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Biennial Symposium on Communications

TS-LDPC analog decoding based on the Min-Sum algorithm

Alireza Rabbani Abolfazli, Yousef R. Shayan, Glenn E. R. Cowan

Published May 1, 2012• 2 citations
Publisher

Abstract

It has been shown that Min-Sum (MS) algorithms have low complexity in the implementation of analog VLSI decoders compared to the Sum-Product (SP) algorithm. Moreover, Turbo-structured LDPC (TS-LDPC) codes are known to have lower error floor than random LDPC codes. In this paper, Min-Sum and Min-Sum with correction factor algorithms are reviewed and adapted with TS-LDPC codes for future analog VLSI implementation. Simulation results show that the error performance of the Min-Sum algorithm is comparable with the Sum-Product algorithm for the same block length. This means that the lower error floor property of TS-LDPC codes is preserved when MS algorithms are used. Moreover, analog decoder implementation of TS-LDPC codes is studied. To test the suitability of the MS algorithm based TS-LDPC decoder some analog impairments such as mismatch, leakage and noise are considered in the decoding procedure of TS-LDPC codes. In each case, it is shown that the degradation of the error performance of TS-LDPC codes due to analog impairments is negligible. Therefore, it can be concluded that the analog decoder of the TS-LDPC code using MS algorithm is fairly robust against analog imperfections and may be considered in future implementation of analog VLSI decoder.

DOI
10.1109/qbsc.2012.6221374

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It has been shown that Min-Sum (MS) algorithms have low complexity in the implementation of analog VLSI decoders compared to the Sum-Product (SP) algorithm. Moreover, Turbo-structured LDPC (TS-LDPC) codes are known to have lower error floor than random LDPC codes. In this paper, Min-Sum and Min-Sum with correction factor algorithms are reviewed and adapted with TS-LDPC codes for future analog VLSI implementation. Simulation results show that the error performance of the Min-Sum algorithm is comparable with the Sum-Product algorithm for the same block length. This means that the lower error floor property of TS-LDPC codes is preserved when MS algorithms are used. Moreover, analog decoder implementation of TS-LDPC codes is studied. To test the suitability of the MS algorithm based TS-LDPC decoder some analog impairments such as mismatch, leakage and noise are considered in the decoding procedure of TS-LDPC codes. In each case, it is shown that the degradation of the error performance of TS-LDPC codes due to analog impairments is negligible. Therefore, it can be concluded that the analog decoder of the TS-LDPC code using MS algorithm is fairly robust against analog imperfections and may be considered in future implementation of analog VLSI decoder.
Low Density Parity Check (LDPC) approaches Shannon -limit performance for binary field and long code lengths. However performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding, while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Low Density Parity Check Codes (LDPC) give groundbreaking performance which is known to approach Shannon's limits for sufficiently large block length. Historically and recently, LDPC have been known to give superior performance than concatenated coding. In the following paper, a proposal to modify the standard Min-Sum (MS) algorithm for decoding LDPC codes is presented. This is done by introduction of a difference to sum ratio factor, κ in the check to bit node updating process. The algorithm is further extended by implementing hard decision of the Bit-Flipping (BF) algorithm over the soft decision of MS algorithm. Simulation results demonstrate that the proposed algorithms are effective in imparting a better performance in terms of a lower bit error rate (BER) at medium to high signal to noise ratio (SNR) when compared to the traditional MS algorithm while adding fair amount of complexity.
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.
Min-sum algorithm(MSA) and its modification are used in LDPC decoder implementations because of its error performance and low computation complexity. In this paper a modified min-sum LDPC decoding algorithm through approximation enhancement using the smallest three minimum values is presented. The proposed algorithm improves error performance and reduces decoder iterations. From the simulation results for 5G NR LDPC codes, we show that the proposed algorithm can achieve about 1.6dB improvement of FER compared to the min-sum decoding algorithm and provide about 10% reduction of the average iteration numbers compare to NMSA with optimum normalization factor.