CN103731159A - Mixed domain fast Fourier transform (FFT) multi-system sum-product decoding algorithm for prior information iteration application - Google Patents

Abstract

The invention belongs to the communication field and provides a mixed domain FFT multi-system sum-product decoding algorithm for prior information iteration application. The algorithm is used for non-binary Low Density Parity Code (LDPC) decoding. Compared with the traditional mixed domain rapid FFT multi-system sum-product decoding algorithm, the algorithm has the advantages that the algorithm decoding performance can be greatly improved, iterations are reduced, the code length is shortened, the decoding efficiency is improved, the decoding algorithm hardware implementation complexity is reduced, and the algorithm is applicable to a high-speed transmission system.

Description

A kind of to the hybrid domain FFT multi-system of prior information iterated application and long-pending decoding algorithm

Technical field

The invention belongs to the communications field, is a kind of high performance interpretation method, can be applicable in high-speed transfer communication system, improves the reliability of system communication.

Background technology

In recent years, along with the raising rapidly of network bandwidth requirements, high speed information transmission system demand is growing.And in the high speed information transmission system generally adopting at present, conventionally need to carry out forward error correction (Forward Error Correction, FEC) and process the transmission performance that improves system.FEC is a kind of error control method, it refer to signal before being admitted to transmission channel in advance by the processing of encoding of certain algorithm, add the redundant code with the feature of signal own, at receiving terminal, according to respective algorithms, decode to the received signal, thereby find out the error code that produces and by the technology of its correction in transmitting procedure.

The fast development of high speed information transmission system, has proposed more and more higher requirement to FEC technology.High-performance, high-throughput, the FEC encoding and decoding algorithm of low complex degree becomes the most important thing in high speed transmission system.Therefore, meeting the LDPC(Low Density Parity Code of above-mentioned requirements, low density parity check code) code progressively becomes the main flow coded system in FEC technology.

Nonbinary LDPC code is compared with traditional binary system LDPC code, has higher decoding performance.It has the stronger ability of entangling burst noise and random noise, is particularly suitable for High Order Modulation System.And in high order modulation, be widely used under the real situation of high speed information transmission system, nonbinary LDPC code will have application and research and development prospect more widely.

The binary system LDPC code C (N, K) being defined in GF (2) finite field is a kind of linear block codes, and code length is N, and information bit is long is K, and code check is R=K/N, meets all conditions of linear block codes, can use Jiao Yanjuzhenshi H _{m * N}with generator matrix G _{m * (N-M)}describe.Different from other block codes is the check matrix H of LDPC code _{m * N}very sparse, in matrix, the number of 1 element is far smaller than 0 number, and this is the origin of its title just also.Just because of this, just can construct low complex degree, high performance LDPC decoded mode.Nonbinary LDPC code (NB-LDPC:Non-binary LDPC) can be regarded binary system LDPC code as at finite field gf (q), (q=2 ^p) on popularization, be also a kind of linear block codes, also can use check matrix H _{m * N}with generator matrix G _{m * (N-M)}describe.Different from binary system LDPC code is the check matrix H of nonbinary LDPC code _{m * N}in each non-zero element H _mntake from GF (q).

Decoding algorithm for nonbinary LDPC code, hybrid domain FFT multi-system and long-pending decoding algorithm are a kind of improvement decoding algorithms that is similar to the long-pending decoding algorithm of binary system LDPC code neutralization, its keynote idea is traditional identical with long-pending decoding algorithm with binary system LDPC code, why adopt hybrid domain and fast Fourier transform, object is effectively to reduce the computation complexity of decoding, improve hardware implementation possibility, and its algorithm performance is particularly behave excellently in the decoding algorithm of many Non-Binary LDPC Codeds.Although its performance is so excellent, for the decoding algorithm of the nonbinary LDPC code of high complexity, its high computation complexity remains a large bottleneck of hardware implementation.And how guaranteeing that its excellent decoding performance loss is little even decoding performance is more excellent in the situation that, and effectively reduce computation complexity, reduce decoding iterations, shorten code length, make it be more convenient for implementing, be to get a good eye at present an also difficult problem urgently to be resolved hurrily of value.

