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A Modified Optimally Quantized Offset Min-Sum Decoding Algorithm for Low-Complexity LDPC Decoder

Michaelraj Kingston Roberts, Ramesh Jayabalan

Published Aug 23, 2014• 9 citations
Publisher
DOI
10.1007/s11277-014-2026-2

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In this paper, we analyze the performance of quantized offset min-sum (MS) decoding algorithm and propose an optimally quantized offset MS algorithm for a flexible low-density parity-check (LDPC) decoder. It is known that the offset MS decoding algorithm is implemented with simplified hardware complexity and achieves good decoding performance. However, the finite precision effects in decoding LDPC codes result in performance different from floating point. The performance degradation is caused by different dynamic ranges of input data at high signal-to-noise ratio (SNR). The proposed offset MS algorithm uses the received data directly instead of log-likelihood ratio (LLR) data as the intrinsic information. It can achieve better performance than the conventional one since its offset factor is more effective at a wide range of SNR and the intrinsic information is quantized more robustly since it is independent of channel information. Also, it is possible for the proposed scheme to use a same quantization scheme for a flexible LDPC decoder, which can decode several kinds of LDPC codes. Simulation results show that our optimally quantized offset MS algorithms with 5-bits for (1728, 864) and (1728, 1296) irregular LDPC codes achieve better performance compared with the conventional offset MS algorithms with 6-bits quantization scheme.

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In order to reduce the implementation complexity of the quantized decoding algorithm for the Low-Density Parity-Check(LDPC)codes, an improved 4-bit quantized Adaptive-Offset Min-Sum(AOMS)algorithm is designed. The improved AOMS algorithm is obtained by introducing a pre-determined iteration number as the condition of adaptive selecting the offset factors. Furthermore, a 4-bit nonuniform quantization scheme is designed, which can guarantee the dynamic range of the extrinsic information and easily utilize the optimized quantized offset factors. The simulation results show that, compared with the floating-point decoding algorithms, the performance degradation of the improved 4-bit nonuniform quantized AOMS algorithm can be neglected.

Computer Engineering and Applications Journal•Jan 1, 2014•0 citations
In this paper, we analyze the performance of quantized offset min-sum (MS) decoding algorithm and propose an optimally quantized offset MS algorithm for a flexible low-density parity-check (LDPC) decoder. It is known that the offset MS decoding algorithm is implemented with simplified hardware complexity and achieves good decoding performance. However, the finite precision effects in decoding LDPC codes result in performance different from floating point. The performance degradation is caused by different dynamic ranges of input data at high signal-to-noise ratio (SNR). The proposed offset MS algorithm uses the received data directly instead of log-likelihood ratio (LLR) data as the intrinsic information. It can achieve better performance than the conventional one since its offset factor is more effective at a wide range of SNR and the intrinsic information is quantized more robustly since it is independent of channel information. Also, it is possible for the proposed scheme to use a same quantization scheme for a flexible LDPC decoder, which can decode several kinds of LDPC codes. Simulation results show that our optimally quantized offset MS algorithms with 5-bits for (1728, 864) and (1728, 1296) irregular LDPC codes achieve better performance compared with the conventional offset MS algorithms with 6-bits quantization scheme.
It is well known that for decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs). In this paper, we demonstrate that, for quantized LDPC decoders, although the MSA achieves better high SNR performance than the AMSA and OMSA, each of the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we propose a novel modification of the MSA for decoding quantized LDPC codes with the aim of lowering the error floor. Compared to the quantized MSA, the proposed modification is also helpful at low SNRs, where it matches the waterfall performance of the quantized AMSA and OMSA. The new algorithm is designed based on the assumption that trapping/absorbing sets (or other problematic graphical objects) are the major cause of the error floor for quantized LDPC decoders, and it aims to reduce the probability that these problematic objects lead to decoding errors.
In order to reduce the implementation complexity of the quantized decoding algorithm for the Low-Density Parity-Check(LDPC)codes, an improved 4-bit quantized Adaptive-Offset Min-Sum(AOMS)algorithm is designed. The improved AOMS algorithm is obtained by introducing a pre-determined iteration number as the condition of adaptive selecting the offset factors. Furthermore, a 4-bit nonuniform quantization scheme is designed, which can guarantee the dynamic range of the extrinsic information and easily utilize the optimized quantized offset factors. The simulation results show that, compared with the floating-point decoding algorithms, the performance degradation of the improved 4-bit nonuniform quantized AOMS algorithm can be neglected.