CN101106380A - An alternative decoding method and device for LDPC code - Google Patents
An alternative decoding method and device for LDPC code Download PDFInfo
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Abstract
The invention relates to a decoding method and a device for LDPC code. Firstly, set default iteration times and maximum iteration times. After each iteration decoding, check if the verification equation cHT=0 is satisfied for output codeword c, the decoding can be successful and can be finished if the verification equation cHT=0 is satisfied, otherwise, if iteration times is more than or equal to default iteration times, decide if mean-variance of LLR (log-likelihood ratio) absolute value of code element in codeword c is more than default fixed threshold value. If satisfied, go on with the iteration decoding, otherwise, determine failure of decoding and finish decoding. If iteration times reach to default maximum iteration times, still determine failure of decoding. Compared with the prior art, the invention does not need to set different stopping criterion threshold according to different channel condition, and can promptly decide decoding state change to reduce large amount of calculation.
Description
Technical Field
The present invention relates to the field of communications technologies, and in particular, to an implementation scheme for iterative decoding of an LDPC code in a communication process.
Background
LDPC (Low Density Parity Check) codes are yet another major development that has emerged in the field of error correction coding following Turbo codes. The research focus of the coding community. The performance of the LDPC code is close to Shannon (Shannon) limit, the LDPC code has larger flexibility and lower error flat-bottom characteristic, the decoding complexity is lower than that of a Turbo code, complete parallel operation can be realized, the hardware complexity is low, the throughput is large, and the LDPC code has high-speed decoding potential. Currently, LDPC codes are adopted by IEEE 802.3an, DVB-s.2 standard and IEEE 802.16e, and have become an alternative to LTE (long term evolution). Due to its many advantages, it can be widely applied to the fields of outer space and satellite communication, optical communication, deep space communication, next generation mobile communication systems, high speed and very high speed digital subscriber lines, optical and magnetic recording systems, network data packet transmission, etc.
The LDPC code is decoded by adopting an iterative decoding method. Iterative decoding is a method with performance close to maximum likelihood decoding, and can achieve good decoding performance when being adopted by Turbo codes, LDPC codes and the like. However, the error correction performance of the LDPC code is not improved with the increase of the iteration times after a certain iteration times, and meanwhile, the decoding calculation amount of the LDPC code is often greatly increased due to the overlarge iteration times. Therefore, there is a problem with the algorithm employing iterative decoding with a stopping criterion.
For LDPC decoding, the criteria typically employed are: setting the maximum iteration times, wherein each iteration passes through a check equation cH T =0, where c represents a decoded codeword and H represents a check matrix of the LDPC code. This criterion is the most ideal decoding stop criterion for Turbo codesThis criterion also minimizes the number of iterations for a correctly decodable LDPC code. However, when the channel decoding has a problem, the iteration number reaches the maximum iteration number or the decoding is not correct, the decoding failure can be judged, and a large amount of calculation is wasted at the moment. Therefore, there is a stopping criterion to determine the decoding trend and stop the iteration when it is considered that the decoding cannot be correctly decoded within a certain number of iterations. Stopping criteria based on this kind of thought have been introduced into Turbo decoding by observing the mean M of the absolute values | LLR | of the log-likelihood ratios LLR (logarithmlikelihoodoratio) of the symbols in the iteratively decoded codewords |L| Setting a threshold Th at the same time, when M |L| Stop iteration > Th.
In this stopping criterion, the threshold value Th is influenced by E b /N 0 The influence of factors such as (signal-to-noise ratio) and code rate needs to be determined according to the actual situation of the system, and when system parameters change, corresponding changes also need to be made, which will increase the calculation amount for the decoder based on the stopping criterion. If the method is used for LDPC decoding, the inherent advantage of low decoding complexity of the LDPC code can be weakened, so that the method for setting the mean threshold is not suitable for controlling the iteration times in an actual communication system.
