CN115549692A - Low-complexity forward-backward decoding method based on weighted editing distance - 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
- H03M13/03—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
- H03M13/1111—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms
- H03M13/1125—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms using different domains for check node and bit node processing, wherein the different domains include probabilities, likelihood ratios, likelihood differences, log-likelihood ratios or log-likelihood difference pairs
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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
- H03M13/63—Joint error correction and other techniques
- H03M13/635—Error control coding in combination with rate matching
- H03M13/6362—Error control coding in combination with rate matching by puncturing
- H03M13/6368—Error control coding in combination with rate matching by puncturing using rate compatible puncturing or complementary puncturing
- H03M13/6393—Rate compatible low-density parity check [LDPC] codes
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- 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
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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
Abstract
The invention discloses a low-complexity forward-backward decoding method based on weighted edit distance, which comprises the following steps: binary information sequencebGenerating a length of N by an encoder of an LDPC code L Code word sequence of symbolsd(ii) a Marking codewUniformly inserted into codeword sequencedIn (2), generating a signal of length N c Is transmitted as a codewordxAnd outputting; transmitting code wordsxAfter insertion/deletion of the substitute channel, a length of
Receive sequence ofy(ii) a Watermark decoder uses low complexity forward-backward decoding to receive sequenceyDecoding and outputting likelihood ratio sequencel；LDPC decoder using likelihood ratio sequencelDecoding and outputting
The invention stores the calculation result of the intermediate metric value in the lookup table, reduces the repeated calculation times of the intermediate metric value, thereby reducing the calculation complexity of the decoding algorithm and improving the decoding speed.
Description
Technical Field
The invention relates to the field of digital communication error control coding, in particular to a low-complexity forward-backward decoding method based on weighted edit distance.
Background
Information may encounter insertion/deletion errors during transmission in addition to substitution errors. The sampling clock rate of a receiver in a communication system is unstable, the length of a transmission symbol is not fixed when differential pulse position modulation is adopted, and the writing of a storage system fails, so that insertion/deletion errors can be generated in the three conditions, and correct data cannot be recovered.
Davey and Mackay designed concatenated code schemes that can correct insertion/erasure errors. The scheme adopts a nonlinear watermark code as an inner code, and an LDPC (low density check) code of a non-binary domain as an outer code. The coding and decoding algorithm of the scheme has excellent error correction performance, but is only suitable for the watermark code, and has limited flexibility. Subsequently, an inner decoding algorithm based on Weighted Edit Distance (WED) is proposed, which introduces a dynamic programming method to calculate the WED to represent the difference between the transceiving sequences, calculates forward/backward metric values by using the WED to obtain insertion/deletion position information, provides likelihood values to an outer decoding algorithm, and then recovers the estimation of the transmitting sequence.
However, the inner decoding algorithm based on WED is too complex and has a long decoding delay. In the process of calculating the forward/backward metrics, the calculation of the intermediate metrics is complex and repetitive, resulting in a long time consuming calculation of likelihood values, which in turn affects the overall decoding speed. Therefore, it is necessary to design a method for reducing the complexity of the inner decoding algorithm, reducing the system delay, and improving the decoding efficiency.
Disclosure of Invention
The invention provides a low-complexity forward-backward decoding method based on weighted edit distance, which stores the calculation result of the intermediate metric value in a lookup table, reduces the repeated calculation times of the intermediate metric value, thereby reducing the calculation complexity of a decoding algorithm and improving the decoding speed, as described in detail in the following:
