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International Conference on Communications and Networking in China (ChinaCom)

Improved parallel weighted bit flipping decoding of finite geometry LDPC codes

Guangwen Li, Dashe Li, Yuling Wang, Wenyan Sun

Published Aug 1, 2009• 5 citations
Publisher

Abstract

To seek a decoding scheme with good performance, low complexity and fast convergence, we present an improved parallel weighted bit flipping (IPWBF) algorithm for finite geometry low-density parity-check codes whose parity check matrix is of heavy row and column weights. In the IPWBF, a bit flipping (BF) function and two parallel BF criteria, all of which scatter in the literature, are exploited jointly to serve our purpose. Meanwhile, differential evolution is used to optimize the involved parameters. Simulation results show that the proposed algorithm achieves an observable performance gain over its counterparts without any complexity penalty. Furthermore, with respect to other known low complexity decodings such as normalized BP-based, the IPWBF yields a new performance versus complexity tradeoff, that is, higher throughput at the expense of moderate performance loss.

DOI
10.1109/chinacom.2009.5339713

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To seek a decoding scheme with good performance, low complexity and fast convergence, we present an improved parallel weighted bit flipping (IPWBF) algorithm for finite geometry low-density parity-check codes whose parity check matrix is of heavy row and column weights. In the IPWBF, a bit flipping (BF) function and two parallel BF criteria, all of which scatter in the literature, are exploited jointly to serve our purpose. Meanwhile, differential evolution is used to optimize the involved parameters. Simulation results show that the proposed algorithm achieves an observable performance gain over its counterparts without any complexity penalty. Furthermore, with respect to other known low complexity decodings such as normalized BP-based, the IPWBF yields a new performance versus complexity tradeoff, that is, higher throughput at the expense of moderate performance loss.
Aiming at seeking a low-complexity decoder with fast decoding convergence speed for short or medium low-density parity-check (LDPC) codes, an improved parallel weighted bit-flipping (IPWBF) algorithm, which is applied flexibly for two classes of codes is presented here. For LDPC codes with low column weight in their parity check matrix, both bootstrapping and loop detection procedures, described in the existing literature, are included in IPWBF. Furthermore, a novel delay-handling procedure is introduced to prevent the codeword bits of high reliability from being flipped too hastily. For large column weight finite geometry LDPC codes, only the delay-handling procedure is included in IPWBF to show its effectiveness. Extensive simulation results demonstrate that the proposed algorithm achieves a good tradeoff between performance and complexity.
For finite geometry low-density parity-check codes, heavy row and column weights in their parity check matrix make the decoding with even Min-Sum (MS) variants computationally expensive. To alleviate it, we present a class of hybrid schemes by concatenating a parallel bit flipping (BF) variant with an Min-Sum (MS) variant. In most SNR region of interest, without compromising performance or convergence rate, simulation results show that the proposed hybrid schemes can save substantial computational complexity with respect to MS variant decoding alone. Specifically, the BF variant, with much less computational complexity, bears most decoding load before resorting to MS variant. Computational and hardware complexity is also elaborated to justify the feasibility of the hybrid schemes.
For finite geometry low-density parity-check codes, heavy row and column weights in their parity check matrix make the decoding with even min–Sum (MS) variants computationally expensive. To alleviate it, the authors present a class of hybrid schemes by concatenating a parallel bit flipping (BF) variant with an MS variant. Meanwhile, the BF variant, with much less computational complexity, attempts decoding the receive sequence firstly, and only decoding failure of the BF variant triggers the MS variant. Hence the BF variant performance heavily impacts the overall hybrid scheme, which is illustrated in two case studies. Computational and hardware complexity is then elaborated to justify the feasibility of the hybrid schemes. In most SNR region of interest, without compromising performance or convergence rate, the proposed hybrid schemes can save substantial computational complexity when compared with the MS variant decoding alone.
Extensive simulations show that for some low density parity-check(LDPC)codes of low row/colum weight,the modified sum of the magnitude based weighted bit flipping(MSMWBF)decoding algorithm performs extraordinarily well.However,this dose not hold when it comes to large row/colum weight finite-geometry LDPC codes,which is first theoretically analyzed.Secondly,improvement in performance is observed for large row/colum weight LDPC codes by considering an additive offset term for the parity-check-equation reliability of the above algorithm.Simulation results show that the performance of the improved scheme is better than that of the MSMWBF algorithm about 0.63 dB at bit-error rate of 10-5 over the additive white Gaussian noise channel with only a modest increase in computational complexity.
An improved bit-flipping(BF) algorithm with low complexity for decoding structured low-density parity-check codes(LDPC) is proposed to improve the performance of the hard-decision BF algorithm.The hard-decision bits are divided into two groups based on the magnitudes of the received symbols,and at each iteration,the proposed algorithm can flip more than one bit with using two thresholds,and the flipping error probability is effectively decreased.The improved BF algorithm requires some real number comparisons before iterations and requires only logical operations during the iterations.Compared with the weighted bit-flipping algorithm and its modifications,the new method is with significantly lower complexity.Simulations show that the proposed algorithm is provided with very fast convergence speed and excellent performance with significantly low complexity.