CN110995282A - Forward/backward decoding method with completely overlapped paths - Google Patents
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Abstract
The invention discloses a forward/backward decoding method with completely overlapped paths, which comprises the following steps: 1) information sequencebGenerating a coded sequence by an LDPC encoderd(ii) a 2) Inserting watermark sequenceswAnd adopts octal phase shift keying modulation with the mapping rule of mu to output the modulated signalx(ii) a 3) Modulated signalxGeneration of received sequence via insertion/deletion-additive white gaussian noise channely(ii) a 4) Receiving sequence of watermark decoderyCorrecting insertion/deletion errors, outputting a likelihood sequencel(ii) a 5) LDPC decoder receptionlDecoding with logarithmic domain belief propagation decoding to output an estimate of the information sequence
The present invention further reduces the amount of memory and computation required for the forward/backward algorithm without degrading its performance.
Description
Technical Field
The invention relates to the field of digital communication error control coding, in particular to a forward/backward decoding method with completely overlapped paths.
Background
In a communication system, the transmission sequence will be affected by insertion and puncturing due to the sampling clock rate instability. Even a single insertion/deletion can cause catastrophic replacement errors, resulting in system out-of-synchronization and reduced system performance. How to design a coding algorithm for inserting/puncturing error correction codes is a challenging problem.
Early coding schemes for correcting insertion/puncturing belonged to algebraic construction codes, which were limited to correcting single insertion/puncturing errors or noise-limited errors. Subsequently, Yazdani devised a concatenated code that combines an internal watermark with an external Low Density Parity Check (LDPC) code that is capable of correcting multiple random insertion, puncturing, and Additive White Gaussian Noise (AWGN) errors. The inner decoder of the cascade code adopts a forward/backward decoder based on a probability domain to estimate the probability of insertion/deletion of each symbol and provides log-likelihood information (LLR) for the outer LDPC decoder; the outer decoder uses the LLRs to estimate the transmitted information of the source. The coding and decoding scheme of the concatenated code has excellent performance and is widely researched by scholars.
However, in conventional concatenated codes, the watermark decoder for correcting the insertion/deletion is based on a decoding trellis diagram containing a large number of redundant states, with the number of states corresponding to each time instant being equal. When the channel condition is bad, i.e. the insertion/deletion probability is high, in order to ensure the error positioning capability of the decoder, the number of corresponding states at each moment is increased; and, as the length of the concatenated code increases, the size of the decoding trellis becomes huge. The forward/backward decoding algorithm designed based on the decoding grid graph has too high calculation amount and large decoding time delay.
Disclosure of Invention
The invention provides a forward/backward decoding method with completely overlapped paths, which further reduces the storage amount and the calculation amount required by a forward/backward algorithm without reducing the performance of the forward/backward algorithm and is described in detail in the following:
a method of forward/backward coding with fully overlapped paths, the method comprising the steps of:
1) information sequencebGenerating a coded sequence by an LDPC encoderd；
2) Inserting watermark sequenceswAnd adopts octal phase shift keying modulation with the mapping rule of mu to output the modulated signalx；
3) Modulated signalxGeneration of received sequence via insertion/deletion-additive white gaussian noise channely；
4) Receiving sequence of watermark decoderyCorrecting insertion/deletion errors, outputting a likelihood sequencel；
5) LDPC decoder receptionlDecoding with logarithmic domain belief propagation decoding to output an estimate of the information sequence
Wherein, the step 4) comprises:
(4.1) calculating a backward metric;
(4.2) calculating the forward measurement at the ith moment, and pruning the grid graph by using the non-zero states of the backward measurement and the forward measurement to determine a state overlapping region;
(4.3) calculating likelihood probabilitiesl。