a low complexity weighted edit distance-based forward-backward coding method, the method comprising:
binary information sequencebGenerating a length of N by an encoder of an LDPC code L Code word sequence of individual symbolsd；
Marking codewUniformly inserted into codeword sequencedIn (1), a length N is generated c Is transmitted as a codewordxAnd outputting;
transmitting code wordsxAfter insertion/deletion of the substitute channel, a length of
Receive sequence ofy(ii) a Watermark decoder uses low complexity forward-backward decoding to receive sequenceyDecoding and outputting likelihood ratio sequencel；
LDPC decoder using likelihood ratio sequenceslDecoding and outputting
Wherein the marking codewUniformly inserted into codeword sequencesdIn (1), a length N is generated c Is transmitted as a codewordxAnd the output is specifically:
dividing a binary LDPC code into N symbols, each symbol having m bits, wherein N = N L /m；
Inner encoder randomly generates mark code with length of NxLambdawCode the markwDividing into N sub-sequences of length lambda, coding the markswEach subsequence of (2) is inserted into a sequence of code wordsdBefore each symbol of (2), generating a length N c Is transmitted as a codewordx。
Further, the watermark decoder uses low complexity forward-backward decoding on the received sequenceyDecoding and outputting likelihood ratio sequencelThe method specifically comprises the following steps: calculating forward and backward metrics, and calculating likelihood ratio sequence based on the forward and backward metricsl；
Wherein the calculating the forward metric value is:
(4.1.1) initializing a forward metric value at the time i = 0;
initializing a lookup table; let the element beta (d) in the table i ,t i ,t i+1 , 0 y) = -1, wherein d i ∈[0,q-1)，t i ∈[-x max ,x max ]； 0 yRepresenting the received subsequence, q representing a symbol value; let i =1; t =2T max +1，
T is the number of states per time, T max Is the maximum amount of drift, P d Representing the puncturing probability of the channel;
(4.1.2) let the symbol probability p (d) i )＝1/2 m ，d i As a sequence of code wordsdThe symbol value corresponding to the ith sub-sequence with the length of m bits; let τ = -t max ；
(4.1.3) determination of β (d) i ＝a,t i ＝c,t i+1 ＝τ, 0 y) If so, performing step (4.1.4); if not, let M i (d i-1 ＝a)＝β(d i ,t i ,t i+1 , 0 y) Executing the step (4.1.5); wherein, t i Is the drift amount at the ith time point, -t max ≤c≤t max ；
(4.1.4) calculating an intermediate metric value M i (d i-1 = a), let β (d) i ,t i ,t i+1 , 0 y)＝M i (d i-1 = a), wherein M i (d i-1 Specific for a);
M i (d i-1 ＝a)＝P(y 0 ,t i |t i-1 ,d i-1 ＝a)
＝exp(WED(s i-1 ,y 0 )+(m+λ)log(P t (1-P s ))),
wherein, P t Is the transmission probability; d i-1 Is thatdThe (i-1) th sub-sequence with the length of m bits corresponds to a symbol value; a is equal to [0, q-1);
s i-1 denotes the i-1 st transmission sub-sequence, w λi-1 Is the lambdai-1 mark bit, d m(i-1) Is the m (i-1) th LDPC code bit; WED (s i-1 , 0 y) Is a subsequence ofs i-1 And 0 yweighted edit distance therebetween;
(4.1.5) calculating t i The time drift is a forward measurement value of tau:
wherein, t i = τ denotes the amount of shift at time i is τ, t i-1 = c denotes that the offset at the i-1 st time is c; (4.1.6) τ = τ +1, if τ ≦ t max Repeating the steps (4.1.3) to (4.1.6), otherwise, jumping to the step (4.1.7);
(4.1.7) i = i +1, if i ≦ N, repeating steps (4.1.2) to (4.1.7); if i > N, a backward metric is calculated.
The calculation backward measurement value is specifically:
(4.2.1) initializing the backward metric value B at the Nth time N (t N τ) =1/T, where-T max ≤τ≤t max ；
(4.2.2) let i = N, b = -t max ，p(d i )＝1/2 m ；
(4.2.3) determination of beta (d) i ＝a,t i ＝τ,t i+1 ＝b, 0 y) If so, performing step (4.2.4); no, let M = beta (d) i ,t i ,t i+1 , 0 y) Step (4.2.6) is performed, wherein-t max ≤τ≤t max ；
(4.2.4) calculating an intermediate metric valueM i+1 (d i = a), let β (d) i ,t i ,t i+1 , 0 y)＝M i+1 (d i = a), wherein M i+1 (d i Specific for a);
M i+1 (d i ＝a)＝P(y 0 ,t i+1 ∣t i ,d i ＝a)
＝exp(WED(s i ,y 0 )+(m+λ)log(P t (1-P s )))，
wherein a is more than or equal to 0 and less than 2 m ，
WED( i s,y 0 ) Representing subsequences i sAndy 0 the weighted edit distance between the two, i s＝(w λi ,…,w λ×(i+1)-1 ,d mi ,…,d m×(i+1)-1 )；
(4.2.5) calculating t i The time drift amount is a backward measurement value of tau;
wherein i is more than or equal to 0 and less than N, d i Is composed ofdThe symbol value, t, corresponding to the ith m-bit sub-sequence i = τ denotes the offset at time i is τ, t i+1 B denotes that the offset at the i +1 th time is b; (4.2.6) b = b +1, if b ≦ t max Repeating the steps (4.2.3) to (4.2.6), otherwise, jumping to the step (4.2.7);
(4.2.7) i = i-1, and if i ≧ 0, repeating steps (4.2.2) through (4.2.7).
