CN102811065B - Mini-sum decoding correcting method based on linear minimum mean error estimation - Google Patents
Mini-sum decoding correcting method based on linear minimum mean error estimation Download PDFInfo
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Abstract
The invention relates to a mini-sum decoding correcting method based on linear minimum mean error estimation. The method comprises the steps of establishing a model on a check message amplitude by a linear minimum mean error estimation method, and accelerating the determination of an estimation parameter by a golden section search algorithm to enable the estimation value approach to the check message amplitude in an error back propagation (BP) method; and revising the estimation parameter by taking the influence of the iterative times on the estimation parameter into consideration. According to the mini-sum decoding correcting method, a fixed estimation parameter is applied to different signal to noise ratios, so as to ensure the decoding performance and to reduce the expense of the hardware; the low density parity check (LDPC) code is decoded after the estimation parameter is obtained. The method not only ensures an excellent decoding performance but guarantees a rapid calculation of the estimation parameter; and is low in decoding complexity and simple in implementation of the hardware.
Description
Technical field
The present invention relates to LDPC coding techniques field, particularly minimum the and coding/decoding method of a kind of correction based on Linear Minimum Mean-Square Error Estimation for standards such as ground digital multimedia TV broad cast DTMB, the second generation satellite digital video broadcast DVB-S2, IEEE802.11n, IEEE802.16e, CCSDS.
Background technology
The soft-decision decoding method that LDPC code is general is based upon on belief propagation (BP) algorithm basis, improves confidence level, thus reach the object of decoding by outer message is transmitted iteration between variable node and check-node.But the computing of BP algorithm check-node Message Processing is too complicated, and hardware implementing expense is larger.Minimum-sum algorithm is a kind of simplification to BP algorithm, and it is in check-node Message Processing, replaces the functional operation in BP algorithm, operand is reduced greatly by minimum value, but its decoding performance have an appointment 0.5 to 1dB loss.In order under the prerequisite not increasing operand, improve the decoding performance of minimum-sum algorithm, mainly contain at present two kinds minimum and correction algorithm, i.e. Normalized BP-Based algorithm and Offset BP-Based algorithm.
The modification method of Normalized BP-Based algorithm is:
，
(11)
The modification method of Offset BP-Based algorithm is:
，
(12)
In formula (11) and (12), L
1for the amplitude of verification message in BP algorithm, L
2for the amplitude of verification message in minimum-sum algorithm,
for the estimated value of verification message amplitude.
Above-mentioned two kinds of correction algorithms are all by introducing modifying factor (a or b) improve decoding performance.But the value needed for drawn modifying factor subvalue and reality exists a certain distance, therefore the mean square error of verification message amplitude valuation is comparatively large, and decoding performance and BP algorithm have a certain distance.
In practical engineering application, also adopt Monte Carlo Method to determine its modifying factor, valuation more accurately can be obtained, but owing to needing a large amount of computer sim-ulation experiments, therefore considerably increase amount of calculation.
Summary of the invention
The object of the invention is to overcome the deficiencies in the prior art, provide a kind of correction based on Linear Minimum Mean-Square Error Estimation minimum and coding/decoding method, the method not only decoding performance is superior, and estimated parameter calculates fast, and decoding complex degree is low, and hardware implementing is simple.