Disclosure of Invention
The invention aims to provide an LDPC code iterative decoding method and device, and provides a new stop criterion to control the iteration times of LDPC iterative decoding, so that the decoding condition can be judged relatively quickly, and a large amount of calculation can be saved.
The purpose of the invention is realized by the following technical scheme:
the invention provides an iterative decoding method of LDPC code, in the method, after iterative decoding, a decoded code word c does not satisfy a check equation cH T When =0, the method comprises:
A. and calculating the variance of the mean value of the absolute values of the log-likelihood ratios (LLR) of the code elements in the decoding code word c, if the variance is judged to be larger than or not smaller than a preset threshold value, continuing to perform iterative decoding, and if not, ending the decoding process.
The method further comprises the following steps:
setting a predetermined number of iterations before decoding, and iteratively decoding after the predetermined number of iterationsAfter the code is decoded, if the decoding code word c does not satisfy the check equation cH in the calculation T If =0, executing the step a.
The method further comprises the following steps: setting the maximum iteration times before decoding, and calculating that the decoded code word c does not satisfy the check equation cH after the iterative decoding of the maximum iteration times T If =0, the decoding is determined to be failed, and the decoding process is ended.
The method further comprises the following steps: and setting the preset iteration times and the maximum iteration times according to the success rate of decoding and the requirement of the system.
The method further comprises the following steps: after each iteration is completed, the number of iterations is increased by 1.
The method further comprises the following steps: the set threshold value is greater than 0 and not greater than 1.
The method further comprises the following steps: in the iterative decoding process, if the check equation cH is satisfied T If =0, the decoding is successful, and the decoding process is ended.
The method for calculating the variance of the absolute value of LLR of the code element in the decoding code word comprises the following steps: calculating the mean of the absolute values of the log-likelihood ratios of the symbols in the decoded codeword c:in the formula: n =1,2 max Denotes the number of iterations, L (u) k ) Is the LLR for the kth symbol, N is the codeword length;
calculating the variance of the mean of the absolute LLR values of the code elements in the decoding code word c by using the mean:
in the formula: the var operator represents a variance operation, defined as,
here, the first and second liquid crystal display panels are,
n is the number of samples.
The invention also provides an iterative decoding device of the LDPC code, which is used for decoding the code word c which does not satisfy the check equation cH after iterative decoding T =0, and the apparatus includes:
a variance calculating unit for calculating the variance of the mean value of the absolute values of the log-likelihood ratios LLR of the symbols in the decoded codeword c;
and the iterative decoding judgment processing unit is used for judging whether the variance calculated by the variance calculation unit is larger than or not smaller than a preset threshold value, if so, triggering iterative decoding operation, and otherwise, ending decoding.
The device further comprises:
the iteration number counting unit is used for adding 1 to the iteration number after each iteration is completed;
a preset iteration number judgment processing unit, after the iterative decoding of the preset iteration number, if the decoding code word c does not satisfy the check equation cH T If =0, the unit will trigger the variance calculation unit.
The device further comprises:
a maximum iteration number judging and processing unit, which calculates the code word c if the maximum iteration number is set after the iterative decodingDoes not satisfy the check equation cH T And =0, the decoding is finished.
The variance calculating unit includes:
a log-likelihood ratio absolute value mean calculation unit for calculating the mean of the log-likelihood ratio absolute values of the symbols in the decoded codeword c, i.e. the mean of the log-likelihood ratio absolute values of the symbols in the decoded codeword c
In the formula: i =1,2,. N max Denotes the number of iterations, L (u) k ) Is LLR of the kth symbol, N is codeword length;
a variance determining unit for determining the variance of the mean of the LLR absolute values of the symbols in the decoded codeword c, i.e. using said mean calculation
In the formula: the var operator represents a variance operation, defined as,
here, the number of the first and second electrodes,
n is the number of samples.
