CN106059596A - Packet Markov superposition coding method by taking binary BCH code as component code, and decoding method - Google Patents

Abstract

The invention belongs to the field of digital communication and digital storage, and discloses a packet Markov superposition coding method by taking a binary BCH code as a component code, and a decoding method. The binary BCH code having the code length of n, the information bit length of k and the error correcting capability of tmin is used as the component code; and a binary information sequence (u)u(/u) having the length of K=kBL is coded into a code (u)c(/u) having the length of N=nB(L+m). The invention further provides a soft iteration decoding method applicable to the packet Markov superposition coding method by taking the binary BCH code as the component code. The soft iteration decoding method comprises the following steps of: generating a turnover pattern according to a tree structure, judging whether a test process is ended or not and whether soft information output is calculated or not by using the lower bound of the unreliability of a potential legal error pattern, etc. According to the packet Markov superposition coding method and the decoding method thereof provided by the invention, the value of the coding memory length m is {1,2,3}; the net coding gain, which is greater than 10 dB, is provided at the bit error rate performance, which is as low as 10-10 to 10-15; and thus, the packet Markov superposition coding method and the decoding method thereof provided by the invention can be applied to a communication system having low bit error rate requirements, such as optical fibre communication.

Description

With binary BCH code be composition code packet markov supercomposed coding method and translate Code method

Technical field

The invention belongs to digital communication and numeral field of storage, particularly to a kind of with dividing that binary BCH code is composition code Group markov supercomposed coding method and interpretation method thereof.

Background technology

In optical communication system, the BCH code of conventional high code check (generally greater than 0.8) is as cascade/product Error Correction of Coding Composition code is to obtain high rate of information transmission and extremely low bit error rate (bit error rate, BER) (generally 10^-10To 10^-15 The order of magnitude).Such as, at International Telegraph Union Telecommunication The standard of Standardization Sector (ITU-T) G.975.1 in, expense be 6.7% BCH-BCH product code can be Output bit error rate is 10^-15Place provides the net coding gain (net coding gain, NCG) of 9.24dB.Open equally using Under conditions of pin, what ladder code (staircase code) can obtain 9.41dB under identical bit error rate encodes increasing only Benefit.But in the design process, under requiring to constant bit rate, ladder code needs to use the mode of force search to obtain and meets performance The design parameter required, considerably increases complexity and the workload of design process.

Packet markov supercomposed coding (Zhongshan University, a kind of packet markov supercomposed coding method [P]: CN105152060A) being a kind of coded method being constructed big convolutional code by short code, short code therein is referred to as basic code.Packet Ma Er The performance lower bound of husband's supercomposed coding can be defined by the performance of basic code and memory span m thereof, be m's for coded memory Packet markov supercomposed coding, its performance of BER can have up to 10log relative to the performance of BER of basic code₁₀ (m+1) gain of dB.For requiring 10^-10To 10^-15When the system of order of magnitude performance of BER is designed, if using short list Parity check code as becoming demal, then requires that system arranges the most tens of memory spans with short duplication code.Memory span is the biggest, The complexity of interpretation method is the highest, and this makes the program not be suitable for some to postponing to require in higher system.

Packet markov supercomposed coding method can be translated by based on Soft Inform ation stroke of window iterative algorithm or two benches Code algorithm (Zhongshan University, a kind of two benches decoding algorithm [P] about packet markov supercomposed coding: CN 103944590A) decode.When interpretation method relates to soft iterative decoding method, it is desirable to basic code provides a kind of software-redundancy Interpretation method is to realize soft iterative decoding process.When the base using binary BCH code composition packet markov supercomposed coding method When this yard, need also exist for providing a kind of software-redundancy interpretation method as the binary BCH code becoming demal.At present, binary BCH code is made For becoming conventional the having based on grid and decode two kinds based on Chase-II of software-redundancy interpretation method during demal.Based on grid Interpretation method is a kind of best practice, can set up state according to the structure of binary BCH code and be displaced through bcjr algorithm and obtain soft Information exports, but this method is only applicable to the short code that error correcting capability is less, spends for general binary BCH code complexity Height, is not particularly suited for real system.Interpretation method based on Chase-II is usually used in being grouped in the soft iterative decoding of Turbo code, The method is used to generally require by repeatedly attempting selected modifying factor.