For achieving the above object, technical scheme of the present invention is:
Definition
c i represent and variable node
ithe set of the check-node be connected,
r j represent and check-node
jthe set of the variable node be connected,
c i jexpression removes
jouter and variable node
ithe set of the check-node be connected,
r j iexpression removes
ithe set of the outer variable node be connected with check-node,
l(
r ji ) represent check-node
jpass to variable node
iexternal information,
l(
q ij ) represent variable node
ipass to check-node
jexternal information,
crepresent code word;
l 1for the verification message amplitude in BP algorithm, its value is:
(1)
Wherein, (
l-1) represent the (
l-1) secondary iteration;
Wherein
;
l 2 for the verification message amplitude in minimum-sum algorithm, its value is:
(2)
The method is carried out as follows:
Step 1, set up the estimation model of verification message amplitude: based on Linear Minimum Mean-Square Error Estimation model, and combine revise after the constant principle of the symbol of verification message, verification message amplitude is set up such as formula the estimation model shown in (3):
(3)
Wherein
a,
bfor calculative estimated parameter;
Step 2, calculating make mean square error function
minimum estimated parameter
a,
b:
Step 2.1, hypothetical boundary
for constant
, when
time, can obtain estimated parameter is:
(4)
Wherein, cov (
l 1,
l 2) represent
l 1with
l 2covariance,
d(
l 2) represent
l 2variance,
e(
l 1),
e(
l 2) represent respectively
l 1,
l 2mean square error;
Step 2.2, compare and to calculate
with
whether equal, if
, obtain
a,
bnot right value, give up; If
, then obtain
a,
bright value;
Step 2.3, employing golden section search algorithm, carry out iteration by above-mentioned steps 2.1,2.2, determine border fast
k, then obtain estimated parameter according to formula (4)
a,
b;
Step 3, according to iterations, estimated parameter to be revised:
By formula (5), average treatment is weighted to the estimated parameter that front n iteration obtains, obtains revised estimated parameter
a,
b, and fixing estimated parameter is used to each time later iteration:
(5)
Wherein,
a i represent the
ithe estimated parameter that secondary iteration obtains
a,
λ i represent
a i weighted average coefficients,
b i represent the
ithe estimated parameter that secondary iteration obtains
b,
μ i represent
b i weighted average coefficients;
Step 4, to different signal to noise ratios adopt same fixing estimated parameter;
Step 5, obtain required estimated parameter after, as follows LDPC code is decoded:
Step 5.1, calculating channel transfer are to variable node
iprobability likelihood ratio message
l (P i ), then calculate all variable nodes
ipass to check-node
jbelong to
c i initial message:
(6)
Iterative processing is carried out in step 5.2, in the steps below (1), (2), (3):
(1) check-node Message Processing
Calculate all check-nodes
jbe transmitted to variable node
ibelong to
r j imessage:
(7)
(2) variable node message process
Calculate all variable nodes
ibe transmitted to check-node
jbelong to
c i jmessage:
(8)
(3) decoding judgement
To all variable nodes
icalculate hard decision message:
(9)
Then code word is:
(10)
Step 5.3, carry out iterative computation by step 5.2, until meet stop condition
or iterations reaches maximum iteration time, then iterative computation terminates, otherwise continues iteration; Wherein,
represent the check matrix of LDPC code,
represent the code word solved,
represent this transpose of a matrix, if
, then the code word solved is correct.
The invention has the beneficial effects as follows and utilize the method for Linear Minimum Mean-Square Error Estimation to obtain estimated parameter, the verification message amplitude in minimum-sum algorithm is made to approach verification message amplitude in BP algorithm, and consider the impact of iterations, the estimated parameter obtained is revised further, thus makes its decoding performance be better than minimum-sum algorithm and traditional correction algorithm thereof.Simultaneously, estimated parameter in the present invention has clear and definite calculation expression when border is determined, do not need a large amount of simulation calculation, and golden section search algorithm accelerates the determination of boundary value further, thus make its computational complexity well below BP algorithm, therefore hardware implementing is simpler.Again due to the minimizing of mean iterative number of time of the present invention, the amount of calculation making it decode is lower than traditional coding/decoding method, and decoding delay is lower.Owing to adopting fixing estimated parameter to different signal to noise ratios, further reduce hardware spending.
Accompanying drawing explanation
Fig. 1 is the workflow diagram of the inventive method.
Fig. 2 is simulation communication system construction drawing in the embodiment of the present invention.
Fig. 3 be in the embodiment of the present invention k with
graph of a relation.
Fig. 4 is the graph of a relation of parameter a in the embodiment of the present invention, b and iterations.
Fig. 5 is the ber curve figure of various decoding algorithm in the embodiment of the present invention.
Fig. 6 is the graph of relation of estimated parameter a, b and SNR in the embodiment of the present invention.
Embodiment
For ease of describing, first the symbol that the inventive method relates to is illustrated.LDPC code can represent by check matrix H and Tanner figure two kinds of methods, and they are one to one between the two.Variable node in row corresponding diagram in check matrix, uses
irepresent; And the check-node in row corresponding diagram in check matrix, use
jrepresent.When in check matrix
jrow
icolumn element is 1, then in Tanner figure
iindividual variable node and
jthe limit that between individual check-node, existence one is connected.