The calculation backward measurement specifically includes:
wherein, Γ'i+1A non-zero state containing the i +1 time backward metric; pbcThe transition probability is that the state at the previous moment is b and the state at the current moment is c;
the output probability when the state at the ith moment is b and the state at the (i + 1) th moment is c; y isi+b,,yi+cThe receiving sequence is a sub receiving sequence corresponding to the known ith time state as b and the i +1 th time state as c; b isi+1(c) The backward measurement value of the state c at the (i + 1) th moment; get Bi(b) The largest front β item, and storing the corresponding β states into Γ'i。
The forward metric at the ith time is specifically:
wherein-tmax≤a≤tmax，tmaxIs the maximum state value, a is the state, i is more than or equal to 0<N，Γi-1Non-zero state containing the forward metric at time i-1, Fi-1(c) Forward metric value, P, for state c at time i-1caThe transition probability is that the state of the previous moment is c and the state of the current moment is a;
the output probability is that the state at the ith-1 moment is c, and the state at the ith moment is a; y isi-1+c,…,yi-1+aA sub receiving sequence corresponding to the known i-1 time state as c and the known i-1 time state as a; gamma-shapedi-1The state set is a state set of which the forward metric value corresponding to the i-1 time is nonzero; take Fi(a) The largest top β entry, and store the corresponding β states into Γi。
The method comprises the following steps: adjusting the forward metric value with the backward metric value if
Fi(a)＝0；
Adjusting the backward metric value again with the forward metric value, if
Bi(b)＝0。
The technical scheme provided by the invention has the beneficial effects that:
1. based on the observation of the forward/backward measurement values on the traditional adaptive decoding grid graph, the invention designs a forward/backward decoding strategy with completely overlapped paths, aiming at the condition that the forward measurement or the backward measurement corresponding to some states is equal to zero, the strategy reasonably prunes the states, and limits the paths of forward transmission and backward transmission in an irregular narrow-band grid graph which is overlapped with each other;
2. in the process of watermark decoding, the deleted states do not participate in the calculation of forward/backward measurement and likelihood probability, so that the storage capacity and the calculation capacity of a watermark decoder can be reduced, and the speed of positioning insertion/deletion errors and recovering the sequence length of the watermark decoder is improved;
3. further, without significant performance loss, the memory and decoding complexity of the entire decoder is reduced.
Drawings
FIG. 1 is a system block diagram of a forward/backward decoding strategy with fully overlapping paths;
figure 2 is a constellation diagram for mapping mu;
FIG. 3 is a flow chart of calculating a forward metric;
FIG. 4 is a diagram of an adaptive puncturing state of a forward/backward decoding strategy with completely overlapping paths;
fig. 5 shows the frame error rate of the proposed algorithm and the conventional algorithm at different grid widths.
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.
In order to solve the problems in the background art, the invention provides a forward/backward decoding method with completely overlapped paths. The method prunes the forward/backward state below the threshold value, and further ensures that the transmission path of the backward measurement is consistent with the forward measurement. As the number of states in the decoding trellis becomes smaller, the amount of memory required for forward/backward decoding is reduced accordingly.
In order to further reduce the calculation amount required by the traditional forward/backward decoding, the invention introduces a forward/backward decoding grid diagram with completely overlapped paths, and designs a decoding algorithm on the basis of the grid diagram. In the invention, the forward transmission path is limited not only by the state metric value, but also by the non-zero backward metric value. Unlike the conventional scheme, in the proposed forward/backward decoding, when the backward state value of the trellis is zero, the corresponding forward state is further pruned, which will enlarge the overlapping area of the non-zero forward/backward state. Using the proposed decoding scheme, the amount of memory of the decoding algorithm can be reduced without affecting its performance compared to conventional schemes.