Summary of the invention

The technical problem to be solved is for above-mentioned deficiency of the prior art, it is provided that a kind of with binary BCH code is the packet markov supercomposed coding method of composition code, and its method step is simple, it is achieved convenient, complexity is low.For The deficiency that at present the software-redundancy interpretation method of binary BCH code exists, the invention provides and a kind of possess end condition in advance Binary BCH code is as software-redundancy interpretation method during one-tenth demal.The present invention selectes the Descartes of satisfactory binary BCH code Long-pending as basic code, 10^-1511dB magnitude net coding gain needed for the bit error rate of magnitude reaches optical communication system is only required Coded memory m=1,2,3, coding and decoding can be reduced and postpone.A kind of binary BCH possessing end condition in advance that the present invention provides Code, as software-redundancy interpretation method during one-tenth demal, can adjust the calculating resource in each stage during soft iterative decoding Distribute thus design processes simplified and reduction decoding complexity, it may be assumed that increase at the initial stage of iteration and calculate the resource soft output of raising Accuracy, reduces calculating resource in the later stage of iteration and reduces expenses, can improve decoding performance in the case of delay is limited, Without the need for using modifying factor.

The technical solution used in the present invention is: a kind of be composition code with binary BCH code packet markov supercomposed coding Method, it is characterised in that: with code length as n, a length of k of information bit and error correcting capability are t_minBinary BCH code be composition code, For by the binary information sequence of length K=kBLuIt is encoded to the code word of length N=nB (L+m)c, its coded method includes following Step:

(1.1) by the information sequence of length K=kBLuIt is divided into L isometric packetu=(u ⁽⁰⁾,u ⁽¹⁾,…u ^(L-1)), each Block length is kB；For t=-1 ,-2 ... ,-(m-1) ,-m, the sequence of a length of nBv ^(t)Initialize；M is coded memory Length, for the positive integer more than or equal to 1；B is positive integer；

(1.1) at t=0,1 ..., the L-1 moment, by the sequence of a length of kBIt is divided into B group to enter Row [n, k] binary BCH code coding, obtains the coded sequence of a length of nBAnd combinev ^(t-1),v ^(t -²⁾,…v ^(t-^m)Calculate code wordcThe t subsequencec ^(t).Describedv ^(t)In conjunction withv ^(t-1),v ^(t-2),…,v ^(t-m)Calculate code word c T (t >=0) individual subsequencec ^(t)Carry out as follows:

Firstly, for 1≤i≤m, by sequencev ^(t-i)Send into interleaver Π_i, the sequence of a length of nB after being interweavedw ⁽ⁱ⁾；

Then, willv ^(t)Withw ⁽¹⁾,w ⁽²⁾,…,w ^(m)Send into aliasing device S symbol-by-symbol, obtain the sequence of a length of nBc ^(t)。

In coded method of the present invention, information sequenceuBeing binary sequence, aliasing device S is by bit mould 2 He symbol-by-symbol Arithmetical unit.Encoder C can be any type of encoder.Interleaver Π_iCan be any type of interleaver, 1≤i≤m.

The present invention propose a kind of be composition code with binary BCH code packet markov supercomposed coding method be applicable on The coded method stated, described interpretation method can use soft iterative decoding method, as drawn window interpretation method, relates to soft iterative process Two benches interpretation method etc..Described decoding algorithm is by overturning pattern Priority QueuesHard decision decoding device and legal error map Sample set ε forms, and comprises the following steps:

(2.1) configuration full test number of times T, T is positive integer.

(2.2) input Soft Inform ation；Hard decision sequence is obtained by the Soft Inform ation inputtedz, and unreliable degree seriesλ。

Described input Soft Inform ation refers to the iterative information of transmission, i.e. each bit of BCH code word in soft iterative decoding algorithm Log-likelihood ratio:

$L_j^a=ln\left(\frac{P_a(c_j=0)}{P_a(c_j=1)}\right),0\≤j\≤n-1,$

Wherein P_a(c_j=0) and P_a(c_j=1) prior probability that code word bits is 0 and 1 is represented respectively.

Described hard decision sequencez=(z₀,z₁,…,z_n-1Each component in) calculates by the following method,

Unreliable degree seriesλ=(λ₀,λ₁,…,λ_n-1Each component in) according toCalculate.