c i represent and variable node
ithe set of the check-node be connected,
r j represent and check-node
jthe set of the variable node be connected,
c i jexpression removes
jouter and variable node
ithe set of the check-node be connected,
r j iexpression removes
ithe set of the outer variable node be connected with check-node,
l(
r ji ) represent check-node
jpass to variable node
iexternal information,
l(
q ij ) represent variable node
ipass to check-node
jexternal information,
crepresent code word;
l 1for the verification message amplitude in BP algorithm, its value is:
(1)
Wherein, (
l-1) represent the (
l-1) secondary iteration;
Wherein
;
l 2 for the verification message amplitude in minimum-sum algorithm, its value is:
(2)
The present invention is based on the minimum and coding/decoding method of the correction of Linear Minimum Mean-Square Error Estimation, as shown in Figure 1, carry out as follows:
Step 1, set up the estimation model of verification message amplitude: based on Linear Minimum Mean-Square Error Estimation model, and combine revise after the constant principle of the symbol of verification message, verification message amplitude is set up such as formula the estimation model shown in (3):
(3)
Wherein
a,
bfor calculative estimated parameter;
The estimated parameter that step 2, calculating make mean square error function minimum
a,
b:
Step 2.1, hypothetical boundary
for constant
, when
time, can obtain estimated parameter is:
(4)
Wherein, cov (
l 1,
l 2) represent
l 1with
l 2covariance,
d(
l 2) represent
l 2variance,
e(
l 1),
e(
l 2) represent respectively
l 1,
l 2mean square error;
Step 2.2, compare calculate with whether equal, if obtain
a,
bnot right value, give up; If then obtain
a,
bright value;
Step 2.3, employing golden section search algorithm, carry out iteration by above-mentioned steps 2.1,2.2, determine border fast
k, then obtain estimated parameter according to formula (4)
a,
b;
Step 3: estimated parameter is revised according to iterations:
Decoding algorithm due to LDPC all needs to calculate through successive ignition, finally just can solve correct code word, and estimated parameter required in each iterative process is not identical.According to the relation of iterations and estimated parameter, by formula (5), average treatment is weighted to the estimated parameter that front n iteration obtains, namely revised shown in formula (5), and in each time later iterative process, thus make hardware implementing simple, ensure that decoding performance simultaneously.The message exported due to check-node during front iteration several times has a significant impact whole decoding performance, therefore, frontly gets larger weight several times, generally only considers first 3 to 4 times.
(5)
Wherein,
a i represent the
ithe estimated parameter that secondary iteration obtains
a,
λ i represent
a i weighted average coefficients,
b i represent the
ithe estimated parameter that secondary iteration obtains
b,
μ i represent
b i weighted average coefficients;
Step 4, consider the uncertainty of signal-to-noise ratio (SNR) estimation cause decoding performance decline and hardware spending, to different signal to noise ratios adopt same fixing estimated parameter;
Step 5, obtain required estimated parameter after, as follows LDPC code is decoded:
Step 5.1, calculating channel transfer are to variable node
iprobability likelihood ratio message
l (P i ), then calculate all variable nodes
ipass to check-node
jbelong to
c i initial message:
(6)
Iterative processing is carried out in step 5.2, in the steps below (1), (2), (3):
(1) check-node Message Processing
Calculate all check-nodes
jbe transmitted to variable node
ibelong to
r j imessage:
(7)
Wherein,
lrepresent the
lsecondary iteration; (
l-1) represent the (
l-1) secondary iteration;
(2) variable node message process
Calculate all variable nodes
ibe transmitted to check-node
jbelong to
c i jmessage:
(8)
(3) decoding judgement
To all variable nodes
icalculate hard decision message:
(9)
Then code word is:
(10)
Step 5.3, carry out iterative computation by step 5.2, until meet stop condition
or iterations reaches maximum iteration time, then iterative computation terminates, otherwise continues iteration; Wherein,
represent the check matrix of LDPC code,
represent the code word solved,
represent this transpose of a matrix, if
, then the code word solved is correct.
By above-described method, the decoding of LDPC code just can be realized.As can be seen from above step, estimated parameter of the present invention has clear and definite calculation expression when border is determined, do not need a large amount of simulation calculation, the algorithm of golden section search simultaneously accelerates again the determination of boundary value further, makes acquisition estimated parameter simple fast.And the decoding performance that the present invention produces and algorithm analysis, the example combined below is provided.
Below in conjunction with drawings and the specific embodiments, the invention will be further described.
In this example, adopt the substandard LDPC(7493 of China Digital Television Terrestrial Broadcasting GB20600,3048) code, simulation result completes under MATLAB emulation platform.Simulation parameter is: LDPC code rate 0.4, Gaussian white noise channel, and BPSK modulates, and frame number is 200 frames, and decoding maximum iteration time is 20 times.Simulation communication system configuration as shown in Figure 2.
1, set up the estimation model of verification message amplitude, and draw the value of estimated parameter.