The technical scheme provided by the invention has the beneficial effects that:
1. on the basis of the WED label code transmission method, the invention establishes the lookup table for storing the intermediate measurement, reduces the calculation repetition rate of the intermediate measurement, reduces the calculation complexity of the forward measurement and the backward measurement, and accelerates the calculation speed of the likelihood value;
2. the invention simplifies the forward-backward decoding operation, reduces the decoding complexity, reduces the decoding time delay and improves the decoding efficiency on the basis of ensuring the system reliability.
Drawings
FIG. 1 is a flow chart of a low complexity weighted edit distance based forward-backward decoding method;
fig. 2 is a schematic diagram of the forward pass of a watermark decoder.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
The embodiment of the invention designs a method for searching a table on the basis of the traditional mark code transmission method, and stores the calculated intermediate metric value in the table, so that the subsequent used intermediate metric value can be directly searched in the table without repeated calculation.
A low-complexity weighted edit distance decoding method based on a lookup table according to an embodiment of the present invention is described in detail below with reference to fig. 1 and fig. 2.
As shown in fig. 2, the embodiment of the present invention includes the following five steps,
(1) Binary information sequencebEncoder with LDPC code to generate length N L Code word sequence of symbolsd；
(2) Sign codewUniformly inserted into codeword sequencesdIn (2), generating a signal of length N c Is transmitted as a codewordxAnd outputting;
wherein the step (2) is as follows:
(2.1) dividing the binary LDPC code into N symbols, each symbol having m bits, where N = N L /m；
(2.2) the inner encoder randomly generates a mark code of length NxLambdawCode the markwDividing into N subsequences of length lambda, coding the markwEach sub-sequence of (2) is inserted into a codeword sequencedBefore each symbol of (2), generating a length N c Is transmitted as a codewordx。
(3) Transmitting code wordsxAfter insertion/deletion of the substitute channel, a length of
Receive sequence ofy；
(4) Watermark decoder uses low complexity forward-backward decoding algorithm to receive sequenceyDecoding and outputting likelihood ratio sequencel；
Wherein, the step (4) specifically comprises:
(4.1) calculating a forward metric F;
(4.1.1) initializing a forward metric value at the time i = 0;
initializing a lookup table; let the element beta (d) in the table i ,t i ,t i+1 , 0 y) =1, wherein d i ∈[0,q-1)，t i ∈[-x max ,x max ]； 0 yRepresenting the received subsequence, q representing a symbol value; let i =1; t =2T max +1，
T is the number of states per time, T max Is the maximum amount of drift, P d Representing the puncturing probability of the channel;
(4.1.2) let the symbol probability p (d) i )＝1/2 m ，d i As a sequence of code wordsdThe symbol value corresponding to the ith sub-sequence with the length of m bits; let τ = -t max ；
(4.1.3) determination of beta (d) i ＝a,t i ＝c,t i+1 ＝τ, 0 y) If so, performing step (4.1.4); if not, let M i (d i-1 ＝a)＝β(d i ,t i ,t i+1 , 0 y) Executing the step (4.1.5); wherein, t i Is the drift amount at the ith time point, -t max ≤c≤t max ；
(4.1.4) calculating an intermediate metric value M i (d i-1 = a), let β (d) i ,t i ,t i+1 , 0 y)＝M i (d i-1 = a), wherein M i (d i-1 = a) in particular;
M i (d i-1 ＝a)＝P(y 0 ,t i |t i-1 ,d i-1 ＝a)
＝exp(WED(s i-1 ,y 0 )+(m+λ)log(P t (1-P s ))),
wherein, P t Is the transmission probability; d is a radical of i-1 Is thatdThe (i-1) th sub-sequence with the length of m bits corresponds to a symbol value; a belongs to [0, q-1) ];
s i-1 denotes the i-1 st transmission sub-sequence, w λi-1 Is the lambdai-1 mark bit, d m(i-1) Is the m (i-1) th LDPC code bit; WED (WED)s i-1 , 0 y) Is a subsequence ofs i-1 And 0 ythe weighted edit distance between the two, calculated by dynamic programming (well known to those skilled in the art);
(4.1.5) calculating t i The time drift is a forward measurement value of tau:
wherein, t i = τ denotes the amount of shift at time i is τ, t i-1 And = c denotes that the offset amount at the i-1 th time is c. (4.1.6) τ = τ +1, if τ ≦ t max Repeating the steps (4.1.3) to (4.1.6), otherwise, jumping to the step (4.1.7);
(4.1.7) i = i +1, if i ≦ N, repeating steps (4.1.2) to (4.1.7); if i > N, jump to step (4.2).
