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International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET)

Performance Analysis of Normalized Min-Sum Decoder for LDPC using non-uniform Quantization

K Pargunarajan, R Gandhiraj, Madaswamy Jayakumar

Published Mar 20, 2025• 2 citations
Publisher

Abstract

Very high data rates and decoding computational complexity place strict constraints in 5G and 6G communications. In this paper, non-uniform Quantized Decoding algorithm is proposed for Low-density Parity Check codes (LDPC). In the proposed algorithm, the check node updating process is carried out using quantization, which reduces complexity. The Sum Product Algorithm (SPA) is iterative message passing decoding techniques offer the optimal performance for LDPC codes. Implementations use message-passing decoding with more precision, results extremely high complexity. In Iterative, message-passing (MP), trapping sets and absorbing sets causes low error floor. In this article non-uniform quantization proposed to overcome dynamic range of values over uniform quantization. Simulation results provide coding gain increases closer to of 0.5 dB in higher SNR and has good error floor at 10−5.

DOI
10.1109/wispnet64060.2025.11004875

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Very high data rates and decoding computational complexity place strict constraints in 5G and 6G communications. In this paper, non-uniform Quantized Decoding algorithm is proposed for Low-density Parity Check codes (LDPC). In the proposed algorithm, the check node updating process is carried out using quantization, which reduces complexity. The Sum Product Algorithm (SPA) is iterative message passing decoding techniques offer the optimal performance for LDPC codes. Implementations use message-passing decoding with more precision, results extremely high complexity. In Iterative, message-passing (MP), trapping sets and absorbing sets causes low error floor. In this article non-uniform quantization proposed to overcome dynamic range of values over uniform quantization. Simulation results provide coding gain increases closer to of 0.5 dB in higher SNR and has good error floor at 10−5.
In this paper, a modified normalized Min-Sum algorithm (MNMSA) is proposed for decoding irregular Low Density Parity Check Codes (LDPC) with non-uniform degree distribution. The proposed algorithm provides an efficient decoding scheme to enhance the error performance of an irregular LDPC code without increasing the hardware complexity. An efficient 6- bit quantization scheme is utilized in the proposed algorithm with optimally combined normalization and down scaling factors to resolve the magnitude overestimation issue which occurs during iterative message passing process between the nodes. The simulation results demonstrate that the proposed algorithm achieves good decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without the requirement of complex arithmetic calculations. Compared to other min- sum based decoding algorithms the decoding process of the proposed MNMSA requires only fewer decoding iterations over wide range of signal- to- noise ratio (SNR) to achieve comparable decoding performance to that of Belief Propagation (BP) algorithm without increasing the hardware complexity.
This paper analyzes the performance of quantized min-sum decoding algorithms for irregular low-density parity-check (LDPC) codes. For regular LDPC codes, it is known that the normalized or offset min-sum decoding algorithm with quantization bits less than 6 bits achieves good performances over wide range of signal-to-noise ratios (SNR). However, finite precision effects in decoding irregular LDPC codes are different from that in decoding regular LDPC codes which is caused by the difference of convergence speeds between low degree nodes and high degree nodes. This paper proposes a novel method to improve the performance of the conventional normalized or offset min-sum decoding algorithm when it is approximated with finite precision for hardware implementations. The proposed method applies down-scaling factors to intrinsic information which has effects on increasing the reliability of extrinsic information at variable nodes and compensating the quantization errors caused by finite precision. Computer simulation results for irregular LDPC codes show that the proposed normalized and offset min-sum decoding algorithms achieve better performances at high SNR compared to the conventional normalized and offset min-sum algorithms under (6:2) quantization scheme.
In this paper, a non-uniform quantization scheme is proposed for the decoding of Low-Density Parity-Check (LDPC) codes with the Sum-Product Algorithm (SPA). With the proposed scheme, the quantization-range and quantization-interval for the soft Log-Likelihood-Ratio (LLR) values of the decoder input, the variable nodes, and the check nodes are set separately, and are also adjusted according to the evolution of the probability density distribution of the LLR values in the iterative decoding procedure to minimize the difference between the decoding values before quantization and that after quantization. Simulation results show that decoding with 3-bit non-uniform quantization of the proposed scheme may obtain a BER performance slightly better than that of decoding with 6-bits quantization of the traditional uniform quantization method.
A code-independent performance bound for a given absorbing set is derived for quantized low-density parity-check (LDPC) decoders. The analysis demonstrates that each absorbing set in the Tanner graph imposes a specific lower bound on the frame error rate (FER) of any code containing that absorbing set under a given quantization scheme. This approach is applicable to any message-passing (MP) decoding algorithm and any uniform or non-uniform quantization scheme for LDPC codes. Simulation results using the sum-product algorithm (SPA) provide FERs that are consistent with the obtained bounds. In addition, the bounds demonstrate that the conventional quantized SPA is not capable of achieving very low FERs if the LDPC codes contain certain absorbing sets.
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.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.