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IEEE International Symposium on Circuits and Systems proceedings

Adaptive quantization in min-sum based irregular LDPC decoder

Sangmin Kim, Gerald E. Sobelman, Hanho Lee

Published May 1, 2008• 21 citations
Publisher

Abstract

In this paper, we present adaptive quantization schemes in the normalized min-sum decoding algorithm considering scaling effects to improve the performance of irregular low-density parity-check (LDPC) decoder for WirelessMAN (IEEE 802.16e) applications. We discuss the finite precision effects on the performance of irregular LDPC codes and develop optimal finite word lengths of variables over an SNR. For floating point simulation, it is known that in the normalized min-sum or offset min-sum algorithms the performance of a min-sum based decoder is not sensitive to scaling in the log-likelihood ratio (LLR) values. However, when considering the finite precision for hardware implementation, the scaling affects the dynamic range of the LLR values. The proposed adaptive quantization approach provides the optimal performance in selecting suitable input LLR values to the decoder as far as the tradeoffs between error performance and hardware complexity are concerned.

DOI
10.1109/iscas.2008.4541473

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In this paper, we present adaptive quantization schemes in the normalized min-sum decoding algorithm considering scaling effects to improve the performance of irregular low-density parity-check (LDPC) decoder for WirelessMAN (IEEE 802.16e) applications. We discuss the finite precision effects on the performance of irregular LDPC codes and develop optimal finite word lengths of variables over an SNR. For floating point simulation, it is known that in the normalized min-sum or offset min-sum algorithms the performance of a min-sum based decoder is not sensitive to scaling in the log-likelihood ratio (LLR) values. However, when considering the finite precision for hardware implementation, the scaling affects the dynamic range of the LLR values. The proposed adaptive quantization approach provides the optimal performance in selecting suitable input LLR values to the decoder as far as the tradeoffs between error performance and hardware complexity are concerned.
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.
This paper presents a low complexity Min-Sum algorithm for decoding irregular Low-Density Parity-Check (LDPC) codes. In the proposed algorithm, the significant improvement in the error correcting performance without enhancing the hardware complexity is achieved by employing adaptive and optimized normalization factors for both the extrinsic information and log-likelihood ratio data bits respectively. The experimental results demonstrate that the proposed algorithm with 6-bit non-uniform quantization achieves reasonable decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without increasing the hardware complexity by avoiding finite word length effects of soft information.
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.
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 proposes a new min-sum algorithm for low-density parity-check decoding. In this paper, we first define the negative and positive effects of the received signal-to-noise ratio (SNR) in the min-sum decoding algorithm. To improve the performance of error correction by considering the negative and positive effects of the received SNR, the proposed algorithm applies adaptive scaling factors not only to extrinsic information but also to a received log-likelihood ratio. We also propose a combined variable and check node architecture to realize the proposed algorithm with low complexity. The simulation results show that the proposed algorithm achieves up to 0.4 dB coding gain with low complexity compared to existing min-sum-based algorithms.
This paper presents an adaptation of the Min-Sum decoders for the Low-Density Parity-Check (LDPC) used in the enhanced mobile broadband (eMBB) scenario in the 5th generation mobile networks (5G). Starting from the structure of the proposed LDPC codes for 5G where a significant part of the Variable Nodes (VNs) is with degree-1 and is sensitively to be erroneous in the traditional Offset Min-Sum decoder, we adapt the Min-Sum decoding principle to decode these 5G LDPC codes, targeting to improve the error correction performance. The proposed decoder, named Adapted Min-Sum (AMS), processes the core and the extension parts of the code differently using different offset factors. By doing that, the error probability of degree-1 VN is significantly depressed. We show through the simulation performance that the proposed decoder, with small number of quantization bits, can even surpass the floating-point counterpart and approaches the performance of the Sum-Product decoder for several 5G LDPC code lengths and code rates, with negligible additional complexity.