CN105577195A - Method for performing correction on belief propagation algorithm - Google Patents

Abstract

The invention discloses a method for performing correction on a belief propagation algorithm, comprising steps of obtaining an initial parameter when a iterations is k, updating bit information outputted by a bit node n and verification information outputted by a verification node m according to an initial parameter, enabling k=k+1, updating hard decision information of various bit nodes in order to obtain the value of the nth element of the hard decision vector at the kth interation and outputting a coding sequence according to a calculated value or executing flipping decoding. The invention can effectively mark the key trap set element scale causing the decoding leveling, effectively reduces the fault leveling of the simulation code work, has lower calculation complexity and good coding possibility and can better satisfy the high reliability transmission requirement of other communication systems like the optical transmission.

Description

A kind of method that belief propagation algorithm is revised

Technical field

The present invention relates to communication technical field, particularly relate to a kind of method that belief propagation algorithm is revised.

Background technology

When utilizing belief propagation algorithm (BeliefPropagation, BP) decoding, LDPC code (LowDensityParityCheckCode, low density parity check code; A kind of channel error correction encoding) the good decoding performance approaching shannon limit can be obtained, and then extensively studied.But, because belief propagation algorithm has higher error floor in decode procedure, therefore effective guarantee optical communication etc. the occasion of data highly-reliable transmission can not be needed.Therefore, the error floor how reducing LDPC code word is the key issue that it applies in Combat Command System.Appear at the trap collection that the error floor in BP decode procedure mainly comprises by LDPC check matrix to cause.

Trap collection is a kind of inherent structure in LDPC check matrix, decoding iteration detailed process is not taken into account in prior art, make it can not very accurate description decode procedure, so utilize the correction BP decoding algorithm of traditional trap collection conceptual design that code word and iterative information in decode procedure can not be utilized to show the feature come effectively locate trap element of set element, and then realize decoding performance lifting by collection destruction, cause the computation complexity of corresponding correction algorithm higher, be unfavorable for hardware implementing.In addition, part is revised BP decoding algorithm and is utilized the trap collection information of specific LDPC code word to design, so they are all be the design of certain LDPC code word, does not have versatility.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of method revised belief propagation algorithm, has the problem of higher error floor in order to solve belief propagation algorithm in prior art in decode procedure.

For solving the problems of the technologies described above, the invention provides a kind of method that belief propagation algorithm is revised, comprising:

Step S101, when iterations is k, obtains initial parameter;

Step S102, according to initial parameter, upgrades the bit information that bit node n exports;

Step S103, according to initial parameter, upgrades the check information that check-node m exports;

Step S104, makes k=k+1, upgrades the hard decision information of each bit node, and the value of vectorial n-th element when the secondary iteration of kth is sentenced in acquisition firmly;

Step S105, works as w _k=0, stop decoding, and export coding sequence z ^k, wherein, z ^kbe kth step iterative decoding firmly sentence vector, be by the vector of composition; w _kfor adjoint vector s ^k=z ^k× H ^tweight, H ^tit is the transposed matrix of the test matrix H of code word;

Work as w _k≠ 0 and k≤K _max, repeat above-mentioned steps S101 ~ 104; Wherein, K _maxfor the maximum iteration time of BP decoding;

Work as w _k≠ 0 and k=K _maxwhen+1, perform upset decoding.

Further, perform upset decoding, specifically comprise:

Calculate wherein, 0≤k≤K _max, and store current iteration hard decision result, be designated as z _a;

For each bit node, according to formula (K _max-G _n) mod (K _max/ 2) its unsteadiness is calculated; Wherein, G _nfor bit node n each iterative decoding result sum;

Select the maximum j of a unstable definite value bit node, form upset collection

For upset collection in element perform u _n=-sgn (u _n) I _max, wherein, I _maxrepresent any maximum likelihood value;

Re-execute step S101 ~ 104, and this step is calculated u _nas u in step S101 _ninitial value;

Work as w _k=0, stop decoding, and export coding sequence z ^k;

Work as w _k≠ 0 and continue to perform above-mentioned steps S102 ~ 104; Wherein for overturning the maximum iteration time of decoding;

Work as w _k≠ 0 and time, export z _a.

Further, during k=0, obtain initial parameter in the following manner:

u _n＝4y _n/δ ²；z _n＝(1-sgn(u _n))/2；u _mn＝0；v _mn＝0；

Wherein, m is the index value of check-node; N is the index value of bit node; N ∈ [1, N], m ∈ [1, M]; δ ²for noise variance; y _nfor receiving vector element; z _nfor firmly sentencing the value of the n-th element of vector; u _nfor the initial likelihood value of bit node n; u _mnfor check-node m passes to the check information of bit node n; v _mnfor bit node n passes to the variable information of check-node m.

Further, the bit information of bit node n output is upgraded according to formula (1);

$v_{mn}=u_n+\underset{m^{\′}\∈M\left(n\right)\backslash m}{\Σ}{u}_{m^{\′}n}---\left(1\right)$

Wherein, m' ∈ [1, M], but m' ≠ m.

Further, the check information of check-node m output is upgraded according to formula (2);

$u_{\mathrm{mn}}=2{\tanh }^{-1}\left(\underset{n^{\′}\∈N\left(m\right)\backslash n}{\mathrm{\Π}}\tanh \left(\frac{1}{2}{v}_{{\mathrm{mn}}^{\′}}\right)\right)---\left(2\right)$

Wherein, n' ∈ [1, N], but n' ≠ n.

Further, the hard decision information of each bit node is upgraded according to formula (3);

${\mathrm{\ϵ}}_n^k=u_n+\underset{m^{\′}\∈M\left(n\right)}{\Σ}{u}_{m^{\′}n}=v_{mn}+u_{mn}---\left(3\right)$

Obtain according to formula (4) and firmly sentence the value of vectorial n-th element when kth time iteration;

$z_n^k=(1-\mathrm{sgn}({\mathrm{\ϵ}}_n^k\left)\right)/2---\left(4\right).$

Beneficial effect of the present invention is as follows:

The inventive method effectively can mark the crucial trap element of set element causing decoding flat bed, reduce trap element of set element scale, effective error floor reducing emulation code word, there is lower computation complexity and good decoding performance, better can meet the demand of other communication system data high reliability transport such as optical communication.

Accompanying drawing explanation

Fig. 1 is the flow chart to the method that belief propagation algorithm is revised in the embodiment of the present invention;

Fig. 2 is the comparison schematic diagram of Mackay504 decoding performance under UPF-BP, BB-BP, BP algorithm in the embodiment of the present invention;

Fig. 3 is the comparison schematic diagram of IEEE576 decoding performance under UPF-BP, BB-BP, BP algorithm in the embodiment of the present invention.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, do not limit the present invention.

Embodiment of the present invention method designs for binary system (N, K) LDPC code word, and the test matrix of code word is H.Any code word c=[c ₁c ₂c _n] send into AWGN (AdditiveWhiteGaussianNoise, additive white Gaussian noise) channel and transmit after BPSK (BinaryPhaseShiftKeying, binary phase shift keying) modulation, modulating rule is x _n=1-2c _n, corresponding reception vector is y=[y ₁y ₂y _n], wherein y _n=x _n+ η _n(n=1,2 ... N), y _nfor receiving vector element.η _nfor zero mean Gaussian white noise, its noise variance is δ ².The vector of firmly sentencing of kth step iterative decoding is z ^k(0≤k≤K _max).W _kfor adjoint vector s ^k=z ^k× H ^tweight (H ^tthe transposed matrix of H).U _mnfor check-node m passes to the check information of bit node n; v _mnfor bit node n passes to the variable information of check-node m; The initial likelihood value of bit node n is u _n.In addition, the hard decision information of bit node n when kth iteration is k _maxthe maximum iteration time of BP decoding, G _nfor bit node n each iterative decoding result sum.

As shown in Figure 1, the method concrete steps of the embodiment of the present invention are as follows:

Step S101, when iterations is k, obtains initial parameter.During initial iteration, work as k=0; Obtain following parameter:

u _n＝4y _n/δ ²；z _n＝(1-sgn(u _n))/2；u _mn＝0；v _mn＝0；

Wherein, m is the index value of check-node; N is the index value of bit node; N ∈ [1, N], m ∈ [1, M].δ ²for noise variance; y _nfor receiving vector element; z _nfor firmly sentencing the value of the n-th element of vector; u _nfor the initial likelihood value of bit node n; u _mnfor check-node m passes to the check information of bit node n; v _mnfor bit node n passes to the variable information of check-node m;

Step S102, upgrades the bit information of bit node n output according to formula (1);

$v_{mn}=u_n+\underset{m^{\′}\∈M\left(n\right)\backslash m}{\Σ}{u}_{m^{\′}n}---\left(1\right)$

Wherein, m' ∈ [1, M], but m' ≠ m; That is: represent u _1n, u _2n..., u _{(m-1) n}, u _{(m+1) n}..., u _mnsummation, namely rejects u in read group total _mn, not to u _mnsue for peace.