Summary of the invention

The invention provides a kind of to the hybrid domain FFT multi-system of prior information iterated application and long-pending decoding algorithm, for carrying out the decoding of nonbinary LDPC, compare with traditional hybrid domain FFT multi-system and long-pending decoding algorithm, this algorithm can improve decoding performance, and then can reduce iterations, shorten code length, thereby improve decoding efficiency, be convenient to hardware implementation.

A kind of hybrid domain FFT multi-system of prior information iterated application is compared with long-pending decoding algorithm with traditional territory FFT multi-system of closing with long-pending decoding algorithm of the present invention's proposition, mainly in decode procedure, variable message log-domain transforms to probability territory and upgrades variable node two parts and improve.

1) variable message log-domain transforms to probability territory

In this process, do following formula (1) (2) operation

$\&ForAll;i,0\&le;i<N,$ ?

be transformed into

${\stackrel{\&OverBar;}{Q}}_k^{(t-1)}=\exp \left({\stackrel{\&OverBar;}{q}}_k^{(t-1)}\right)/T,\&ForAll;k\&Element;\mathrm{GF}\left(q\right).---\left(2\right)$

Contrast traditional algorithm

${\stackrel{\&OverBar;}{Q}}_k^{(t-1)}={\stackrel{\&OverBar;}{q}}_k^{(t-1)}-\ln \left(T\right),\&ForAll;k\&Element;\mathrm{GF}\left(q\right).---\left(3\right)$

Can find, this algorithm is more pressed close to log-domain and is transformed to this operation original idea of probability territory, and the result that traditional algorithm obtains remains the information of log-domain, cannot guarantee it and be the satisfied fundamental property of 1 this probability domain information, thereby need the operations such as further normalization, and will be filled up by our this defect of this algorithm, algorithm is more efficient strong.

2) upgrade variable node

This part, this algorithm is done the operation of following formula (4) (5)

●

upgrade variable node reliability vector LQ ^(t):

${\mathrm{LQ}}_k^{\left(t\right)}={\mathrm{\&lambda;}}^k+\underset{j\&Element;M\left(i\right)}{\mathrm{\&Sigma;}}{r}_k^{\left(t\right)}\{j,i\},\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.---\left(4\right)$

● calculate q ^(t)external information:

$q_k^{\left(t\right)}\{i,j\}={\mathrm{LQ}}_k^{\left(t\right)}-r_k^{\left(t\right)}\{j,i\},\&ForAll;k\&Element;M\left(i\right),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.---\left(5\right)$

● return to step 0.

Contrast traditional algorithm

●

upgrade variable node reliability vector LQ ^(t):

${\mathrm{LQ}}_k^{\left(t\right)}=\underset{j\&Element;M\left(i\right)}{\mathrm{\&Sigma;}}{r}_k^{\left(t\right)}\{j,i\},\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.---\left(6\right)$

●

calculate q ^(t)external information:

$q_k^{\left(t\right)}\{i,j\}={\mathrm{LQ}}_k^{\left(t\right)}-r_k^{\left(t\right)}\{j,i\},\&ForAll;k\&Element;M\left(i\right),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.---\left(7\right)$

● return to step 0.

Obviously, this algorithm is upgrading variable node reliability vector LQ ^(t)process in, additionally add the initial priori probability information obtaining from channel, in the renewal variable node step of each iterative decoding process, all adopt this mode.This variation seems simply, but its shortening to the reduction of the lifting of algorithm decoding performance, iterations and code length plays the important and pivotal role.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, to the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skills, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.

Fig. 1 is a kind of to the hybrid domain FFT multi-system of prior information iterated application and the schematic flow sheet of long-pending decoding algorithm

Fig. 2 is decoding judgement partial interior schematic flow sheet

Fig. 3 is for upgrading check-node partial interior schematic flow sheet

Fig. 4 is for upgrading variable node partial interior schematic flow sheet

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment is only the present invention's part embodiment, rather than whole embodiment.Embodiment based in the present invention, those of ordinary skills, not making the every other embodiment obtaining under creative work prerequisite, belong to the scope of protection of the invention.

