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IST Mobile and Wireless Communications Summit

On the Decoding of LDPC Codes in Finite-Precision Arithmetics

Massimo Rovini, Guido Masera, Luca Fanucci, Francesco Rossi, Nicola E. L’Insalata, Federico Quaglio, Fabrizio Vacca

Published Jan 1, 2006• 0 citations
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While several implementations of LDPC codes decoders are available, the effects of fixed-point quantisation are still somewhat obscure. This paper aims at defining a systematic and general methodology to attack the LDPC decoding problem under finite–precision arithmetic. Statistical analysis is completed with Monte Carlo simulations to deploy the basics of the quantisation problem; the key aspect of this work is the independent study of channel reliability and extrinsic messages. As a case example, a short block, structured LDPC code is considered, and the results are shown. The extension to different codes confirms the validity of our method in relating design parameters and performance. This study is at the basis of the exploration of the trade-off between system performance and hardware complexity and can be easily extended to other applications.

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While several implementations of LDPC codes decoders are available, the effects of fixed-point quantisation are still somewhat obscure. This paper aims at defining a systematic and general methodology to attack the LDPC decoding problem under finite–precision arithmetic. Statistical analysis is completed with Monte Carlo simulations to deploy the basics of the quantisation problem; the key aspect of this work is the independent study of channel reliability and extrinsic messages. As a case example, a short block, structured LDPC code is considered, and the results are shown. The extension to different codes confirms the validity of our method in relating design parameters and performance. This study is at the basis of the exploration of the trade-off between system performance and hardware complexity and can be easily extended to other applications.
Low-density parity-check (LDPC) codes are among the most powerful known error correcting codes and they have been shown to achieve performance very close to the Shannon bound. In practical hardware implementations of LDPC decoders, bit error rate performances are affected strongly by fixed-point representation of processed data and, although many papers have been published in recent years on the subject of LDPC codes, only a few of them report results on the effects of finite precision. In the paper two novel arithmetic approximations for the basic processing operations of the decoding algorithm are presented. The two proposed solutions are analysed in terms of bit error rate performance for different finite precison representations of both external and internal data; the estimated performance loss is comparable to that reported by previous works and limited to approximately 0.1 dB for cases of interests. However the proposed solutions support a reduced complexity formulation of the decoding algorithm, so enabling the implementation of flexible decoders that can be adapted to different LDPC codes, block sizes and code rates.
Classically, the quantization of the soft information supplied to a finite-precision decoder is chosen to optimize a certain criterion which does not depend on the characteristics of the existing code. This work studies code-aware quantizers, for finite-precision min-sum decoders, which optimize the noise threshold of the existing family of Low-Density Parity-Check (LDPC) codes. We propose a code-aware quantizer with lower complexity than that obtained by optimizing all decision levels and approaching its performance, for few quantization bits. We show that code-aware quantizers outperform code-independent quantizers in terms of noise threshold for both regular and irregular LDPC codes. To overcome the error floor behavior of LDPC codes, we propose the design of the quantizer for a target error probability at the decoder output. The results show that the quantizer optimized to get a zero error probability could lead to a very bad performance for practical range of signal to noise ratios. Finally, we propose to design jointly irregular LDPC codes and code-aware quantizers for finite-precision min-sum decoders. We show that they achieve significant decoding gains with respect to LDPC codes designed for infinite-precision belief propagation decoding, but decoded by finite-precision min-sum.