(2.3) initialize: order test counting τ=0；RightλSequence obtains ascending sequenceAnd calculateIn each component existλ In corresponding location index sequencea；As legal error pattern, z is calculated unreliable degree can not as the minimum currently encountered By degree λ^*, and willzPut in ε；WillIt is initialized as empty queue and full null graph sample is put intoIn.Institute in described step (2.3) The location index sequence obtaineda=(a₀,a₁,…,a_n-1) should meetDescribed legal error pattern is not The computational methods of reliability are as follows: given error patterne=(e₀,e₁,…,e_n-1), its unreliable degree is equal to

(2.4) following iteration is carried out, until τ >=T, orFor sky, orLower bound corresponding to stem element not Less than λ^*:In, call Hard decision decoding device and implement test decoding according to the upset pattern that head of the queue provides, and τ adds 1, if Successfully decoded, the legal error pattern obtained is put in ε, and calculates unreliable degree, if this unreliable degree is less than λ^*, then Assign it to λ^*；WillHead of the queue is assigned to f and goes out team, produces new upset pattern according to f based on tree construction, each for obtain Individual upset pattern calculates the unreliable degree lower bound of corresponding potential legal error pattern, Priority QueuesAccording to this lower bound conduct The upset pattern that lower bound is minimum is also positioned over head of the queue by magnitude relationship.

(2.5) Soft Inform ation is calculated finally according to the ε obtainedAnd export.Output Soft Inform ationCalculate by the following method:

(2.5.1) by legal error pattern set ε, codeword set is calculated in accordance with the following methods

$S_j^u=\left\{\underset{\‾}{c}\right|c_j=u,\underset{\‾}{c}=\underset{\‾}{z}+\underset{\‾}{e},\underset{\‾}{e}\∈\mathrm{\ϵ}\}$

(2.5.2) output Soft Inform ationCalculate by the following method:

If

IfThen

Wherein,With

Especially, the test interpretation method in described step (2.4) is described as follows: given upset pattern f=(f₀,f₁,…, f_n-1), at position { a_j|f_jAt=1,0≤j≤n-1} rightzOverturn, obtainzFlipped versionUse Hard decision decoding Device pairDecode.Wherein, Hard decision decoding device can use and include but are not limited to Berlekamp-Massey (BM) calculation The Hard decision decoding algorithms such as method, Euclidean algorithm, Welch-Berlekamp (WB) algorithm.

And, upset pattern production method based on tree construction is described as follows: given upset pattern f=(f₀,f₁,…, f_n-1), the rank of definition f are

If R (f) >=n-t_min, the most do not produce new upset pattern；Otherwise, its left son f is produced_↓With right brother f_→.Left youngster Sub-f_↓Carried out upset by f in position R (f)+1 to obtain.Right brother f_→Carried out overturning in position R (f) and R (f)+1 by f Arrive.

And, the computational methods of lower bound B (f) of potential legal error pattern are: given upset pattern f=(f₀,f₁,…, f_n-1),

The present invention compared with prior art has the advantage that

1, the present invention use binary BCH code as the one-tenth demal of packet markov supercomposed coding method, and based on product Other codings being applicable to optic communication of code are compared, and have holding basic code code check, the simple advantage of design process.

2, the present invention is compared with packet markov supercomposed coding method based on short duplication code and short parity check code, choosing Fixed satisfactory binary BCH code is as the one-tenth demal of packet markov supercomposed coding method, 10^-10To 10^-15The order of magnitude Under the requirement of bit error rate, required coded memory is m=1,2,3, it is possible to reduce coding and decoding postpones and complexity.

3, the present invention proposes a kind of for using binary BCH code as the packet markov supercomposed coding method becoming demal Binary BCH become the software-redundancy interpretation method of demal, the two benches that can be used for drawing a window interpretation method, relating to soft iterative process is translated In the interpretation methods such as code method.So that performance of BER can reach to be grouped the reason of markov supercomposed coding method Opinion lower bound.Compared with traditional based on grid chart and based on Chase-II software-redundancy interpretation method, there is complexity Low, it is not necessary to modifying factor to be set, and the advantage calculating resource stage adjustable strategies with optimization performance can be provided.No matter make The two benches interpretation method of soft iterative process is also related to, with use software-redundancy based on Chase-II by stroke window interpretation method Interpretation method is compared, and uses the method that the present invention proposes, and all has more excellent performance in waterfall district and decoding flat bed.

In sum, the present invention proposes a kind of using binary BCH code as composition code division group markov superposition volume Code method and interpretation method thereof, can be with coded memory m=1, and 2,3 reach optical communication system wants the performance of forward error correction coding Ask, reduce and postpone and reduce complexity.

Accompanying drawing explanation

Fig. 1 is with binary BCH code for becoming the flow chart of the software-redundancy interpretation method of demal.

The packet markov supercomposed coding method that Fig. 2 is composition code with binary BCH code uses when drawing window interpretation method Performance map.

Fig. 3 with binary BCH code be composition code packet markov supercomposed coding method use two benches interpretation method time Performance map.