(4.2) calculating the backward measurement B specifically comprises the following steps:
(4.2.1) initializing the backward metric value B at the Nth time N (t N τ) =1/T, where-T max ≤τ≤t max ；
(4.2.2) let i = N, b = -t max ，p(d i )＝1/2 m ；
(4.2.3) determination of beta (d) i ＝a,t i ＝τ,t i+1 ＝b, 0 y) If so, performing step (4.2.4); no, let M = beta (d) i ,t i ,t i+1 , 0 y) Step (4.2.6) is performed, wherein-t max ≤τ≤t max ；
(4.2.4) calculating an intermediate metric value M i+1 (d i = a), let β (d) i ,t i ,t i+1 , 0 y)＝M i+1 (d i = a), wherein M i+1 (d i Specific for a);
M i+1 (d i ＝a)＝P(y 0 ,t i+1 ∣t i ,d i ＝a)
＝exp(WED( i s,y 0 )+(m+λ)log(P t (1-P s )))，
wherein a is more than or equal to 0 and less than 2 m ，
WED( i s,y 0 ) Representing subsequences i sAndy 0 the weighted edit distance between the two, i s＝(w λi ,…,w λ×(i+1)-1 ,d mi ,…,d m×(i+1)-1 )。
(4.2.5) calculating t i The time drift amount is a backward measurement value of tau;
wherein i is more than or equal to 0 and less than N, d i Is composed ofdThe symbol value, t, corresponding to the ith m-bit sub-sequence i = τ denotes the offset at time i is τ, t i+1 = b denotes the i +1 th timeThe offset of (b) is b. (4.2.6) b = b +1, if b ≦ t max Repeating the steps (4.2.3) to (4.2.6), otherwise, jumping to the step (4.2.7);
(4.2.7) i = i-1, and if i ≧ 0, repeating steps (4.2.2) through (4.2.7); if i is less than 0, jumping to the step (4.3).
(4.3) calculating likelihood ratio sequence based on forward and backward metricl；
i - ＝n×i，i + ＝n×(i+1)， 0 rRepresenting received bits
(5) LDPC decoder using likelihood ratio sequenceslDecoding and outputting
The computational complexity required for conventional decoding algorithms is shown in table 1.
TABLE 1 computational complexity required for the conventional and improved algorithms
Calculating an intermediate metric, fixed d, using a dynamic programming method i ，t i ，t i+1 ， 0 yThe number of additions required is defined as a, where a =5NI max α (α + 1). Wherein α is a symbol length, α = m + λ, N is a mark code length, and I max Is the maximum number of consecutive insertions. The number of additions and multiplications of the backward metric values is the same as the forward metric values and will not be described.
Table 1 shows that the addition times of the forward metric values in the conventional decoding algorithm are (Xd-1) XN c A, the addition times of the forward metric values of the inner decoding algorithm in the embodiment of the invention are reduced to (Xd-1) XN c . Similarly, the number of additions of the backward measure is also from (Xd-1) XN c A is reduced to (Xd-1) XN c The number of times of addition is reduced to 1/A of the number of times of addition of the traditional decoding algorithm. Compared with the traditional decoding method, the method simplifies the calculation of the forward-backward metric value, improves the speed of an internal decoding algorithm, shortens the decoding time delay and does not cause performance loss.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (4)
1. A low complexity weighted edit distance based forward-backward decoding method, the method comprising:
binary information sequencebGenerating a length of N by an encoder of an LDPC code L Code word sequence of symbolsd；
Sign codewUniformly inserted into codeword sequencedIn (1), a length N is generated c Is transmitted as a codewordxAnd outputting;
transmitting code wordsxAfter insertion/deletion-substitution channel, the length is generated as
Receive sequence ofy(ii) a Watermark decoder uses low complexity forward-backward decoding to receive sequenceyDecoding and outputting likelihood ratio sequencel；
LDPC decoder using likelihood ratio sequenceslDecoding and outputting
2. The method as claimed in claim 1, wherein the flag code is applied to forward-backward decodingwUniformly inserted into codeword sequencedIn (1), a length N is generated c Is transmitted as a codewordxAnd the output is specifically:
dividing a binary LDPC code into N symbols, each symbol having m bits, wherein N = N L /m；
