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International Conference on Advanced Communication Technology

Intensity reflection coefficient based Min-Sum decoding for Low Density Parity Check Codes

Md. Moshiur Rahman Farazi, Mohammad Rakibul Islam, Khandaker Sultan Mahmood, Md Farhan Tasnim Oshim

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

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 factor, intensity reflection coefficient (IRC) in the check to bit node updating process. Simulation results demonstrate that the proposed algorithms are effective in imparting a better performance in terms of a lower bit error rate (BER) at low to medium signal to noise ratio (SNR) when compared to the traditional MS or Belief Propagation (BP) algorithm while adding a minimum amount of complexity.

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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 factor, intensity reflection coefficient (IRC) in the check to bit node updating process. Simulation results demonstrate that the proposed algorithms are effective in imparting a better performance in terms of a lower bit error rate (BER) at low to medium signal to noise ratio (SNR) when compared to the traditional MS or Belief Propagation (BP) algorithm while adding a minimum amount of complexity.
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.
A modified Min-Sum algorithm for low-density parity check codes is proposed in this paper. The inaccurate check node messages of the Min-Sum algorithm compared to the belief propagation (BP) algorithm are compensated by modified variable node messages, which is different from the normalized Min-Sum algorithm. The modified factor is obtained before decoding program and only one extra multiplication is needed in one cycle. So the increased complexity is fairly low. The simulation results show that the bit error rate (BER) and average number of iteration of the modified Min-Sum algorithm are very close to the BP algorithm, the modified algorithm can improve the BER performance compared to the Min-Sum algorithm while added complexity slightly.
A check node degree-based modified min-sum algorithm which classifies the codes was developed to reduce the complexity and improve the performance of decoding algorithm for low-density parity-check(LDPC) codes.The algorithm corrects both the minimum and sub-minimum absolute values of incoming messages in the check nodes.Two correction factors are obtained by calculating the offset between the belief propagation(BP) algorithm and the min-sum algorithm based on the check node degree.Simulations show that the algorithm achieves better performance than the BP algorithm at high signal noise ratio.The algorithm is also less complex than the BP algorithm and provides a good tradeoff between performance and complexity for any check node degree distribution in the LDPC codes.
In this paper, a modified min-sum decoding algorithm based on classified correction is proposed for low density parity check (LDPC) codes. Different from the single correction in the normalized belief propagation (BP)-based and offset BP-based algorithms [4], the proposed algorithm utilizes two corrections for both minimum and sub-minimum magnitudes of input messages in check nodes. These two correction factors can be obtained by analyzing the offset of updated messages in check nodes between the BP and the min-sum algorithms associated with check node degree. Simulation results show that the proposed algorithm can achieve performance very close to that of the BP algorithm. Furthermore, the FPGA implementation of this algorithm can reach a throughput of 200 Mbps at BER=10-6with lower complexity and fewer resources than the BP algorithm.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.