Detailed description of the invention

Two specific embodiments are below described for the enforcement step of the present invention that remarks additionally and advantage.

Embodiment 1

This detailed description of the invention uses draws window interpretation method, and relative with using Chase-II software-redundancy interpretation method Ratio, illustrates the effectiveness of the binary BCH code software-redundancy interpretation method that the present invention proposes.Specific as follows:

Use BCH [31,16] as the one-tenth demal of packet markov supercomposed coding method, configure B=160.Drawing window Arranging decoding window size in interpretation method is (d+1) nBbits, wherein d=3m, uses Chase-II software-redundancy to translate respectively The software-redundancy interpretation method (configuration full test number of times T=256) of the binary BCH code that code method and the present invention propose carries out base Monte Carlo simulation experiment in the additive white Gaussian noise channel of binary phase shift keying.By Fig. 2, it is seen that relative to use Chase-II software-redundancy interpretation method, uses the software-redundancy interpretation method of binary BCH code of present invention proposition in waterfall district More excellent performance of BER is had with error floor.Use the software-redundancy interpretation method of the binary BCH code of present invention proposition, Statistics gained average test number of times at 2.5dB and 3.0dB is respectively 5.484020 and 3.315167, is below Chase-II Required testing time 8 times.

Embodiment 2

This detailed description of the invention uses two benches interpretation method, it is provided that one meets optical communication system forward error correction coding The coding and decoding scheme of performance requirement.Specific as follows:

Design is 10 in bit error rate^-15What place provided up 11dB magnitude net coding gain meets optical communication system requirement Packet Markov supercomposed coding method, use two benches interpretation method to decode, based on binary phase shift keying add Property Gaussian white noise channel carries out Monte Carlo simulation experiment and carries out performance evaluation.Wherein, the first stage of two benches decoding Use sliding window length limited (decoding window size is (d+1) nBbits, wherein d=m) draws window interpretation method.Use BCH [127,106], as becoming demal, configures B=50.Use the software-redundancy interpretation method of the binary BCH code of present invention proposition, Configuration full test number of times T=256.By the theory lower-bound of packet markov supercomposed coding method, the coding that can need is remembered Recall length m=2, therefore d=m=2 is set.Simulation result is shown in Fig. 3.As seen from Figure 3, it is 10 in bit error rate^-15Time, use two rank The net coding gain that the heuristic upper bound prediction that section decoding provides can reach is 11.3dB, reaches optical communication system and entangles forward direction The performance requirement of miscoding.

The above, be only presently preferred embodiments of the present invention, not impose any restrictions the present invention, every according to the present invention Technical spirit to any simple modification made for any of the above embodiments, change equivalent structure change, all still fall within skill of the present invention In the protection domain of art scheme.

Claims (7)

1. the packet markov supercomposed coding method being composition code with binary BCH code, is characterized in that: with code length as n, letter Breath bit length is k and error correcting capability is t_minBinary BCH code be composition code, for by the binary information sequence of length K=kBL RowuIt is encoded to the code word of length N=nB (L+m)c, its coded method comprises the following steps:

(1.1) by the information sequence of length K=kBLuIt is divided into L isometric packetu=(u ⁽⁰⁾,u ⁽¹⁾,…u ^(L-1)), each packet A length of kB；For t=-1 ,-2 ... ,-(m-1) ,-m, the sequence of a length of nBv ^(t)Initialize；Wherein, m is coded memory Length, for the positive integer more than or equal to 1；B is positive integer；

(1.2) at t=0,1 ..., the L-1 moment, by the sequence of a length of kBBe divided into B group carry out [n, K] binary BCH code coding, obtain the coded sequence of a length of nBAnd combinev ^(t-1),v ^(t-2),…v ^(t-m)Calculate code wordcThe t subsequencec ^(t)；Describedv ^(t)In conjunction withv ^(t-1),v ^(t-2),…,v ^(t-m)Calculate code wordcT (t >=0) individual subsequencecT () is carried out as follows:

Firstly, for 1≤i≤m, by sequencev ^(t-i)Send into interleaver Π_i, the sequence of a length of nB after being interweavedw ⁽ⁱ⁾；

Then, willv ^(t)Withw ⁽¹⁾,w ⁽²⁾,…,w ^(m)Send into aliasing device S symbol-by-symbol, obtain the sequence of a length of nBc ^(t)。

The most according to claim 1 a kind of be composition code with binary BCH code packet markov supercomposed coding method, its It is characterised by: the value of described coded memory length m is preferably 1,2 or 3.