It can be seen from the above technical solutions provided by the present invention that, the present invention relates to a decoding method of LDPC code, and the predetermined iteration times and the maximum iteration times are first set according to the success rate of decoding and the requirements of the system. After each iterative decoding, checking the check equation cH for the output decoding code word c T If yes, determining that the decoding is successful, and ending the decoding process; otherwise, if the iteration number is greater than or equal to the preset iteration number, calculating the variance of the mean value of absolute values of LLR (log likelihood ratio) of code elements in the decoded code word c, simultaneously judging whether the variance exceeds a preset fixed threshold value, and if so, continuing to calculate the mean value of the absolute values of LLR (log likelihood ratio) of the code elements in the decoded code word c, otherwise, continuing to calculate the variance of the absolute values of LLR of the code elements in the decoded code word c, and if so, continuing to calculate the mean value of LLR of the code elements in the decoded code word cAnd carrying out iterative decoding, otherwise, determining that the decoding fails, and ending the decoding process. And after each iteration is completed, adding 1 to the iteration number. Of course, if the iteration number reaches the preset maximum iteration number and the decoding is still unsuccessful, the decoding is determined to be failed, and the decoding process is ended.
The invention adopts the iteration termination criterion of the fixed threshold in the LDPC code iterative decoding algorithm, thereby not only avoiding the defect that different stop criterion thresholds need to be set according to different conditions such as channel conditions and the like in the prior art, but also being capable of quickly judging the decoding state change, and further saving a large amount of calculation processing processes. Therefore, the realization of the invention can ensure that the iterative decoding operation process aiming at the LDPC code in the LDPC decoder does not need to consume a large amount of calculation processing resources, and can greatly improve the decoding efficiency.
Drawings
FIG. 1 is a graph showing the variation of the mean absolute LLR value with the number of iterations and the variation of the mean absolute LLR value with the number of iterations under the condition of correct decoding;
FIG. 2 is a graph showing the variation of the mean absolute LLR value with the number of iterations and the variation of the mean absolute LLR value with the number of iterations when correct decoding is not possible;
FIG. 3 is a decoding flow chart of the iterative decoding method of LDPC codes according to the present invention;
FIG. 4 is a graph of signal-to-noise ratio (SNR) versus Bit Error Rate (BER) for various stopping criteria;
FIG. 5 is a plot of signal-to-noise ratio (SNR) versus block error rate (BLER) for different stopping criteria;
FIG. 6 is a plot of signal-to-noise ratio (SNR) versus average iteration number for different stopping criteria;
fig. 7 is a schematic diagram of a specific implementation structure of the device according to the present invention.
Detailed Description
The invention provides a realization scheme for realizing iterative decoding of LDPC codes in a decoder, wherein, preset iteration times and maximum iteration times are set according to the success rate of decoding and the requirements of the system; after iterative decoding of preset iterative times, calculating decoding code wordWhether c satisfies the check equation cH T =0, if not, calculate log likelihood ratio of code element in decoding code word cAnd if the variance of the mean value of the absolute LLR is judged to be larger than or equal to a preset fixed threshold value, the iterative decoding is continued, otherwise, the decoding failure is determined, and the decoding process is ended. Of course, in the iterative decoding process, if the check equation cH T And =0, decoding is successful, and the decoding process is finished. And after finishing each iteration, adding 1 to the iteration number. In the process, after iterative decoding of the maximum iteration number, the calculated decoding code word c still does not satisfy the check equation cH T If =0, the decoding is determined to be failed, and the decoding process is ended.
The LLR of the iterative decoding, namely the LLR of the code element represents the accuracy of the information transmitted by a certain node, the reliability of the information of the node is gradually improved by updating the LLRs of the information node and the check node in the iterative decoding, and finally the value of the LLR approaches to a certain limit, so that the successful decoding is realized. Therefore, LLRs are key factors in determining the performance of iterative decoding. The change trend of the LLR can reflect the decoding performance, and the decoding performance can be predicted by using the useful information.