Step S103, upgrades the check information of check-node m output according to formula (2);

$u_{\mathrm{mn}}=2{\tanh }^{-1}\left(\underset{n^{\′}\∈N\left(m\right)\backslash n}{\mathrm{\Π}}\tanh \left(\frac{1}{2}{v}_{{\mathrm{mn}}^{\′}}\right)\right)---\left(2\right)$

Wherein, n' ∈ [1, N], but n' ≠ n; That is: when even taking advantage of calculating, not to tanh (v _mn/ 2) carry out company to take advantage of.

Step S104, makes k=k+1, upgrades the hard decision information of each bit node according to formula (3);

${\mathrm{\ϵ}}_n^k=u_n+\underset{m^{\′}\∈M\left(n\right)}{\Σ}{u}_{m^{\′}n}=v_{mn}+u_{mn}---\left(3\right)$

Obtain according to formula (4) and firmly sentence the value of vectorial n-th element when kth time iteration;

$z_n^k=(1-sgn({\mathrm{\ϵ}}_n^k\left)\right)/2---\left(4\right)$

Whether step S105, detect iteration stopping condition and meet:

If w _k=0, stop decoding, and export coding sequence z ^k(z ^kbe kth step iterative decoding firmly sentence vector, be by the vector of composition); K≤K else if _max, repeat step S101 ~ 104, work as k=K _maxwhen+1, go to step S106.Wherein, K _maxfor the maximum iteration time of BP decoding.Wherein, w _kfor adjoint vector s ^k=z ^k× H ^tweight, H ^tit is the transposed matrix of the test matrix H of code word.

Step S106, performs upset decoding.

Calculate that is: when k gets different numerical value, by minimum w _kcorresponding k value assignment in and store current iteration hard decision result, be designated as z _a.

For each bit node, according to formula (K _max-G _n) mod (K _max/ 2) its unsteadiness is calculated.Select the maximum j of unstable definite value bit node and form upset collection wherein, G _nfor bit node n each iterative decoding result sum.

For upset collection in element perform u _n=-sgn (u _n) I _max, wherein, I _maxrepresent any maximum likelihood value.Then re-execute step S101 ~ 104, and this step is calculated u _nas u in step S101 _ninitial value, that is: in step S101, no longer by formula u _n=4y _n/ δ ²calculate u _nvalue, but will u be utilized _n=-sgn (u _n) I _maxthe numerical value calculated is as u _nvalue.Re-execute step S101 ~ 104, until or w _k=0 (works as w _k=0, stop upset decoding and export z ^k), in formula for overturning the maximum iteration time of decoding.

Step S107, upset decoding failure, exports z _a.

Below provide two examples to be described in detail:

Example 1

Utilize random LDPC code Mackay (504,252) (referred to as Mackay504) instantiation invention algorithm, structure correspondingly revises belief propagation LDPC decoder.The maximum iteration time of BP decoding is 50, and the maximum iteration time of upset decoding is 30.The backtracking thresholding τ value of BB-BP algorithm is 15.The element number of unstable trap collection gets the emulation testing that j=4 and j=9 carries out algorithm respectively.Test data is through being transmitted by awgn channel after BPSK modulation, and the average of noise is 0, variance is N0/2.

See Fig. 2, compared to original BP algorithm, UPF-BP (invention algorithm) and BB-BP algorithm all effectively reduce the error floor of Mackay504, and wherein UPF-BP algorithm decoding performance of the present invention is optimum.For emulation use two kinds of code words, as j=4, UPF-BP algorithm obtains the decoding performance suitable with BB-BP algorithm, and as j=9 the decoding performance of UPF-BP algorithm more than BB-BP algorithm.With BER=10 ^-6for example, Mackay504, UPF-BP algorithm (j=9) is obtained to the performance boost of about 0.45dB relative to BP algorithm, and BB-BP algorithm only obtains the performance boost of about 0.2dB.