3. the packet markov superposition interpretation method being composition code with binary BCH code, is characterized in that: described interpretation method Being applicable to the coded method described in claim 1, described interpretation method is by overturning pattern Priority QueuesHard decision decoding device and Legal error pattern set ε forms, and comprises the following steps:

(2.1) configuration full test number of times T, T is positive integer；

(2.2) input Soft Inform ation；Hard decision sequence is obtained by the Soft Inform ation inputtedz, and unreliable degree seriesλ；

The Soft Inform ation of described input is the log-likelihood ratio of BCH code each bit of word

$L_j^a=\ln \left(\frac{P_a(c_j=0)}{P_a(c_j=1)}\right),0\≤j\≤n-1,$

Wherein P_a(c_j=0) and P_a(c_j=1) prior probability that code word bits is 0 and 1 is represented respectively；

Described hard decision sequencez=(z₀,z₁,…,z_n-1Each component in) calculates by the following method,

$z_j=\left\{\begin{array}{c}1,L_j^a\≤0\\ 0,L_j^a>0\end{array}\right.,,0\≤j\≤n-1;$

Reliability sequenceλ=(λ₀,λ₁,…,λ_n-1Each component in) according toCalculate；

(2.3) initialize: order test counting τ=0；RightλSequence obtains ascending sequenceAnd calculateIn each component existλMiddle phase Corresponding location index sequencea；WillzUnreliable degree is calculated as the unreliable degree of the minimum currently encountered as legal error pattern λ^*, and willzPut in ε；WillIt is initialized as empty queue and full null graph sample is put intoIn；Described location index sequencea= (a₀,a₁,…,a_n-1) meetThe computational methods of the unreliable degree of described legal error pattern are as follows: Given error patterne=(e₀,e₁,…,e_n-1), its unreliable degree is equal to

(2.4) following iteration is carried out, until τ >=T, orFor sky, orLower bound corresponding to stem element be not less than λ^*:In, call Hard decision decoding device and implement test decoding according to the upset pattern that head of the queue provides, and τ adds 1, if decoding Successful then the legal error pattern obtained is put in ε, and calculate unreliable degree, if this unreliable degree is less than λ^*, then by it It is assigned to λ^*；WillHead of the queue is assigned to f and goes out team, produces new upset pattern according to f based on tree construction, turns over for each obtained Turn pattern and calculate the unreliable degree lower bound of corresponding potential legal error pattern, Priority QueuesAccording to this lower bound as size The upset pattern that lower bound is minimum is also positioned over head of the queue by relation；

(2.5) output Soft Inform ation is calculated finally according to the ε obtainedAnd export；Described output Soft Inform ationCalculate by the following method:

(2.5.1) by legal error pattern set ε, codeword set is calculated in accordance with the following methods

$S_j^u=\left\{\underset{\‾}{c}\right|c_j=u,\underset{\‾}{c}=\underset{\‾}{z}+\underset{\‾}{e},\underset{\‾}{e}\∈\mathrm{\ϵ}\},$

(2.5.2) output Soft Inform ationCalculate by the following method:

If

IfThen

Wherein,With

The most according to claim 3 a kind of be composition code with binary BCH code packet markov superposition interpretation method, its It is characterised by: the test interpretation method in step (2.4) is described as follows: given upset pattern f=(f₀,f₁,…,f_n-1), in place Put { a_j|f_jAt=1,0≤j≤n-1} rightzOverturn, obtainzFlipped versionUse Hard decision decoding device pairCarry out Decoding.

The most according to claim 3 a kind of be composition code with binary BCH code packet markov superposition interpretation method, its Be characterised by: described Hard decision decoding device use include Berlekamp-Massey (BM) algorithm, Euclidean algorithm, The Hard decision decoding algorithms such as Welch-Berlekamp (WB) algorithm.

The most according to claim 3 a kind of be composition code with binary BCH code packet markov superposition interpretation method, its It is characterised by: in step (2.4), upset pattern production method based on tree construction is described as follows: given upset pattern f=(f₀, f₁,…,f_n-1), the rank of definition f are

If R (f) >=n-t_min, the most do not produce new upset pattern；Otherwise, its left son f is produced_↓With right brother f_→；Described left youngster Sub-f_↓Carried out upset by described f in position R (f)+1 to obtain；Described right brother f_→By described f at position R (f) and R (f)+1 Carry out upset to obtain.

The most according to claim 3 a kind of be composition code with binary BCH code packet markov superposition interpretation method, its It is characterised by: in step (2.4), the computational methods of lower bound B (f) of potential legal error pattern are: given upset pattern f= (f₀,f₁,…,f_n-1),