteration several times Turn through deserializer (7) Get sequence in return By obtaining decoding symbol sebolic addressing after AC decoder (8)
Ldpc decoder receives channel information sequence r=(r1,r2,...,rN) after start to decode, decoding process it is as follows:
1) initializing variable node ciPass to check-node v connected to itjInformation:
Wherein, δ2For the mean square deviation of white Gaussian noise, wiInitial value be 0；
2) check-node v is calculatedjIt is transmitted to variable node c connected to itiInformation, and i ∈ C (j), C (j) indicate all same schools Test node vjThe set of the variable node of connection:
Wherein, C (j) i indicate remove variable node ciAll same check-node v in additionjThe set of the variable node of connection, t are LDPC decoding iteration number, referred to as the inner iteration number of joint decoding；
3) variable node c is calculatediIt is transmitted to check-node v connected to itjInformation, and j ∈ V (i), V (i) indicate it is all with become Measure node ciThe set of the check-node of connection:
Wherein, V (i) j indicate remove check-node vjAll same variable node c in additioniThe set of the check-node of connection；
4) the hard decision information of whole variable nodes is calculated:
If Ti (t)>=0, then coding sequenceI-th of code wordOtherwiseThe check matrix of LDPC code is H, ifThen the iterative joint decoding of AC and LDPC terminates；IfAnd do not reach maximum inner iteration number, then it returns Step 2) is returned to continue to decode；IfAnd having reached maximum inner iteration number, then ldpc decoder is by coding sequenceAnd Its confidence level qi=Ti (t)Chase-SISO decoder is passed to as external information；
Coding sequenceAnd its confidence level qiD length is obtained after S/P7 is converted as khCoding sequenceAnd its it is corresponding credible Degree series qh, Chase-SISO AC decoder (6) is to this D sequence pairIt is decoded, decoding process is as follows:
1) according to qhDetermine sequenceThe position of α minimum bit of middle confidence level；
2) i-th of test vector is generatedWherein Q=2α；tiHaving traversed only allows in confidence level There is " 1 " in the corresponding position of α minimum bit, " 0 " occurs in remaining position and maximum code is no more than all binary systems of α again Sequence；
3) i-th of cycle tests is generatedWherein It indicates 2 He of mould, ykIt is coding sequenceK-th of hard-decision bits；
4) using the arithmetic decoder of standard to Q cycle tests ziIt is decoded, if sequence ziDecode obtained symbol sebolic addressing Length is equal to L, which is added in set Γ, otherwise by sequence ziGive up；
5) sequence z in set of computations ΓiCorresponding Maximize:
Wherein,For sequence ziThe sequence modulated through BPSK, siFor sequence ziArithmetically decoding through standard Obtained symbol sebolic addressing, P (si) indicate symbol sebolic addressing siThe prior probability of appearance；
6) sequence of calculation pairThe external information w of outputh:
Wherein,To have the corresponding sequence of maximum MAP value in set Γ, J is of sequence in set Γ Number, σ are experiment value, and E is the smallest bit of α confidence level in sequenceIn corresponding position；
7) D sequence pairD external information sequence w is obtained through Chase-SISO AC decoder (6) decodingh, then through P/S2 Obtain passing to the information w of variable node after conversion, if having reached maximum outer iteration number, decoding terminates；Otherwise it returns to Ldpc decoder continues to decode.
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