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Gaussian Approximation of Irregular Repeat-Accumulate Codes over Mixed Gaussian/Erasure Channels

Gao Hong-feng, XU Zong-ze

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Gaussian approximation models the message density in message passing decoders as Gaussian distribution.In this paper,irregular repeat accumulate(IRA) codes over the mixed white Gaussian noise/erasure channels are designed using Gaussian approximation.Recursive equations of density evolution and analytic expressions of bit error rate are derived.The analytic results not only provide a way to predict asymptotic performance of IRA codes but also help us design good IRA codes over the mixed channel.Comparison between simulation results and thresholds computed from analytic results shows that predication from the theoretical results is accurate enough.The optimized IRA codes designed for the mixed channels have better performance than that of IRA codes designed for AWGN channels when the designed erasure probability is close to the actual probability.

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IEEE International Symposium on Information Theory (ISIT)•Jan 1, 2003•11 citations
Gaussian approximation models the message density in message passing decoders as Gaussian distribution.In this paper,irregular repeat accumulate(IRA) codes over the mixed white Gaussian noise/erasure channels are designed using Gaussian approximation.Recursive equations of density evolution and analytic expressions of bit error rate are derived.The analytic results not only provide a way to predict asymptotic performance of IRA codes but also help us design good IRA codes over the mixed channel.Comparison between simulation results and thresholds computed from analytic results shows that predication from the theoretical results is accurate enough.The optimized IRA codes designed for the mixed channels have better performance than that of IRA codes designed for AWGN channels when the designed erasure probability is close to the actual probability.
In this paper we will introduce an ensemble of codes called irregular repeat-accumulate (IRA) codes. IRA codes are a generalization of the repeat-accumulate codes introduced in [1], and as such have a natural linear time encoding algorithm. We shall prove that on the binary erasure channel, IRA codes can be decoded reliably in linear time, using iterater] sum-product decoding,a# ra#SJ a#SJ8T a#SJ8 close tocha#T36 ca pa#J464 Asimila# resulta#u ea#S to be true on the AWGN channel, although we have no proof of this. We illustrate our results with numerical and experimenta# examples.
We address the error floor problem of low-density parity check (LDPC) codes on the binary-input additive white Gaussian noise (AWGN) channel, by constructing a serially concatenated code consisting of two systematic irregular repeat accumulate (IRA) component codes connected by an interleaver. The interleaver is designed to prevent stopping-set error events in one of the IRA codes from propagating into stopping set events of the other code. Simulations with two 128-bit rate 0.707 IRA component codes show that the proposed architecture achieves a much lower error floor at higher SNRs, compared to a 16384-bit rate 1/2 IRA code, but incurs an SNR penalty of about 2 dB at low to medium SNRs. Experiments indicate that the SNR penalty can be reduced at larger blocklengths.
Short non-binary irregular repeat-accumulate (IRA) codes based on well-known Hamiltonian and Hypohamiltonian graphs with large girth are presented. The mapping of the code coordinates on the graph edges is discussed for Hamiltonian graphs, and two encoding methods on Hypohamiltonian graphs are introduced. The performance of the presented codes on order-256 finite fields (F256) is provided for both the additive white Gaussian (AWGN) channel and the binary erasure channel (BEC) under iterative (IT) decoding. For the latter case, the performance under maximum likelihood (ML) decoding is also presented, to illustrate that the proposed codes not only attain performances close to the random coding bound, but also show limited losses when decoded iteratively.
This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q>2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.
Abstract:Code structure is an important factor which affects performance of IRA codes. THe structure of IRA codes was optimized based on Gaussian approximation. The graph model theory of IRA codes was introduced, and the Tanner graph was presented. The impact of 2 degree to the structure of codes was analysed. Based on given noise variance, the Gaussian approximation of IRA codes was researched on AWGN channel, and the degree sequences was designed. IRA codes were designed based on Gaussian approximation and simulated by computer. Simulation results showed that the IRA codes have better performance than MacKay LDPC codes, and the convergence of message are well.