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IEEE Communications Letters

Q-ary LDPC decoder with euclidean-distance-based sorting criterion

Xiao Xia Shen, Francis C. M. Lau

Published May 1, 2010• 3 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2010.05.092493

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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.
Immediate generalization of Gallager's binary low-density parity-check (LDPC) codes gave birth to the LDPC codes over GF(q), which demonstrated error performance exceeding that of binary codes with compromised complexity. Various methods had been proposed for the decoder with an aim to simplifying the belief propagation algorithm. One of the algorithms was the "extended min-sum (EMS)" decoder which concerned only a limited number of incoming messages at the checks. In this paper, we propose a modification to further simplify the EMS decoder without sacrificing performance.
The extended min-sum algorithm (EMS) for decoding non-binary low density parity check (NB-LDPC) codes reduces the decoding complexity by truncating the message vector by retaining only the most reliable symbols. However, the EMS algorithm does not consider that the noise of the received codeword is gradually reduced as the iteration count goes up. In this paper, we propose a low-complexity adaptive EMS algorithm, called threshold-based EMS (TB-EMS). The TB-EMS algorithm has a simple adaptive rule to calculate the new message vector length compared to the A-EMS. The proposed algorithm selects one of two message vector lengths. Experimental results show that the proposed algorithm reduces the decoding complexity with minimal performance degradation compared with the EMS algorithm. Further, the decoding performance of the TB-EMS is better than A-EMS.
Non-binary low-density parity-check (NB-LDPC) codes are robust to various channel impairments. In this paper, we present a new decoding algorithm for the NB-LDPC decoder that is based on the q-ary min-sum algorithm (QMSA). The new one modifies the check node (CN) computations of the QMSA into two steps. By reorganizing the message entries and providing the most likely symbol, a compressed intermediate message can be easily obtained and stored, from which the check-to-variable messages can be computed with a look-up table. Thus the decoder architecture can have a straightforward design for the CN with reduced complexity and memory requirements. Besides, the simulation results demonstrate that the proposed algorithm has negligible performance loss compared to the QMSA over AWGN channel.
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.
Short non-binary (NB) low-density parity-check (LDPC) codes provide excellent error rate performance compared to their binary counterparts. This paper presents an efficient layered decoder architecture for short high-order non-binary LDPC codes. A hardware-friendly message-adaptation extended Min-Sum (MA-EMS) algorithm is proposed, where a variety of truncation sizes and message compressions are used, such that the number of decoding cycles and the storage requirements can be reduced. A configurable design that supports a variety of truncation sizes is also proposed such that the hardware efficiency can be significantly increased. An early termination (ET) scheme is used so as to decrease the required number of decoding cycles. These techniques can greatly reduce the complexity of the decoder with almost no loss in performance. To demonstrate these techniques, a (64, 32) 256-ary LDPC decoder is implemented in a 90 nm process, which can provide a throughput of 322.9 Mbps and occupies an area of 6.74 mm2. The proposed MA-EMS decoder is able to achieve a similar error-rate performance and a much better area efficiency compared to the original EMS decoder.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.