Fig. 1 and fig. 2 are a graph showing the variation of the mean LLR absolute value with the number of iterations and a graph showing the variation of the mean LLR absolute value with the number of iterations in the case where correct decoding is possible and in the case where correct decoding is not possible, respectively. As can be seen from fig. 1 and fig. 2, if correctly decoded, the absolute value of the LLR mean and the mean of the absolute values of the LLR both continuously increase with the increase of the number of iterations, and if not correctly decoded, the value is small and the amplification is small. In addition, the higher the signal-to-noise ratio, the faster the mean rise speed of the absolute values of the LLRs, and the smaller the number of iterations required for successful decoding.
TABLE 1. Different SNR
And probability of coding error
| SNR(dB) | 0 | 1 | 2 | 2.5 | 3 |
| σ M|L| 2 < 1 and probability of |
1 | 0.9998 | 0.9996 | 0.99995 | 0.99968 |
As can be seen from table 1, with a large number of collected samples,
when the decoding fails, the probability of decoding failure is close to 0.9999, which indicates that the empirical information can be used to predict the decoding performance, that is, the threshold value is selected to be a fixed value "1". Further, to allow for performance and complexity optimization, a suitable threshold 0 < α ≦ 1 may be selected. Although this threshold may also be fixed empirically.
There are two more cases of coding errors occurring in the coding process: firstly, errors which cannot be detected by decoding;
the second is error detection occurring in the decoding process. A good stopping criterion should be to make the probability of undetected errors and the probability of false detections as small as possible.
Let the maximum number of iterations be n max Defining the mean of the ith sub-iteration code word symbol | LLR |:
i＝1，2，...n max denotes the number of iterations, u k Is the LLR of the kth bit, N is the codeword length. Setting an observation length M, calculating (M) of previous M iterations |L| 1 ，ΛM |L| i ，ΛM L‖ m ) Variance σ of M|L| 2 ：
Wherein the var operator represents a variance operation, defined as:
here, the first and second liquid crystal display panels are,
n is the number of samples.
The specific scheme of the invention is as follows:
firstly, decoding, adding 1 to the number of iterations, and then judging whether cH exists or not T If the number of iterations is greater than or equal to m, starting the stopping criterion of the invention, and at the moment, dividing into two cases:
(I) The number of iterations is more than or equal to m, and
judging the decoding failure and stopping decodingCode
(II) the number of iterations is more than or equal to m, and
judging whether the decoding is possible to obtain correct decoding, and continuing iteration until the decoding is possible to obtain correct decoding
Or the iteration reaches the maximum iteration number and still has no correct decoding, the decoding is stopped
The specific process is shown in fig. 3:
and 39, judging whether the iteration times are less than the maximum iteration times, if so, executing the step 32, and otherwise, executing the step 38.
It can be seen that the performance of the stopping criterion is related to the set observation length m, which can be set according to the system requirements. The proposed stopping criterion is still used when the number of successfully decoded iterations is smallStarting cH T The number of times of decoding is not yet decoded, and if the decoding is judged to be impossible to correctly decode, the decoding is stopped. Therefore, the stopping criterion can obviously save the average iteration number, and the error rate performance is hardly lost when being verified by the subsequent simulation results, especially under the condition of low signal-to-noise ratio.
Fig. 4-6 are performance verification curves of the present invention, and the performance of the proposed stopping criterion at m =15 and m =25 and the maximum number of iterations at 50 (i.e., iter-max = 50) using the original stopping criterion are analyzed from several points of bit error rate, block error rate and average number of iterations.
As can be seen from fig. 4, when the snr is less than 5dB, the BER (biterror rate) curves of the stop criterion and the original criterion (i.e. the decoding stop criterion provided in the prior art) are overlapped, the number of iterations is reduced without increasing the BER, and when the snr is greater than 5dB, the snr is not increasedWhen the BER using the original criterion is lower than the BER of the proposed criterion, but not much different, BER =10 -5 And when m =25, the signal-to-noise ratio is different by less than 0.1dB. In addition, an increase in the value of m may also result in a gain in performance, e.g., BER at m =25 is lower than BER at m = 15.