Table 1

	1.8dB	2.1dB	2.4dB	2.7dB	3.0dB 4 -->
						BB-BP	34.28	26.32	18.95	13.14	8.32
UPF-BP(j＝9)	7.19	6.23	6.36	5.29	4.45
						UPF-BP(j＝4)	3.51	3.22	3.27	3.05	2.73

Table 1 gives Mackay504 average upset decoding number of times under UPF-BP and BB-BP algorithm and compares.As can be seen from data in table, under different upset collection length, the average upset decoding number of times needed for UPF-BP algorithm of the present invention is all less than BB-BP algorithm.Such as, for Mackay504 when 1.8dB, BB-BP algorithm on average needs to overturn decoding 34.28 times, and UPF-BP algorithm only needs 3.51 and 7.19 times respectively when j=4 and j=9.It can thus be appreciated that under this signal to noise ratio point, the required average upset decoding number of times of UPF-BP algorithm declines at most compared to BB-BP algorithm and can reach 10 times.

Example 2

Utilize irregular LDPC codes IEEE802.16 (576,288) (referred to as IEEE576) instantiation invention algorithm, structure correspondingly revises belief propagation LDPC decoder.The maximum iteration time of BP decoding is 50, and the maximum iteration time of upset decoding is 30.The backtracking thresholding τ value of BB-BP algorithm is 15.The element number of unstable trap collection gets the emulation testing that j=4 and j=9 carries out algorithm respectively.Test data is through being transmitted by awgn channel after BPSK modulation, and the average of noise is 0, variance is N0/2.

See Fig. 3, compared to BP algorithm before, UPF-BP and BB-BP algorithm all effectively reduces the error floor of IEEE576, and wherein UPF-BP algorithm decoding performance of the present invention is optimum.For emulation use two kinds of code words, as j=4, UPF-BP algorithm obtains the decoding performance suitable with BB-BP algorithm, and as j=9 the decoding performance of UPF-BP algorithm more than BB-BP algorithm.With BER=10 ^-5for example, IEEE576, UPF-BP algorithm (j=9) is obtained to the performance boost of about 0.3dB relative to BP algorithm, and BB-BP algorithm only obtains the performance boost of about 0.2dB.

Table 2

	1.8dB	2.1dB	2.4dB	2.7dB	3.0dB
						BB-BP	25.03	13.55	10.62	8.06	6.21
UPF-BP(j＝9)	6.95	5.57	5.03	4.57	4.69
						UPF-BP(j＝4)	3.50	3.12	3.05	2.97	2.81

Table 2 gives the IEEE576 comparison of the average upset decoding number of times under UPF-BP and BB-BP decoding.As can be seen from data in table, under different upset collection length, the average upset decoding number of times needed for UPF-BP algorithm of the present invention is all less than BB-BP algorithm.Such as, for IEEE576 when 1.8dB, BB-BP algorithm on average needs to overturn decoding 25.03 times, and UPF-BP algorithm only needs 3.50 and 6.95 times respectively when j=4 and j=9.It can thus be appreciated that under this signal to noise ratio point, the required average upset decoding number of times of UPF-BP algorithm declines at most compared to BB-BP algorithm and can reach 7 times.

Compared to existing technology, the present invention has following beneficial effect:

1), original trap collection only describes a kind of structure being harmful to decoding in LDPC check matrix, do not consider concrete decode procedure.Therefore, can not the decoding failure of accurate description LDPC code.The information concussion behavior that in methods combining BP decode procedure of the present invention, bit node occurs, provide the crucial trap element of set element (i.e. the element of unstable trap collection) that a kind of effective method mark causes decoding flat bed, effective reduction trap element of set element scale, and then significantly can reduce the number of times revising decoding trial needed for BP decoding algorithm; The error floor of various Different L DPC code word can be reduced more efficiently, there is lower computation complexity; Better can meet the demand of other communication system data high reliability transport such as optical communication.

2), the Candidate Set length of the select unstable trap element of set element of the inventive method is only code word size about 1%.The correction belief propagation algorithm utilizing the method to construct effectively destroys the unstable trap collection occurred in decode procedure, effectively reduces the error floor of emulation code word, has good decoding performance.