Inner encoder randomly generates mark code with length of NxLambdawCode the markwDividing into N subsequences of length lambda, coding the markwEach subsequence of (2) is inserted into a sequence of code wordsdBefore each symbol of (2), generating a length of N c Is transmitted as a codewordx。
3. The method of claim 1, wherein the watermark decoder uses low complexity forward-backward decoding to decode the received sequenceyDecoding and outputting likelihood ratio sequencelThe method comprises the following specific steps: calculating forward and backward metrics, and calculating likelihood ratio sequence based on the forward and backward metricsl；
Wherein the calculating the forward metric value is:
(4.1.1) initializing a forward metric value at a time i = 0;
initializing a lookup table; let the element beta (d) in the table i ,t i ,t i+1 , 0 y) =1, wherein d i ∈[0,q-1)，t i ∈[-x max ,x max ]； 0 yRepresenting the received subsequence, q representing a symbol value; let i =1; t =2T max +1，
T is the number of states per time, T max Is the maximum amount of drift, P d Representing the puncturing probability of the channel;
(4.1.2) let the symbol probability p (d) i )＝1/2 m ，d i As a sequence of code wordsdThe symbol value corresponding to the ith sub-sequence with the length of m bits; let τ = -t max ；
(4.1.3) determination of β (d) i ＝a,t i ＝c,t i+1 ＝τ, 0 y) If so, performing step (4.1.4); if not, let M i (d i-1 ＝a)＝β(d i ,t i ,t i+1 , 0 y) Executing the step (4.1.5); wherein, t i Is the drift amount at the ith time point, -t max ≤c≤t max ；
(4.1.4) calculating an intermediate metric value M i (d i-1 = a), let β (d) i ,t i ,t i+1 , 0 y)＝M i (d i-1 = a), wherein M i (d i-1 Specific for a);
M i (d i-1 ＝a)＝P(y 0 ,t i |t i-1 ,d i-1 ＝a)
＝exp(WED(s i-1 ,y 0 )+(m+λ)log(P t (1-P s ))),
wherein, P t Is the transmission probability; d i-1 Is thatdThe (i-1) th sub-sequence with the length of m bits corresponds to a symbol value; a is equal to [0, q-1);
s i-1 denotes the i-1 st transmission sub-sequence, w λi-1 Is the lambd i-1 mark bit, d m(i-1) Is the m (i-1) th LDPC code bit; WED (WED)s i-1 , 0 y) Is a subsequence ofs i-1 And 0 yweighted edit distance therebetween;
(4.1.5) calculating t i The time drift is a forward measurement value of tau:
wherein, t i = τ denotes the amount of shift at time i is τ, t i-1 = c denotes that the offset at the i-1 st time is c; (4.1.6) τ = τ +1, if τ ≦ t max Repeating the steps (4.1.3) to (4.1.6), otherwise, jumping to the step (4.1.7);
(4.1.7) i = i +1, if i ≦ N, repeating steps (4.1.2) to (4.1.7); if i > N, a backward metric is calculated.
4. The method as claimed in claim 3, wherein the calculating the backward metric value is specifically:
(4.2.1) initializing the backward metric value B at the Nth time N (t N = τ) =1/T, where-T max ≤τ≤t max ；
(4.2.2) let i = N, b = -t max ，p(d i )＝1/2 m ；
(4.2.3) determination of beta (d) i ＝a,t i ＝τ,t i+1 ＝b, 0 y) If it is less than 0, executing step (4.2.4); no, let M = β (d) i ,t i ,t i+1 , 0 y) Step (4.2.6) is performed, wherein-t max ≤τ≤t max ；
(4.2.4) calculating an intermediate metric value M i+1 (d i = a), let β (d) i ,t i ,t i+1 , 0 y)＝M i+1 (d i = a), wherein M i+1 (d i Specific for a);
M i+1 (d i ＝a)＝P(y 0 ,t i+1 ∣t i ,d i ＝a)
＝exp(WED( i s,y 0 )+(m+λ)log(P t (1-P s )))，
wherein a is more than or equal to 0 and less than 2 m ，
WED( i s,y 0 ) Representing subsequences i sAndy 0 the weighted edit distance between the two, i s＝(w λi ,…,w λ×(i+1)-1 ,d mi ,…,d m×(i+1)-1 )；
(4.2.5) calculating t i The time drift amount is a backward measurement value of tau;
wherein i is more than or equal to 0 and less than N, d i Is composed ofdThe symbol value, t, corresponding to the ith m-bit sub-sequence i = τ denotes the offset at time i is τ, t i+1 = b represents an offset amount b at the i +1 th time; (4.2.6) b = b +1, if b ≦ t max Repeating the steps (4.2.3) to (4.2.6), otherwise, jumping to the step (4.2.7);
(4.2.7) i = i-1, and if i ≧ 0, repeating steps (4.2.2) through (4.2.7).
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