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Journal of Convergence Information Technology

Joint Demodulation and EMS Decoding Algorithm for Q-ary LDPC Codes

Wei Lin -, Baoming Bai, Sheng Tong

Published Jun 30, 2011• 3 citations
Publisher

Abstract

To reduce the high decoding complexity of q-ary LDPC codes, a joint-demodulation and extended min-sum (JD-EMS) decoding algorithm is presented in this paper. By utilizing the squares of the distances between signal and constellation points over constellation graph as the decoder input soft messages, the proposed algorithm not only facilitates the computations of the decoder initial messages, but also avoids the performance loss due to conversions between probabilities and log-likelihoodratios. The elementary check node (ECN) processing is also improved in JD-EMS algorithm, thus the number of real additions can be reduced. Moreover, we also give an upper bound of the number of comparison candidates in the sorter at each ECN step. Simulation results indicate that, while significantly reducing the number of real additions at check nodes, JD-EMS algorithm performs as well as EMS algorithm on both AWGN and Rayleigh fading channels.

DOI
10.4156/jcit.vol6.issue6.47

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To reduce the high decoding complexity of q-ary LDPC codes, a joint-demodulation and extended min-sum (JD-EMS) decoding algorithm is presented in this paper. By utilizing the squares of the distances between signal and constellation points over constellation graph as the decoder input soft messages, the proposed algorithm not only facilitates the computations of the decoder initial messages, but also avoids the performance loss due to conversions between probabilities and log-likelihoodratios. The elementary check node (ECN) processing is also improved in JD-EMS algorithm, thus the number of real additions can be reduced. Moreover, we also give an upper bound of the number of comparison candidates in the sorter at each ECN step. Simulation results indicate that, while significantly reducing the number of real additions at check nodes, JD-EMS algorithm performs as well as EMS algorithm on both AWGN and Rayleigh fading channels.
Decoded with the extended min-sum(EMS) algorithm,q-ary LDPC codes suffer great performance degradation compared with that decoded with the q-ary sum-product algorithm(QSPA) in case the length nm of message vectors is too small.To solve this problem,a dynamic EMS(D-EMS) algorithm is proposed in this paper.First,we examined the distribution of likelihood values among GF(q) symbols in the message vectors,and concluded that the likelihood values would concentrate to a small portion of symbols as the iteration number increases.Therefore,the D-EMS algorithm first set the length of message vectors to nm1,then truncate it to nm2 after certain decoding iterations,thus the decoding computational complexity can be efficiently reduced.Meanwhile,in order to reduce the complexity of real comparisons in the decoder,the proposed algorithm employs the bubble check(BC) algorithm during the check node elementary steps.Complexity analysis and simulation results indicate that,under appropriate parameter configurations,while efficiently reducing the decoding complexity of the EMS algorithm,the D-EMS algorithm performs nearly as well as the corresponding EMS algorithm over both AWGN and Rayleigh fading channels,and thus can be efficiently applied to practical communication systems based on q-ary LDPC codes.
The extended min-sum (EMS) algorithm is adopted for non-binary low density parity check (NB-LDPC) codes. The high complexity of EMS algorithm is a hot topic in recent years. Aiming at the problem, a low-complexity EMS algorithm based on NB-LDPC codes is proposed. Dynamic bubble-check (DBC) algorithm in elementary check node (ECN) steps is adopted to reduce the complexity of check node. Furthermore, the proposed algorithm dynamically truncates the length of the message vector by the number of decoding iterations. Taking the length of message vector truncated again as half of the original one as an example, the simulation results and complexity are analyzed. Analysis shows that, compared to the EMS algorithm, computational complexity of comparisons and real additions of check node of the proposed algorithm have reduced by about 70% and 25% respectively. Meantime, the decoding performance of the proposed algorithm approach that of EMS algorithm and the loss is only near 0.08 dB when the bit error rate (BER) is 10−3and the Galois fieldGF(q)(q=16)GF(q)(q=16)GF(q)(q=16).
To overcome the drawback of the extended min-sum algorithm(EMS),an improved EMS decoding algorithm is proposed,which is designed for LDPC over GF(q).The algorithm adaptively chooses the rank of FHT in each iteration step according to the average variance of bit nodes' probability pairs.It differs from the original EMS algorithm in which the rank of FHT for each iteration step is a constant.Moreover,for oscillating variable nodes,the message of the previous iteration is added to the current message in the iterative procedure to reduce loss of performance and effects of oscillation.Experimental results show that the proposed algorithm can achieve better performance and converge faster than EMS with the same decoding complexity.
A simplified algorithm for check node processing of extended min-sum (EMS) q-ary LDPC decoders is presented in this letter. Compared with the bubble check algorithm, the so-called dynamic bubble-check (DBC) algorithm aims to further reduce the computational complexity for the elementary check node (ECN) processing. By introducing two flag vectors in ECN processing, The DBC algorithm can use the minimum number of comparisons at each step. Simulation results show that, DBC algorithm uses significantly fewer comparison operations than the bubble check algorithm, and presents no performance loss compared with standard EMS algorithm on AWGN channels.
Q-ary low-density parity-check (LDPC) codes, compared with binary ones, produce a better error performance but with a higher decoding complexity. Various solutions, such as speeding up single operations or reducing the total number of operations, have been proposed for accelerating the decoding process. In this letter, we propose a modification to the extended min-sum (EMS) decoding algorithm. The aim is to improve the decoding speed without sacrificing any error performance over an additive white Gaussian noise (AWGN) channel environment.
In comparison to the binary LDPC codes, the nonbinary low-density parity-check (NB-LDPC) codes have the advantage of solving burst errors. In order to improve the accuracy of the decoding results, an improved extended min-sum (EMS) algorithm is proposed in this paper. By adopting the feedback idea of joint iterative detection algorithm and introducing the reliability and stability parameters, the new algorithm can mitigate the influence of Log-likelihood ratio (LLR) oscillation on the decoding result and adjust the update information of the check node properly, thereby improving the decoding accuracy. This method can effectively restrain the LLR oscillation and speed up the convergence rate, thus the final decision result can be amended. Simulation results show that, the proposed improved EMS decoding algorithm heightens the bit error rate performance and reduces average number of iterations, meanwhile the additional computations are within acceptable range.