The invention provides a forward/backward decoding strategy with completely overlapped paths on the basis of self-adaptive cutting grid graphs. The definitions of some symbols are given first below:
information sequencebGenerating a code sequence by an outer encoderdWhereinbLength of KLOne bit of the data is transmitted to the receiver,dlength NL. Watermarking sequences of length NwUniform embeddingdAnd modulating according to the mapping mu. Modulated signalxGenerating a receive sequence over a channely. The watermark decoder willyInferring whether insertion/puncturing has occurred and calculating bit likelihood information in comparison to elements in a known symbol setl。δmaxIs the maximum number of decoding iterations, F, of the LDPC codei(a) Is a forward metric vector at time i, Bi(b) Is a backward measurement vector at the ith time, i is more than or equal to 0<N, T ∈ T is drift amount, namely state of grid graph, T ═ 2Tmax+1 is the number of states per time, xiFor the ith transmitted symbol, N is the transmitted sequencexI is the maximum insertion amount. Thereafter, the LDPC decoder utilizeslPerforming iterative decoding to output an estimate of the information sequence
Wherein the outer code is a binary LDPC code, the watermark code is a pseudo-random sequence,zelement z in (1)i～N(0,σ2) And σ is the standard deviation of the noise.
The invention provides a forward/backward decoding strategy with completely overlapped paths based on a self-adaptive cut grid diagram, which can reduce the decoding loss degree without obvious performance loss.
A forward/backward decoding strategy with completely overlapped paths according to the present invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the present invention includes the following five steps:
1) information sequencebGenerating a coded sequence by an outer LDPC encoderd；
2) Inserting watermark sequenceswAnd adopts octal phase shift keying modulation with the mapping rule of mu to output the modulated signalx；
3) Modulated signalxHigh in insertion/deletion-addition propertyGenerating a receive sequence for a white noise (ID-AWGN) channely；
4) Internal watermark decoder receiving sequenceyCorrecting insertion/deletion errors by adopting a forward/backward decoding strategy with completely overlapped paths and outputting a likelihood sequencel；
(4.1) calculating a backward metric;
(4.2) calculating a forward metric;
(4.3) calculating likelihood probabilitiesl。
5) LDPC decoder receptionlDecoding by using a logarithmic domain confidence propagation (BP) decoding algorithm to output an estimate of the information sequence
The following describes the specific implementation steps of the above five steps.
Inserting watermark sequence in the step 2), and adopting the step of octal phase shift keying modulation, comprising the following steps:
(2.1) coding the wordsdDividing the data into N parts, wherein each part comprises m bits;
(2.2) inserting a watermark bit every m bits, the length of the watermark code being NL/m；
(2.3) mapping m +1 bits composed of watermark bits and information bits to a symbol x in a constellation diagrami；
(2.4) N xiForming a transmission sequencex。
Modulated signal in step 3)xGenerating a receive sequence over a channelyComprises the following steps:
(3.1) transmitting symbol xiThrough the ID channel;
(3.2) the output of the ID channel is fed into the AWGN channel, resulting iny。
The backward measure calculated in the step (4.1) is specifically:
(4.1.1) initializing the ith ═ N +5tmaxBackward measure of time:
(4.1.2) judging that i < N, if the judgment condition is satisfied, calculating a backward measurement value:
wherein, Γ'i+1A non-zero state containing the i +1 th time backward measurement; pbcThe transition probability is that the state at the previous moment is b and the state at the current moment is c;
the output probability when the state at the i-th time is b and the state at the i + 1-th time is c, yi+b,…,yi+cThe receiving sequence is a sub receiving sequence corresponding to the known ith time state as b and the i +1 th time state as c; b isi+1(c) The backward measurement value of the state c at the (i + 1) th moment; get Bi(b) The largest front β item, and storing the corresponding β states into Γ'iSetting the backward measurement values corresponding to other states to be zero; and (4) if the judgment condition is not satisfied, jumping to the step (4.2).
Wherein the transition probability PbcAnd output probability
The calculation is well known to those skilled in the art, and the embodiment of the present invention will not be described in detail.
