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arXiv:0709.4466

Serially Concatenated IRA Codes

Taikun Cheng, Krishnamoorthy Sivakumar, Benjamin J. Belzer

Published Sep 27, 2007• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0709.4466

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Abstract: Small stopping sets have been proved to be harmful to the error floor performance of a finite-length irregular low-density parity-check (LDPC) code over the binary erasure channel (BEC). On the additive white gaussian noise (AWGN) channel, small stopping sets are expected to have a similar effect. This paper proposes an algorithm that iteratively removes the small-stopping-set-inducing patterns from the graph of a randomly generated irregular LDPC code by means of node exchange, aiming at enlarging the average size of stopping sets in this code. Computer simulation results show that the short-length LDPC codes after our processing achieve a considerable performance improvement in the low-BER region compared to the randomly generated codes. Key words: Error floor, irregular LDPC codes, iterative processing, small stopping set 1

•Jan 1, 2005•1 citation
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.
Low-density parity-check (LDPC) codes have been intensively studied in the past decade for their capacity-approaching performance. LDPC code implementation complexity and the error-rate floor are still two significant unsolved issues which prevent their application in some important communication systems. In this dissertation, we make efforts toward solving these two problems by introducing the design of a class of LDPC codes called structured irregular repeat-accumulate (S-IRA) codes. These S-IRA codes combine several advantages of other types of LDPC codes, including low encoder and decoder complexities, flexibility in design, and good performance on different channels. It is also demonstrated in this dissertation that the S-IRA codes are suitable for rate-compatible code family design and a multi-rate code family has been designed which may be implemented with a single encoder/decoder.The study of the error floor problem of LDPC codes is very difficult because simulating LDPC codes on a computer at very low error rates takes an unacceptably long time. To circumvent this difficulty, we implemented a universal quasi-cyclic LDPC decoder on a field programmable gate array (FPGA) platform. This hardware platform accelerates the simulations by more than 100 times as compared to software simulations. We implemented two types of decoders with partially parallel architectures on the FPGA: a circulant-based decoder and a protograph-based decoder. By focusing on the protograph-based decoder, different soft iterative decoding algorithms were implemented. It provides us with a platform for quickly evaluating and analyzing different quasi-cyclic LDPC codes, including the S-IRA codes. A universal decoder architecture is also proposed which is capable of decoding of an arbitrary LDPC code, quasi-cyclic or not. Finally, we studied the low-floor problem by focusing on one example S-IRA code. We identified the weaknesses of the code and proposed several techniques to lower the error floor. We successfully demonstrated in hardware that it is possible to lower the floor substantially by encoder and decoder modifications, but the best solution appeared to be an outer BCH code.
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 order to suppress error floors of low density parity check (LDPC) codes, we study a parallel concatenation scheme with an intermediate single parity check (SPC) code and interleavers. The interleavers of the concatenation play an important role to lower error floors, because it is highly possible that interleaved bits in a trapping set are not to be in error even if the bits in the trapping set are originally in error. For quasi-cyclic LDPC codes, our simulation results confirm that the integrated parallel interleaved concatenation with circulant-size cyclic-shift interleavers improves error-floor performance, and it is better than serial concatenation schemes with BCH codes. If a decoder can afford to accommodate higher-hardware complexity, the decoding performance of our scheme improves so that the error floor can be lowered further.
Abstract: Small stopping sets have been proved to be harmful to the error floor performance of a finite-length irregular low-density parity-check (LDPC) code over the binary erasure channel (BEC). On the additive white gaussian noise (AWGN) channel, small stopping sets are expected to have a similar effect. This paper proposes an algorithm that iteratively removes the small-stopping-set-inducing patterns from the graph of a randomly generated irregular LDPC code by means of node exchange, aiming at enlarging the average size of stopping sets in this code. Computer simulation results show that the short-length LDPC codes after our processing achieve a considerable performance improvement in the low-BER region compared to the randomly generated codes. Key words: Error floor, irregular LDPC codes, iterative processing, small stopping set 1