It can be seen from fig. 5 that the stop criterion proposed by the present invention is substantially consistent with the block error rate of the original criterion when the SNR is less than 3dB, and after the SNR is increased, the block error rate of the original criterion is lower than the stop criterion proposed by the present invention, but the difference is not large, which is consistent with the conclusion of fig. 4.
It can be seen from fig. 6 that the average iteration times required by different stopping criteria and the original criteria are significantly different, and the stopping criteria proposed by the present invention significantly reduces the average iteration times when the signal-to-noise ratio is low, but the average iteration times gradually tend to be consistent when the signal-to-noise ratio is increased, because the probability of successful decoding is also relatively high when the signal-to-noise ratio is high.
The invention also provides an iterative decoding device of the LDPC code, which is arranged onIn the decoder, the decoding code word c does not satisfy the check equation cH after being subjected to iterative decoding T The iterative decoding process is performed when =0, and the specific implementation structure of the apparatus is as shown in fig. 7, and mainly includes the following processing units:
(1) Variance calculation unit
The unit is used for calculating the variance of the mean of the absolute values of the log-likelihood ratios LLR of the code elements in the decoded code words c, and the variance calculating unit comprises:
a mean of Log Likelihood Ratio (LLR) calculation unit for calculating the mean of Log Likelihood Ratio (LLR) absolute values of the symbols in the decoded codeword (c), i.e. the mean of LLR absolute values of the symbols in the decoded codeword (c)
In the formula: i =1,2,. N max Denotes the number of iterations, L (u) k ) Is LLR of the kth symbol, N is codeword length;
a variance determining unit for determining the variance of the mean of the LLR absolute values of the symbols in the decoded codeword c, i.e. using said mean calculationIn the formula: var operator represents variance operation, constantThe meaning is that,
here, the first and second liquid crystal display panels are,n is the number of samples.
(2) Iterative decoding judgment processing unit
The unit is used for judging whether the variance calculated by the variance calculating unit is larger than or not smaller than a preset threshold value, if so, the iterative decoding operation is triggered, otherwise, the iterative decoding operation is determined to be failed, and the iterative decoding process is ended.
The iterative decoding device of the LDPC code further comprises an iteration frequency counting unit and a preset iteration frequency judging and processing unit, and the device further comprises a maximum iteration frequency judging and processing unit, wherein:
the iteration count counting unit is used for counting the executed iteration decoding count, namely adding 1 to the iteration count after each iteration is finished;
a preset iteration number judgment processing unit, after the iterative decoding of the preset iteration number, if the decoding code word c does not satisfy the check equation cH T If the variance is not less than 0, the unit triggers the variance calculation unit and judges the corresponding iterative decoding by the iterative decoding judgment processing unit;
a maximum iteration number judging and processing unit, after the iterative decoding of the set maximum iteration number, if the calculated decoding code word c does not satisfy the check equation cH T And =0, determining that the iterative decoding operation is failed, and ending the iterative decoding process.
It can be seen that, the invention adopts the iteration termination criterion of the fixed threshold in the iterative decoding algorithm of LDPC code, namely the defect that different stop criterion thresholds need to be set according to different conditions such as channel conditions and the like in the prior art is avoided, and the decoding state change can be judged quickly, thus saving a large amount of calculation.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (12)
1. An iterative decoding method of LDPC codes is characterized in that after iterative decoding, a decoded code word c does not satisfy a check equation cH T When =0, the method comprises:
A. and calculating the variance of the mean value of the absolute values of the log-likelihood ratios (LLR) of the code elements in the decoding code word c, if the variance is judged to be larger than or not smaller than a preset threshold value, continuing to perform iterative decoding, and if not, ending the decoding process.
