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Computer Engineering and Applications Journal

Concatenation decoding algorithm based on BP and WED

PI De-fu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Weighted Erasure Decoding(WED) algorithm is investigated in this paper,based on which,a new BP-WED concatenation algorithm for LDPC codes is proposed.Belief Propagation(BP) algorithm is a kind of soft-in-soft-out algorithm.When BP algorithm fails,the soft LLR reliable information is quantized and sent to the WED algorithm.WED algorithm is a very attractive solution for practical implementations of low-complexity reliability-based algorithms owing to its simplicity,therefore the BP-WED concatenation algorithm is more easy in hardware implementation compared to other concatenation algorithms,such as BP-OSD,BP-BMA,etc.The simulation results show that the proposed concatenation algorithm is effective,and can achieve a good tradeoff between computational complexity and decoding performance.

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Weighted Erasure Decoding(WED) algorithm is investigated in this paper,based on which,a new BP-WED concatenation algorithm for LDPC codes is proposed.Belief Propagation(BP) algorithm is a kind of soft-in-soft-out algorithm.When BP algorithm fails,the soft LLR reliable information is quantized and sent to the WED algorithm.WED algorithm is a very attractive solution for practical implementations of low-complexity reliability-based algorithms owing to its simplicity,therefore the BP-WED concatenation algorithm is more easy in hardware implementation compared to other concatenation algorithms,such as BP-OSD,BP-BMA,etc.The simulation results show that the proposed concatenation algorithm is effective,and can achieve a good tradeoff between computational complexity and decoding performance.
This paper analyses the ordered statistic decoding(OSD) algorithm of short LDPC codes and investigates BP-OSD concatenation algorithm and LLR accumulation algorithm.Considering the tradeoff between the complexity and performance of decoding,the min-sum algorithm was used instead of the BP algorithm,and it was concatenated with LLR accumulation algorithm.Simulation results show that compared with the original BP algorithm,the performance of the improved concatenation algorithm has been greatly raised,and compared with the BP-OSD concatenation algorithm,its decoding complexity has been reduced and the performance is nearly the same.
Low-density parity-check (LDPC) codes have been widely used in practice due to their excellent error correction capabilities. However, the error correction performance of traditional decoding algorithms for LDPC codes is limited under short block lengths. To address this problem, this paper proposes an effective scheme that contains two stages for decoding short LDPC codes. In the first stage, the traditional belief propagation (BP) iterative algorithm is used to decode an LDPC code. The decoding process terminates if a codeword is obtained in this stage. Otherwise, the second stage decoding is invoked, in which the ordered reliability bits guessing random additive noise decoding (ORBGRAND) algorithm is applied. The accumulated log-likelihood ratios in the first stage are used to order the test error patterns in the ORBGRAND algorithm. Simulation results indicate that the proposed BP-ORBGRAND scheme can outperform the traditional BP iterative algorithm with relatively low additional complexity. Compared with the decoding scheme that concatenates the BP algorithm and the order statistics decoding (OSD) algorithm, the proposed decoding scheme has similar performance and the operations involved can be efficiently implemented in the hardware platform. All these indicate that the proposed scheme is desirable for practical purposes.
A hybrid belief propagation (BP) decoding algorithm for low-density parity-check code is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. The hybrid scheme is presented by integrating the BP algorithm with the bit-flipping function which is used as adaptive weighted factor in the BP iteration decoding. The adaptive weighting factor is based on the average weighted reliability measure of the hard output of decoder. The proposed hybrid adaptive weighted iteration scheme can efficiently increase the convergence speed of the belief propagation decoding and therefore improve the error performance. Simulation results show that the proposed algorithm can significantly reduce the decoding complexity and achieve better error performances as compared with the sum-product algorithm.
Recently, both polar codes and low-density parity-check (LDPC) codes have been adopted by 3GPP eMBB scenario. Since both codes exist in one system, it is natural to consider the concatenation scheme of them. In this paper, a merged belief propagation (BP) decoding algorithm for the concatenated codes of polar and LDPC codes is proposed. By jointing factor graphs, this merged algorithm is designed by serially executing the LDPC and polar decoding. According to numerical results, the bit error rate (BER) of this proposed algorithm can achieve a notable improvement for different code rates compared with the conventional separated approach. For (1024, 512) polar code, the performance gain of the proposed scheme is at least 0 5 dB even at a low BER of 1 × 10-2. Finally, further refinements of computational complexity and hardware implementation are also provided in this paper.
A new strategy of belief propagation (BP) decoder for LDPC codes is presented by sequentially concatenating the scheduling algorithms of flooding and node-wise residual belief propagation (NW RBP) without increasing the complexity of hardware implementation. Compared to NW RBP, the concatenated BP decoder significantly decreases the decoding latency caused by computing and sorting the residual of each message in the factor graph of an LDPC code. As the signal-to-noise ratio (SNR) increases, the decoding performance of the concatenated BP decoder outperforms that of purely applying flooding or NW RBP, and the average number of decoding iterations required for the concatenated decoder decreases and tends to be approximately the same as the other two.
In this work, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between BP decoding which remains suboptimum, and maximum likelihood decoding (MLD) which is too complex to be implemented for the codes considered. A stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is also proposed for this combined decoding approach. Simulations results for several Gallager LDPC codes and different set cyclic (DSC) codes of hundreds of information bits are given and elaborated.