?
sNR=2.2dBtime,
kwith
relation as shown in Figure 3.As can be seen from the figure, have and only have one
kcan meet
condition.Border
kdetermination can adopt golden section search algorithm, obtain fast.Suppose
khunting zone from 0 to 0.5, get
kprecision be 0.0001, only need 18 search, just can obtain border
kvalue be 0.3318.Can draw according to formula (4)
a=0.66497,
b=0.22064, now
, satisfy condition, namely obtain the value of unique estimated parameter.
2, according to iterations, estimated parameter is revised.
Under giving different signal to noise ratio in Fig. 4, the relation of iterations and estimated parameter.According to formula (5), estimated parameter is modified to
a=0.72282,
b=0.20652, and in each time later iterative process.
3, same fixing estimated parameter is adopted to different signal to noise ratios.
Revised estimated parameter when getting SNR=2.2dB in this example, can ensure that its decoding performance is unaffected.Namely different SNR point estimation parameters is all got
a=0.72282,
b=0.20652.
4, LDPC decoding is carried out.
Wherein check-node Message Processing, shown in (11):
(11)
Through above step, just complete decoding.The decoding performance of various decoding algorithm as shown in Figure 5.In figure, LMMSE-MinSum-1,2,3 is the ber curve that the method adopting the present invention to propose obtains, and difference is the value of estimated parameter.The estimated parameter of LMMSE-MinSum-1 is the estimated parameter adopting iteration for the first time to obtain,
a,
bvalue corresponding with Fig. 6.The estimated parameter of LMMSE-MinSum-2 is that employing formula (5) carries out revised estimated parameter to it.LMMSE-MinSum-3 adopts same fixing estimated parameter to different SNR,
a=0.72282,
b=0.20652.
As can be seen from Figure 5, the decoding performance of log-domain BP algorithm is best, and when 2.2dB, its error rate is lower than 10
-7; Decoding performance obvious decline compared with log-domain BP algorithm of minimum-sum algorithm, when 3.2dB, its error rate is just lower than 10
-7, differed 1dB; And traditional two kinds are revised minimum-sum algorithm, in same bit error rate situation, its decoding performance all increases than minimum-sum algorithm, and Offset BP-Based algorithm and Normalized BP-Based algorithm reach 10 when 2.5dB and 2.7dB respectively
-7the error rate, but compared with log-domain BP algorithm, also have the gap of 0.3dB and 0.5dB respectively; The LMMSE that the present invention proposes revises minimum-sum algorithm, and when estimated parameter is not revised, when 2.3dB, the error rate just can reach 10
-7; After being revised estimated parameter, its decoding performance improves further, and when 2.2dB, the error rate just can reach 10
-7, identical with log-domain BP algorithm, but when signal to noise ratio is less than 2.1dB, its error rate is slightly larger than the error rate of log-domain BP algorithm; During to different SNR employing same fixing estimated parameter, its decoding performance is influenced hardly.Can draw thus, the present invention, while improve decoding performance, reduces hardware spending.
Can draw to draw a conclusion from this example, the LDPC coding/decoding method that the present invention proposes, its decoding performance is not only better than the performance of minimum-sum algorithm greatly, and is better than the performance of traditional correction algorithm, and has more precipitous ber curve than BP algorithm.Also there is the advantages such as estimated parameter calculates fast, coding/decoding method complexity is low, hardware implementing is simple simultaneously.
Above by embodiment to invention has been detailed description, but these are not construed as limiting the invention.Protection scope of the present invention should comprise those apparent conversion or alternative and improvement for a person skilled in the art.