Step (4.2) calculates the forward measurement of the ith moment, prunes the grid diagram by using the non-zero state of the backward measurement and the forward measurement, and determines the state overlapping area which can be subdivided into the following steps:
(4.2.1) initializing the forward metric value at time 0:
(4.2.2) calculating the forward metric at the ith time:
wherein-tmax≤a≤tmax，tmaxIs the maximum state value, a is the state, i is more than or equal to 0<N，Γi-1Non-zero state containing the forward metric at time i-1, Fi-1(c) The forward measurement value of the state c at the i-1 th moment; pcaThe transition probability is that the state of the previous moment is c and the state of the current moment is a;
the output probability is that the state at the ith-1 moment is c and the state at the ith moment is a; y isi-1+c,…,yi-1+aΓ is the sub-receive sequence corresponding to the known i-1 time state being c and the i time state being ai-1The state set is a state set of which the forward metric value corresponding to the i-1 time is nonzero; take Fi(a) The largest top β entry, and store the corresponding β states into ΓiThe forward metrics for the other states are set to zero.
(4.2.3) adjusting the forward metric value with the backward metric value if
Fi(a)＝0；
(4.2.4) adjusting the backward metric value with the forward metric value if
Bi(b)＝0；
(4.2.5) judging that i < N, if the judgment condition is satisfied, repeating the steps (4.2.2) to (4.2.4), and if the judgment condition is not satisfied, jumping to the step (4.3).
Wherein, the step (4.3) calculates the likelihood sequencelComprises the following steps:
(4.3.1) calculating the conditional probability:
wherein,
wherein, αIIs equal to 1/(1- (P)i)I)，M＝2m，
The sub-reception sequences are in a condition that the state of time i is a and the state of time i +1 is b.
(4.3.2) calculating bit likelihood probabilities:
wherein,
represents known wiAnd d ismi+jA constellation point set corresponding to 1 hour; p: (y|dmi+j＝0,w) Is shown inwAnd dmi+jReceiving the sequence under the condition of 0yThe probability of (d); p: (y|d mi+j1, w) are as defined inwAnd dmi+jUnder the condition of 1, a sequence is receivedyThe probability of (d); p (d)mi+j＝0|yW) is as defined inwAnd a receiving sequenceyUnder the condition of (d)mi+jProbability of 0; p (d)mi+j＝1|yW) is as defined inwAnd a receiving sequenceyUnder the condition of (d)mi+jProbability of 1.
Step 5) LDPC decoder utilizationlPerforming iterative decoding to output an estimate of the information sequence
Comprises the steps oflSending the data to an LDPC decoder; by means of two-stage feedingDecoding by a logarithm domain BP decoding algorithm of the LDPC code; repeating the decoding steps until reaching the preset maximum iteration number deltamax。
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The invention uses the code length NLAt 4000, a binary regular LDPC code with a code rate of 1/2 is a special case, and introduces a forward/backward decoding method with completely overlapped paths provided by the present invention.
In the simulation, a pseudo-random sequence is used as an internal watermark code, a binary LDPC code is used as an external code, and the modulation mode is octal phase shift keying modulation. The transmission symbols are divided into N parts, N being 2000, each part comprising a number m of bits of 2,
the decoder of the LDPC code adopts a confidence propagation decoding algorithm and has the maximum iteration number delta max20 times, SNR 20dB, maximum number of insertions in the channel I5, Pi＝Pd，PiFor the insertion probability of the channel, PdIs the puncturing probability of the channel.
Fig. 4 records the state that the forward/backward metric value is not zero at each time, and compares with the conventional state diagram. In the figure, a is a traditional state distribution diagram with a non-zero forward/backward metric, and b is a forward/backward state distribution diagram with overlapped paths. In the diagram a, an overlapping area exists between a state area with a forward measurement being not zero and a state area with a backward measurement being not zero, but the overlapping area does not completely cover the state area. In the b diagram, the state region with the forward measurement not being zero completely overlaps with the state region with the backward measurement not being zero. Because the forward/backward decoding algorithm deletes the state which does not contribute much to the error correction capability, and the backward measurement is utilized to correct the transmission path of the forward measurement, the path widths of the forward measurement and the backward measurement in the grid graph are further limited; therefore, the storage capacity of a forward/backward decoding algorithm can be reduced, and the decoding speed of the watermark decoder is improved.