Although be example object, disclose the preferred embodiments of the present invention, it is also possible for those skilled in the art will recognize various improvement, increase and replacement, and therefore, scope of the present invention should be not limited to above-described embodiment.

Claims (6)

1. to the method that belief propagation algorithm is revised, it is characterized in that, comprising:

Step S101, when iterations is k, obtains initial parameter;

Step S102, according to initial parameter, upgrades the bit information that bit node n exports;

Step S103, according to initial parameter, upgrades the check information that check-node m exports;

Step S104, makes k=k+1, upgrades the hard decision information of each bit node, and the value of vectorial n-th element when the secondary iteration of kth is sentenced in acquisition firmly;

Step S105, works as w _k=0, stop decoding, and export coding sequence z ^k, wherein, z ^kbe kth step iterative decoding firmly sentence vector, be by the vector of composition; w _kfor adjoint vector s ^k=z ^k× H ^tweight, H ^tit is the transposed matrix of the test matrix H of code word;

Work as w _k≠ 0 and k≤K _max, repeat above-mentioned steps S101 ~ 104; Wherein, K _maxfor the maximum iteration time of BP decoding;

Work as w _k≠ 0 and k=K _maxwhen+1, perform upset decoding.

2. the method revised belief propagation algorithm as claimed in claim 1, is characterized in that, performs upset decoding, specifically comprises:

Calculate wherein, 0≤k≤K _max, and store current iteration hard decision result, be designated as z _a;

For each bit node, according to formula (K _max-G _n) mod (K _max/ 2) its unsteadiness is calculated; Wherein, G _nfor bit node n each iterative decoding result sum;

Select the maximum j of a unstable definite value bit node, form upset collection

For upset collection in element perform u _n=-sgn (u _n) I _max, wherein, I _maxrepresent any maximum likelihood value;

Re-execute step S101 ~ 104, and this step is calculated u _nas u in step S101 _ninitial value;

Work as w _k=0, stop decoding, and export coding sequence z ^k;

Work as w _k≠ 0 and continue to perform above-mentioned steps S102 ~ 104; Wherein for overturning the maximum iteration time of decoding;

Work as w _k≠ 0 and time, export z _a.

3. the method revised belief propagation algorithm as claimed in claim 1 or 2, is characterized in that, during k=0, obtain initial parameter in the following manner:

u _n＝4y _n/δ ²；z _n＝(1-sgn(u _n))/2；u _mn＝0；v _mn＝0；

Wherein, m is the index value of check-node; N is the index value of bit node; N ∈ [1, N], m ∈ [1, M]; δ ²for noise variance; y _nfor receiving vector element; z _nfor firmly sentencing the value of the n-th element of vector; u _nfor the initial likelihood value of bit node n; u _mnfor check-node m passes to the check information of bit node n; v _mnfor bit node n passes to the variable information of check-node m.

4. the method revised belief propagation algorithm as claimed in claim 3, is characterized in that, upgrades the bit information of bit node n output according to formula (1);

$v_{mn}=u_n+\underset{m^{\′}\∈M\left(n\right)\backslash m}{\Σ}{u}_{m^{\′}n}---\left(1\right)$

Wherein, m' ∈ [1, M], but m' ≠ m.

5. the method revised belief propagation algorithm as claimed in claim 4, is characterized in that, upgrades the check information of check-node m output according to formula (2);

$u_{mn}=2{\tanh }^{-1}\left(\underset{n^{\′}\∈N\left(m\right)\backslash n}{\Π}\tanh \right(\frac{1}{2}{v}_{m^{\′}n}\left)\right)---\left(2\right)$

Wherein, n' ∈ [1, N], but n' ≠ n.

6. the method revised belief propagation algorithm as claimed in claim 5, is characterized in that, upgrade the hard decision information of each bit node according to formula (3);

${\mathrm{\ϵ}}_n^k=u_n+\underset{m^{\′}\∈M\left(n\right)}{\Σ}{u}_{m^{\′}n}=v_{mn}+u_{mn}---\left(3\right)$

Obtain according to formula (4) and firmly sentence the value of vectorial n-th element when kth time iteration;

$z_n^k=(1-\mathrm{sgn}({\mathrm{\ϵ}}_n^k\left)\right)/2---\left(4\right).$