Claims (1)
1. an and coding/decoding method minimum based on the correction of Linear Minimum Mean-Square Error Estimation, is characterized in that:
Definition
c i represent and variable node
ithe set of the check-node be connected,
r j represent and check-node
jthe set of the variable node be connected,
c i jexpression removes
jouter and variable node
ithe set of the check-node be connected,
r j iexpression removes
ithe set of the outer variable node be connected with check-node,
l(
r ji ) represent check-node
jpass to variable node
iexternal information,
l(
q ij ) represent variable node
ipass to check-node
jexternal information,
crepresent code word;
l 1for the verification message amplitude in BP algorithm, its value is:
(1)
Wherein, (
l-1) represent the (
l-1) secondary iteration;
Wherein
;
l 2for the verification message amplitude in minimum-sum algorithm, its value is:
(2)
The method is carried out as follows:
Step 1, set up the estimation model of verification message amplitude: based on Linear Minimum Mean-Square Error Estimation model, and under the prerequisite that the symbol of verification message is constant after correction, verification message amplitude is set up such as formula the estimation model shown in (3):
(3)
Wherein
a,
bfor calculative estimated parameter;
Step 2, calculating make mean square error function
minimum estimated parameter
a,
b:
Step 2.1, hypothetical boundary
b/
afor constant
, when
l 2>
ktime, can obtain estimated parameter is:
(4)
Wherein, cov (
l 1,
l 2) represent
l 1with
l 2covariance,
d(
l 2) represent
l 2variance,
e(
l 1),
e(
l 2) represent respectively
l 1,
l 2mean square error;
Step 2.2, compare and to calculate
b/
awith
kwhether equal, if
, obtain
a,
bnot right value, give up; If
, then obtain
a,
bright value;
Step 2.3, employing golden section search algorithm, carry out iteration by above-mentioned steps 2.1,2.2, determine border fast
k, then obtain estimated parameter according to formula (4)
a,
b;
Step 3, according to iterations, estimated parameter to be revised:
By formula (5), average treatment is weighted to the estimated parameter that front n iteration obtains, obtains revised estimated parameter
a,
b, and fixing estimated parameter is used to each time later iteration:
(5)
Wherein,
a i represent the
ithe estimated parameter that secondary iteration obtains
a,
λ i represent
a i weighted average coefficients,
b i represent the
ithe estimated parameter that secondary iteration obtains
b,
μ i represent
b i weighted average coefficients;
Step 4, to different signal to noise ratios adopt same fixing estimated parameter;
Step 5, obtain required estimated parameter after, as follows LDPC code is decoded:
Step 5.1, calculating channel transfer are to variable node
iprobability likelihood ratio message
l (P i ), then calculate all variable nodes
ipass to check-node
jbelong to
c i initial message:
(6)
Iterative processing is carried out in step 5.2, in the steps below (1), (2), (3):
(1) check-node Message Processing
Calculate all check-nodes
jbe transmitted to variable node
ibelong to
r j imessage:
(7)
(2) variable node message process
Calculate all variable nodes
ibe transmitted to check-node
jbelong to
c i jmessage:
(8)
(3) decoding judgement
To all variable nodes
icalculate hard decision message:
(9)
Then code word is:
(10)
Step 5.3, carry out iterative computation by step 5.2, until meet stop condition
or iterations reaches maximum iteration time, then iterative computation terminates, otherwise continues iteration; Wherein,
hrepresent the check matrix of LDPC code,
represent the code word solved,
represent this transpose of a matrix, if
, then the code word solved is correct.
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| CN103219998B (en) * | 2013-03-27 | 2016-01-20 | 哈尔滨工业大学 | A kind of mixed parameter estimation method under multichannel CS framework |
| CN107005251A (en) * | 2014-11-19 | 2017-08-01 | 领特投资两合有限公司 | The LDPC decodings of dynamic adjustment with finite accuracy and iterations |
| CN105227191B (en) * | 2015-10-08 | 2018-08-31 | 西安电子科技大学 | Based on the quasi-cyclic LDPC code coding method for correcting minimum-sum algorithm |
| CN108023679B (en) * | 2017-12-07 | 2020-06-16 | 中国电子科技集团公司第五十四研究所 | Iterative decoding scaling factor optimization method based on parallel cascade system polarization code |
| CN108988872B (en) * | 2018-08-23 | 2020-11-10 | 中国科学院计算技术研究所 | LDPC decoding method based on hierarchical minimum sum algorithm |
| CN112260698A (en) * | 2019-07-22 | 2021-01-22 | 上海高清数字科技产业有限公司 | Dynamic correction factor configuration method in LDPC decoder |
| CN113271111B (en) * | 2021-06-03 | 2022-08-02 | 北京邮电大学 | Decoding method and system based on improved minimum sum algorithm |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| US6141788A (en) * | 1998-03-13 | 2000-10-31 | Lucent Technologies Inc. | Method and apparatus for forward error correction in packet networks |
| CN1717871A (en) * | 2002-10-05 | 2006-01-04 | 数字方敦股份有限公司 | Systematic encoding and decoding of chain reaction codes |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US6141788A (en) * | 1998-03-13 | 2000-10-31 | Lucent Technologies Inc. | Method and apparatus for forward error correction in packet networks |
| CN1717871A (en) * | 2002-10-05 | 2006-01-04 | 数字方敦股份有限公司 | Systematic encoding and decoding of chain reaction codes |
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