FIG. 5 shows a comparison of the performance of the proposed algorithm with the conventional algorithm, where FER represents the frame error rate, α is the width of the state region of the proposed algorithm, as shown, α145 corresponds to β ═ 50, and α2With 26 corresponding to two sets of parameters β -30, the proposed algorithm does not cause performance loss with reduced memory, almost completely fits the frame error rate of the conventional algorithm, especially when β -20, α3When the error frame rate is approximately equal to 17, the error frame rate of the algorithm is even lower than that of the traditional algorithm, and the performance is better than that of the traditional algorithm.
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 is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (4)
1. A forward/backward decoding method with completely overlapped paths, the method comprising the steps of:
1) information sequencebGenerating a coded sequence by an LDPC encoderd；
2) Inserting watermark sequenceswAnd adopts octal phase shift keying modulation with the mapping rule of mu to output the modulated signalx；
3) Modulated signalxGeneration of received sequence via insertion/deletion-additive white gaussian noise channely；
4) Receiving sequence of watermark decoderyCorrecting insertion/deletion errors, outputting a likelihood sequencel；
5) LDPC decoder receptionlDecoding with logarithmic domain belief propagation decoding to output an estimate of the information sequence
Wherein, the step 4) comprises:
(4.1) calculating a backward metric;
(4.2) calculating the forward measurement at the ith moment, and pruning the grid graph by using the non-zero states of the backward measurement and the forward measurement to determine a state overlapping region;
(4.3) calculating likelihood probabilitiesl。
2. The forward/backward decoding method with completely overlapped paths as claimed in claim 1, wherein said calculating the backward metric is specifically:
wherein, Γ'i+1A non-zero state containing the i +1 th time backward measurement; pbcThe transition probability is that the state at the previous moment is b and the state at the current moment is c;
the output probability when the state at the ith moment is b and the state at the (i + 1) th moment is c; y isi+b,…,yi+cThe sub-receiving sequence is corresponding to the known i +1 th time state as c and the i th time state as b; b isi+1(c) The backward measurement value of the state c at the (i + 1) th moment; i is more than or equal to 0 and less than N; get Bi(b) The largest front β item, and storing the corresponding β states into Γ'i。
3. The forward/backward decoding method with completely overlapped paths as claimed in claim 1, wherein the forward metric at the i-th time is specifically:
wherein-tmax≤a≤tmax，tmaxIs the maximum state value, a is the state, i is more than or equal to 0<N，Γi-1Non-zero state containing the forward metric at time i-1, Fi-1(c) Forward metric value, P, for state c at time i-1caThe state of the previous time is c, the state of the current time is cTransition probability when state is a;
the output probability is that the state at the ith-1 moment is c, and the state at the ith moment is a; y isi-1+c,…,yi-1+aA sub receiving sequence corresponding to the known i-1 time state as c and the known i-1 time state as a; gamma-shapedi-1The state set is a state set of which the forward metric value corresponding to the i-1 time is nonzero; take Fi(a) The largest top β entry, and store the corresponding β states into Γi。
4. The forward/backward decoding method with completely overlapped paths according to claim 1, wherein said method comprises:
adjusting the forward metric value with the backward metric value if
Fi(a)＝0；
Further, the forward metric value is used to adjust the backward metric value if
Bi(b)＝0。
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| US20040205445A1 (en) * | 2003-04-14 | 2004-10-14 | Shuzhan Xu | Turbo decoder employing simplified log-map decoding |
| CN106712901A (en) * | 2016-12-02 | 2017-05-24 | 天津大学 | Hard decision-directed forward and backward estimation method under symbol insertion and deletion channel |
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| US20040205445A1 (en) * | 2003-04-14 | 2004-10-14 | Shuzhan Xu | Turbo decoder employing simplified log-map decoding |
| CN106712901A (en) * | 2016-12-02 | 2017-05-24 | 天津大学 | Hard decision-directed forward and backward estimation method under symbol insertion and deletion channel |
Non-Patent Citations (1)
| Title |
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| 柳元: "插入/删节错误纠错码的研究", 《中国博士学位论文全文数据库信息科技辑》 * |
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