A kind of specific implementation process to the hybrid domain FFT multi-system of prior information iterated application and long-pending decoding algorithm is as follows:

We represent 2 with H ^pthe check matrix of system LDPC code, k element v of vector v _krepresent the element h of the capable i row of j in H _jirepresent, first we first define the symbol that needs in subsequent algorithm to use:

λ: channel transfer is to the prior information of variable node

Q ^(t){ i, j}: in the t time iterative process, variable node i passes to the information of check-node j

R ^(t){ j, i}: in the t time iterative process, check-node j passes to the information of variable node i

LQ ^(t): the reliability information vector that finally carries out decoding judgement at the t time iterative decoding

N (j): the set of all variable nodes that are connected with check-node j

M (i): the set of all check-nodes that are connected with variable node i

N (j) remove variable node i in i:N (j)

M (i) remove check-node j in j:M (i)

GF (q): 0 to q-1 q number

$\mathrm{GF}{\left(q\right)}^{*}:\mathrm{GF}{\left(q\right)}^{*}=\{\&PartialD;,{\&PartialD;}^2,...{\&PartialD;}^{q-2},{\&PartialD;}^{q-1}=1\}$

Next, this algorithm implementation step is specifically described

Step-1:101, initialization

● t=0 is set.

● $\&ForAll;i,0\&le;i<N,$ Calculate ${\mathrm{\&lambda;}}_k=\ln (\mathrm{Pr}(v_i=k|z)/\mathrm{Pr}(v_i=0|z)),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*},$ Here z is the signal vector receiving.

● $\&ForAll;i,0\&le;i<N,$ Order ${\mathrm{LQ}}_k^{\left(0\right)}={\mathrm{\&lambda;}}_k$ And $q_k^{\left(0\right)}={\mathrm{\&lambda;}}_k,\&ForAll;j\&Element;M\left(i\right),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.$

● $\&ForAll;j,0\&le;j<M,$ Order $r_k^{\left(0\right)}\{j,i\}=0,\&ForAll;i\&Element;N\left(j\right),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.$

Step 0:102, decoding judgement

● 201, pass through

${\hat{v}}_i=\underset{k\&Element;\mathrm{GF}\left(q\right)}{\arg \max }\left\{{\mathrm{LQ}}_k^{\left(t\right)}\right\},\&ForAll;i,0\&le;i<N.---\left(8\right)$

Calculate code word estimate vector v.

● 202, stop to detect:

If there is one of them in following three kinds of situations

vH ^T＝0，

reach maximum iteration time t _max,

reach other end conditions

Decoding stops, and return vector as estimating code word;

Otherwise, increasing iterations, t=t+1, carry out step 1.

Step 1:103, variable message are reset

$\&ForAll;i,0\&le;i<N,$ Q ^(t-1)be transformed into

by

${\stackrel{\&OverBar;}{q}}^{(t-1)}\{i,j\}=q_{k\&CenterDot;e^{-1}}^{(t-1)}\{i,j\},\&ForAll;j\&Element;M\left(i\right),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*},---\left(9\right)$

Wherein multiplying is the multiplying on GF (q), and e=h _ji∈ GF (q) be check matrix H the weights of corresponding Turner figure top, and e ^-1∈ GF (q) is its inverse.

Step 2:104, variable message log-domain transform to probability territory

$\&ForAll;i,0\&le;i<N,$ ?

be transformed into

${\stackrel{\&OverBar;}{Q}}_k^{(t-1)}=\exp \left({\stackrel{\&OverBar;}{q}}_k^{(t-1)}\right)/T,\&ForAll;k\&Element;\mathrm{GF}\left(q\right).---\left(11\right)$

Step 3:105, renewal check-node

$\&ForAll;j,0\&le;j<M,$ Calculate

${\stackrel{\&OverBar;}{R}}^{\left(t\right)}\{j,i\}=\mathrm{\&Psi;}\left({\stackrel{\&OverBar;}{Q}}^{(t-1)}\right\{i^{\&prime;},j\},{\&ForAll;i}^{\&prime;}\&Element;N\left(j\right)\backslash i),\&ForAll;i\&Element;N\left(j\right).---\left(12\right)$

Further, can be subdivided into following a few step by wushu (10)

● 301,

right

be 2 FFT of p dimension, result still turns back to

in:

${\stackrel{\&OverBar;}{Q}}^{(t-1)}\{i,j\}=\mathrm{FFT}\left({\stackrel{\&OverBar;}{Q}}^{(t-1)}\right\{i,j\left\}\right).---\left(13\right)$

● 302,

?

transform to log-domain, and represent by the logarithm value of its symbol and absolute value:

${\stackrel{\&OverBar;}{Q}}^{(t-1)}\{i,j\}=(\mathrm{sign}\left({\stackrel{\&OverBar;}{Q}}^{(t-1)}\right\{i,j\left\}\right),\ln \left(\right|{\stackrel{\&OverBar;}{Q}}^{(t-1)}\{i,j\}\left|\right)).---\left(14\right)$

● 303, to all logarithm value size summation obtaining, obtain and be stored in A, the symbol of all logarithms that obtain is done to XOR, the result obtaining is stored in S:

$A_k=\underset{i\&Element;N\left(j\right)}{\mathrm{\&Sigma;}}\ln \left(\right|{\stackrel{\&OverBar;}{Q}}_k^{(t-1)}\{i,j\}\left|\right),\&ForAll;k\&Element;\mathrm{GF}\left(q\right),---\left(15\right)$

$S_k=\underset{i\&Element;N\left(j\right)}{\&CirclePlus;}\mathrm{sign}\left({\stackrel{\&OverBar;}{Q}}_k^{(t-1)}\right\{i,j\left\}\right),\&ForAll;k\&Element;\mathrm{GF}\left(q\right),---\left(16\right)$

Here represent XOR.

● 304,

in probability territory, calculate outside probabilistic information X{j, i}:

$X_k\{j,i\}=(S_k\&CirclePlus;\mathrm{sign}\left({\stackrel{\&OverBar;}{Q}}_k^{(t-1)}\right\{i,j))\&CenterDot;\exp (A_k-\ln \left(\right|{\stackrel{\&OverBar;}{Q}}_k^{(t-1)}\{i,j\}\left|\right)),\&ForAll;k\&Element;\mathrm{GF}\left(q\right),---\left(17\right)$

The multiplication here and subtraction are all the computings of real number field.

● 305,

to X{j, i} carries out the IFFT computing of 2 of p dimensions, obtains result and is defined as

${\stackrel{\&OverBar;}{R}}^{\left(t\right)}\{j,i\}=\mathrm{IFFT}\left(X\right\{j,i\left\}\right),---\left(18\right)$

Step 4:106, verification message probability territory transform to log-domain

$\&ForAll;i,0\&le;i<N,$ ? be transformed to

${\stackrel{\&OverBar;}{r}}_k^{\left(t\right)}=\ln \left({\stackrel{\&OverBar;}{R}}_k^{\left(t\right)}\right)-\ln \left({\stackrel{\&OverBar;}{R}}_0^{\left(t\right)}\right),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.---\left(19\right)$

Step 5:107, verification message are reset

$\&ForAll;i,0\&le;i<N,$ ? be transformed to r ^(t)

$r_k^{\left(t\right)}\{j,j\}={\stackrel{\&OverBar;}{r}}_{k\&CenterDot;e}^{\left(t\right)}\{j,i\},\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*},---\left(20\right)$

The multiplication is here the computing on GF (q), and e=h _ji∈ GF (q) be check matrix H the weights of corresponding Turner figure top.

Step 6:108, renewal variable node

● 401,

upgrade variable node reliability vector LQ ^(t):

${\mathrm{LQ}}_k^{\left(t\right)}={\mathrm{\&lambda;}}^k+\underset{j\&Element;M\left(i\right)}{\mathrm{\&Sigma;}}{r}_k^{\left(t\right)}\{j,i\},\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.---\left(21\right)$

● 402,

calculate q ^(t)external information:

$q_k^{\left(t\right)}\{i,j\}={\mathrm{LQ}}_k^{\left(t\right)}-r_k^{\left(t\right)}\{j,i\},\&ForAll;j\&Element;M\left(i\right),\&ForAll;k\&Element;\mathrm{GF}{\left(q\right)}^{*}.---\left(22\right)$

● 403, return to step 0.

Specific embodiment of the invention step can be simple be summarized in that initialization, variable message are reset, variable message log-domain is transformed into probability territory, upgrade check-node, verification message probability territory is transformed into log-domain, verification message is reset, upgrade variable node and decoding judgement eight step greatly.

The above; be only the specific embodiment of the present invention, but protection scope of the present invention is not limited to this, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; can expect easily changing or replacing, within all should being encompassed in protection scope of the present invention.Therefore, described in protection scope of the present invention, the protection range with claim is as the criterion.

