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International Symposium on Information Theory and its Applications

Adaptive quantization for low-density-parity-check decoders

Cha-Hao Chung, Yeong-Luh Ueng, Ming-Che Lu, Mao‐Chao Lin

Published Oct 1, 2010• 6 citations
Publisher

Abstract

For the implementation of low-density parity-check (LDPC) decoders, the associated error performance and the complexity are significantly affected by the number of quantization bits used. In this paper, we propose an adaptive quantization scheme, which uses different quantization schemes at different iteration numbers based on a fixed number of quantization bits. Simulation results show that the proposed adaptive quantization can reduce the number of quantization bits without error performance degradation.

DOI
10.1109/isita.2010.5649830

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For the implementation of low-density parity-check (LDPC) decoders, the associated error performance and the complexity are significantly affected by the number of quantization bits used. In this paper, we propose an adaptive quantization scheme, which uses different quantization schemes at different iteration numbers based on a fixed number of quantization bits. Simulation results show that the proposed adaptive quantization can reduce the number of quantization bits without error performance degradation.
A. class of combinatorial structures, called absorbing sets, strongly influences the performance of low-density parity- check (LDPC) decoders. In particular, the quantization scheme strongly affects which absorbing sets dominate in the error-floor region. Absorbing sets may be characterized as weak or strong. They are a characteristic of the parity check matrix of a code. Conventional quantization schemes applied to a (2209,1978) array-based LDPC code can induce low-weight weak absorbing sets and, as a result, elevate the error floor. Adaptive quantization schemes alleviate the effects of weak absorbing sets, and, as a result, only the strong ones dominate the error floor of an optimized decoder implementation. Another benefit of an adaptive quantization scheme is that it performs well even in very few iterations.
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.
Low-density parity-check (LDPC) codes are capacity approaching codes that have rapidly been adopted in modern systems such as the IEEE 802.11n and long term evolution advanced (LTE-A) communications standards. The decoders based on the iterative belief propagation offer exceedingly high performance but unfortunately have high computational complexity. Therefore significant research has focused on lower complexity architectures based on the family of so-called bit-flipping algorithms. In the basic bit-flipping algorithm the number of failed parity checks for each bit is calculated and the sign of the bit with the maximum failed checks is inverted. Inverting bits above a certain threshold removes the complexity of calculating a maximum function and adaptive thresholds on each bit further simplifies the design. The choice of threshold updates directly affects the error and convergence performances. Here we describe a simple architecture that has two decoders with different scaling factors and select the branch with the lowest syndrome sum. It is shown that the addition of a random uniform perturbation to the threshold can reduce the average iteration count further by providing an escape from stuck decoding states.
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.
In practical implementation, the input and intermediate signals of Low-Density Parity-Check (LDPC) message passing decoders are quantized into fixed-point messages with finite bit-width. The quantization operation with limited bit-width enhances the data throughput and reduces the computation and storage overhead of LDPC decoder, but confronts the problem of performance degradation. Existing improved algorithms of min-sum algorithm (MSA) generally do not consider the effect of quantization, and thus lack the optimization of the quantization strategy. To fill this gap, we first propose adaptive asymmetric quantization strategy. Then, based on the proposed quantization strategy, combined with conventional adaptive normalization technique, we propose adaptive quantized and normalized MSA (AQNMSA), which significantly alleviates the performance degradation of fixed quantized and normalized MSA (NMSA) with negligible increment of computational complexity. Concurrently, we provide a novel look-up table design algorithm for AQNMSA based on the tool of multi-edge-type density evolution (MET-DE). Finally, we apply AQNMSA to DTMB-A LDPC codes with a very low quantization bit-width of 4 bits, and observe a superior threshold performance and lower error floor compared with its non-adaptive float-point counterparts.
The bit-flipping (BF) algorithm for decoding of low-density parity-check (LDPC) codes requires less complex hardware than other decoding algorithms, but its error correcting performance needs to be improved. In this letter, a threshold adaptation scheme is applied to BF algorithm based decoding of LDPC codes. Our experiments show that the optimal threshold value for BF depends on the error conditions, and threshold adjustment during decoding helps to prevent meaningless no-flipping iterations. Based on these statistical observations, the adaptive threshold technique is proposed to pursue both the maximum error correcting capability and the fastest decoding convergence.