2. The iterative decoding method of LDPC codes according to claim 1, further comprising:
setting preset iteration times before decoding, and after iterative decoding of the preset iteration times, if the calculated decoding code word c does not satisfy the check equation cH T If =0, executing the step a.
3. The method of iterative decoding of an LDPC code according to claim 1, the method further comprising:
setting the maximum iteration times before decoding, calculating that the decoded code word c does not satisfy the check equation cH after the iterative decoding of the maximum iteration times T If =0, the decoding is determined to be failed, and the decoding process is ended.
4. The iterative decoding method of LDPC codes according to claim 2 or 3, further comprising:
and setting the preset iteration times and the maximum iteration times according to the success rate of decoding and the requirement of the system.
5. The iterative decoding method of LDPC codes according to claim 2 or 3, further comprising:
after each iteration is completed, the number of iterations is increased by 1.
6. The iterative decoding method of LDPC codes according to claim 1, further comprising:
the set threshold value is greater than 0 and not greater than 1.
7. The iterative decoding method of LDPC codes according to any one of claims 1 to 6, further comprising:
in the iterative decoding process, if the check equation cH is satisfied T And =0, decoding is successful, and the decoding process is finished.
8. The iterative decoding method of LDPC codes according to any of claims 1 to 6 wherein the method of calculating the variance of absolute LLR values of symbols in the decoded codewords comprises:
calculating the mean value of the absolute value of the log-likelihood ratio of the code elements in the decoding code word c:
in the formula: n =1,2 max Denotes the number of iterations, L (u) k ) Is the LLR for the kth symbol, N is the codeword length;
calculating the variance of the mean of the absolute LLR values of the symbols in the code word c by using the mean:
in the formula: the var operator represents a variance operation, defined as,
here, the number of the first and second electrodes,
n is the number of samples.
9. An iterative decoding apparatus for LDPC codes, the apparatus being adapted to decode a code word c which does not satisfy a check equation cH after iterative decoding T =0, and the apparatus includes:
a variance calculating unit for calculating the variance of the mean value of the absolute values of the log-likelihood ratios LLR of the symbols in the decoded codeword c;
and the iterative decoding judgment processing unit is used for judging whether the variance calculated by the variance calculating unit is greater than or not less than a preset threshold value, if so, triggering iterative decoding operation, and otherwise, ending decoding.
10. The apparatus for iterative decoding of LDPC codes as claimed in claim 9, wherein said apparatus further comprises:
the iteration number counting unit is used for adding 1 to the iteration number after each iteration is completed;
a preset iteration number judgment processing unit, after the iterative decoding of the preset iteration number, if the decoding code word c does not satisfy the check equation cH T If =0, the unit will trigger the variance calculation unit.
11. The apparatus for iterative decoding of an LDPC code according to claim 10, further comprising:
a maximum iteration number judging and processing unit, after the iterative decoding of the set maximum iteration number, if the calculated decoding code word c does not satisfy the check equation cH T And =0, the decoding is finished.
12. The apparatus for iterative decoding of LDPC codes as claimed in claim 9, 10 or 11, wherein said variance calculating unit comprises:
a mean of Log Likelihood Ratio (LLR) calculation unit for calculating the mean of Log Likelihood Ratio (LLR) absolute values of the symbols in the decoded codeword (c), i.e. the mean of LLR absolute values of the symbols in the decoded codeword (c)
In the formula: i =1,2.. Nm ax table Indicates the number of iterations, L (u) k ) Is the LLR for the kth symbol, N is the codeword length;
a variance determining unit for determining the variance of the mean of the LLR absolute values of the symbols in the decoded codeword c, i.e. using said mean calculation
In the formula: the Var operator represents a variance operation, defined as,
here, the first and second liquid crystal display panels are,
n is the number of samples.
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