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International Conference on Wireless Communications and Signal Processing (WCSP)

Threshold-based extended minimum-sum algorithm for non-binary LDPC codes

Ke Lai, Erbao Li, Jing Lei

Published Oct 1, 2016• 0 citations
Publisher

Abstract

In this paper, we propose a new improved algorithm to reduce the decoding complexity of NB-LDPC codes especially when the number of iteration is large. The proposed algorithm is based on the extended min-sum (EMS) which truncates the message vectors and trellis-based EMS (T-EMS) which employs the trellis representation. Our modification of EMS introduces the thresholds to further truncate the incoming messages to the check node. The performance of our improved new algorithm is only 0.05dB (resp 0.2dB) to BP in the waterfall region over GF(8) (resp GF(128)), but the complexity will reduce to lower than half of the EMS when the threshold is chosen reasonable.

DOI
10.1109/wcsp.2016.7752595

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In this paper, we propose a new improved algorithm to reduce the decoding complexity of NB-LDPC codes especially when the number of iteration is large. The proposed algorithm is based on the extended min-sum (EMS) which truncates the message vectors and trellis-based EMS (T-EMS) which employs the trellis representation. Our modification of EMS introduces the thresholds to further truncate the incoming messages to the check node. The performance of our improved new algorithm is only 0.05dB (resp 0.2dB) to BP in the waterfall region over GF(8) (resp GF(128)), but the complexity will reduce to lower than half of the EMS when the threshold is chosen reasonable.
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.
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).
In this paper, we present an improvement and a new implementation of a simplified decoding algorithm for non-binary low density parity-check codes (NB-LDPC) in Galois fields GF(q). The base algorithm that we use is the Extended Min-Sum (EMS) algorithm, which has been widely studied in the recent literature, and has been shown to approach the performance of the belief propagation (BP) algorithm, with limited complexity. In our work, we propose a new way to compute modified configuration sets, using a trellis representation of incoming messages to check nodes. We call our modification of the EMS algorithm trellis-EMS (T-EMS). In the T-EMS, the algorithm operates directly on the deviation space by considering a trellis built from differential messages, which serves as a new reliability measure to sort the configurations. We show that this new trellis representation reduces the computational complexity, without any performance degradation. In addition, we show that our modifications of the algorithm allows to greatly reduce the decoding latency, by using a larger degree of hardware parallelization.
In this paper, we propose a new method to implement the Extended Min-Sum (EMS) algorithm based on trellis representation of inputting messages to the check node. The original EMS reduces the decoding complexity by choosing only nmmost reliable values and by introducing the idea of configuration sets conf(nm, nc), where ncis the number of deviations from the most reliable output configuration. We propose to work directly on the deviation space by building a configuration trellis based on delta messages, which serves as a new reliability measure. The algorithm is called trellis-EMS (T-EMS). By using the new trellis representation, only nc+1 minimum values from each row of the trellis need to be considered, which reduces the ordering complexity. The trellis representation in the deviation space also reduces the number of output configurations tested, without any performance degradation. Our method is especially suitable for moderate field size q and large check node degree nonbinary LDPC codes.
This paper presents a novel truncation rule for the extended min-sum (EMS) decoding of non-binary low-density parity-check (NB-LDPC) codes. The conventional NB-LDPC decoders involve vector-messages of length equal to the field size q. The complexity of these decoders increases significantly as q increases. In the EMS algorithm, the vector-messages are truncated by discarding the less-likely symbols. In this paper, we propose a truncation rule so that the lengths of the vector-messages are reduced to the so-far best limit without compromising on the error correction capability. We devise a proximity matrix which helps to identify the essential components of a vector-message for truncation. The proposed truncation rule has been applied to several NB-LDPC codes of different field sizes. Simulation results for these codes show that the proposed rule can achieve the maximum truncation with negligible performance loss.
In this paper, we proposed a modified Trellis extended min-sum (T-EMS) algorithm with L truncations for non-binary low density parity check (NB-LDPC) codes. The proposed algorithm achieves to reduce complexity of T-EMS algorithm, especially on large order Galois fields GF(q). In order to improve the error-correcting performance of the algorithm, an elitist selection (ES) strategy is presented, which enlarges the belief value of the selected symbols. As a proof, the simulation results and complexity analysis show that with the increase of q, the complexity decreases obviously. However, in the case of a suitable L value, the LT-EMS algorithm with ES strategy is not inferior to the T-EMS algorithm in performance. In addition, the ES strategy can accelerate the convergence rate and reduce the number of iterations of the decoding process, which will enhance the decoding throughput.