Claims (10)

1. to the hybrid domain FFT multi-system of prior information iterated application and a long-pending decoding algorithm, it is characterized in that, comprise the following steps:

(1) initialization: calculate initial value and iterations is set according to receipt message;

(2) decoding judgement: compute codeword estimate vector, carries out decoding and stops detecting;

(3) variable message is reset: according to weights on the corresponding Turner figure of nonbinary check matrix limit, carry out variable message rearrangement;

(4) variable message log-domain is transformed into probability territory: the probability messages of variable node log-domain is transformed into the corresponding probability messages in probability territory;

(5) upgrade check-node: the probability messages of coming according to variable node transmission is calculated the check-node information of upgrading;

(6) verification message probability territory is transformed into log-domain: the probability messages on check-node probability territory is transformed on log-domain;

(7) verification message is reset: according to weights on the corresponding Turner figure of nonbinary check matrix limit, carry out verification message rearrangement;

(8) upgrade variable node: the log-domain probability messages of coming according to check-node transmission is calculated the reliability information that upgrades variable node, returns to step (2).

2. (1) according to claim 1 initialization step, it is characterized in that: current iterations and maximum iteration time are set, according to reception information, calculate prior probability log-likelihood ratio, and information, decoding decision reliability information that variable node i passes to check-node j, give prior probability log-likelihood and be compared to initial value, the information that check-node j is passed to variable node i composes 0 as initial value.

3. (2) according to claim 1 decoding decision steps, is characterized in that, comprises the following steps:

(1) try to achieve and make the vector of reliable probability maximum as code word estimate vector;

(2) carrying out decoding stops detecting, if the transposition multiplied result of code word estimate vector and check matrix is null vector, or reach maximum iteration time, or run into the situation that meets other end conditions, decoding finishes to return code word estimate vector, otherwise iterations adds 1, proceed step (3).

4. (3) according to claim 1 variable message rearrangement step, is characterized in that: the corresponding variable node i of the corresponding k/e of one-tenth of information that the corresponding variable node i of k is passed to check-node j passes to the information of check-node j, wherein

and

e is weights on the corresponding Turner figure of nonbinary check matrix limit, e=h _ji∈ GF (q).

5. (4) according to claim 1 variable message log-domain is transformed into probability territory step, it is characterized in that: the log-domain information conversion that first the corresponding variable node i of all k values is passed to check-node j, to probability territory, is sued for peace according to formula (a)

Then the information that transforms to probability territory that passes to check-node j with the corresponding variable node i of k value divided by and T, by formula (b), be normalized operation

。

6. (5) according to claim 1 upgrade check-node step, it is characterized in that, comprise the following steps:

(1) the probability domain information that variable node i is passed to check-node j carries out 2 FFT operations of p dimension;

(2) the probability domain information that variable node i is passed to check-node j transforms to log-domain, tries to achieve its corresponding symbol and logarithm value;

(3) to all logarithm value size summation obtaining, obtain and be stored to A _kin, the symbol of all logarithms that obtain is done to XOR (or quadrature) computing, the result obtaining is stored to S _kin;

(4) in probability territory, according to formula (c), calculate outside probabilistic information X{j, i};

(5) to X{j, i} carries out the IFFT computing of 2 of p dimensions, and the check-node j after being upgraded passes to the probability domain information of variable node i.

7. (6) according to claim 1 verification message probability territory is transformed into log-domain step, it is characterized in that: the check-node j after the renewal that step (5) is obtained passes to the probability domain information of variable node i, asks its likelihood ratio.

8. (7) according to claim 1 verification message rearrangement step, it is characterized in that: the corresponding check-node j of the corresponding k * e of one-tenth of log-domain information that the corresponding check-node j of k is passed to variable node i passes to the log-domain information of variable node i, wherein

and

e is weights on the corresponding Turner figure of nonbinary check matrix limit, e=h _ji∈ GF (q).

9. (8) according to claim 1 upgrade variable node step, it is characterized in that, comprise the following steps:

(1) upgrade variable node reliability vector LQ ^(t), for decoding, adjudicate;

(2) calculate and upgrade the log-domain probabilistic information that variable node i passes to check-node j, for next round iteration;

(3) return to decoding decision steps.

10. (1) according to claim 9 upgrades variable node reliability vector LQ ^(t)step, is characterized in that: variable node reliability vector LQ ^(t)the log-domain information transmitting by all check-nodes relevant with variable node i and add the initial priori probability information that it is corresponding,

Images