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IEEE Military Communications Conference (MILCOM)

Efficient quantization schemes for LDPC decoders

Radivoje Zarubica, Ryan Hinton, Stephen G. Wilson, E.K. Hall

Published Nov 1, 2008• 22 citations
Publisher

Abstract

LDPC codes have attracted much attention recently for their near-capacity performance and high throughput owing to parallel decoding architectures. While simulations are normally done with floating point computation, any practical implementation (ASIC or FPGA) will be built with fixed-point computation. Obviously, decoder speed will increase, and resource requirements will drop, with low-precision implementations, say 3,4, or 5-bit architectures. In this paper we study the effects of quantization in this regime, using density evolution and decoder simulation. Detailed sum-product decoder implementations are given, and performance losses relative to floating point decoding are given. In particular, 4-bit decoder architectures sustain only 0.1 dB penalty.

DOI
10.1109/milcom.2008.4753231

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LDPC codes have attracted much attention recently for their near-capacity performance and high throughput owing to parallel decoding architectures. While simulations are normally done with floating point computation, any practical implementation (ASIC or FPGA) will be built with fixed-point computation. Obviously, decoder speed will increase, and resource requirements will drop, with low-precision implementations, say 3,4, or 5-bit architectures. In this paper we study the effects of quantization in this regime, using density evolution and decoder simulation. Detailed sum-product decoder implementations are given, and performance losses relative to floating point decoding are given. In particular, 4-bit decoder architectures sustain only 0.1 dB penalty.
After the introduction of iterative coding, Low Density Parity Check (LDPC) codes have received a lot of attention due to their remarkable near Shannon-limit performance and practical decoder implementation. However, when employing an LDPC code for various applications, multiple issues do arise at the simulation, algorithm and implementation levels. The first issue is the performance evaluation of the iterative LDPC decoder in the very low Bit Error Rate (BER) regions. So far, no analytical tool has been developed to evaluate the performance of LDPC codes. Unfortunately standard Monte Carlo (MC) simulations cannot be used for performance estimation in these low BER regions due to prohibitive execution times. The second issue is the efficiency of the decoding algorithm. Due to the presence of short cycles in the bipartite graph, sum-product decoding algorithms lead to considerable performance loss for short block-length LDPC codes and produce error floors for longer codes. In addition, the iterative processing and estimation of soft probabilistic values with these algorithms result in very high computational complexity, which in turn impedes the adoption of LDPC codes for power constrained systems. Another prime objective is to design a high throughput decoder architecture which is capable of supporting multiple rates and variable code lengths within minimal area. This work aims to address and provide solutions to the above problems. As a solution to the performance estimation problem of LDPC codes, a highly efficient and novel fast BER simulation technique is developed. At the algorithm level, a performance improvement and error floor avoidance method is introduced, and a computationally efficient algorithm is developed for the sum-product decoding of LDPC codes. And finally, at the architecture level, a high throughput multi-rate variable code length implementation is presented which, when implemented, efficiently minimizes device resources while alleviating the routing complexity of the decoder.
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 studies the finite precision effects on the LDPC decoding performance with high order modulation over Rayleigh fading channels. We compare the performance of different quantization schemes and decoding algorithms using discretized density evolution over code ensembles of various code rates. We find that the min-sum algorithm with a simple correction term using 5 bits for quantization offers a very good performance in all code rate and modulation combinations. The loss is only 0.1 dB compared to floating point implementation. Direct implementation of the sum product algorithm with 6-bit quantization suffers a much larger performance loss when high rate LDPC codes are used. Both software simulations and test results of a hardware decoder implemented on FPGA verify these conclusions.
We present a scalable decoding architecture for a certain class of structured LDPC codes. The codes are designed using a small (n, r) protograph that is replicated Z times to produce a decoding graph for a (Z/spl times/n, Z/spl times/r) code. Using this architecture, we have implemented a decoder for a (4096, 2048) LDPC code on a Xilinx Virtex-II 2000 FPGA, and achieved decoding speeds of 31 Mbps with 10 fixed iterations. The implemented message-passing algorithm uses an optimized 3-bit nonuniform quantizer that allows near floating point performance in the waterfall region, with drastically smaller hardware implementation requirements.
Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders