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IEEE Communications Letters

Robust LDPC decoding using irregular decoders

Raman Yazdani, Masoud Ardakani

Published Dec 1, 2008• 1 citation
Publisher

Abstract

It has been observed that irregular decoders for low density parity-check (LDPC) codes can be more robust to channel estimation errors compared to conventional decoders. In this work, by presenting a robustness measure, we propose a method for the joint optimization of irregular LDPC code-decoder pairs to have the widest convergence region when channel estimation errors exist.

DOI
10.1109/lcomm.2008.080977

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It has been observed that irregular decoders for low density parity-check (LDPC) codes can be more robust to channel estimation errors compared to conventional decoders. In this work, by presenting a robustness measure, we propose a method for the joint optimization of irregular LDPC code-decoder pairs to have the widest convergence region when channel estimation errors exist.
Irregular decoding of low-density parity-check codes, i.e., using different algorithms in one iteration of the decoding of a single word, is studied. We formulate density evolution for irregular decoders. Using a one-dimensional representation of density evolution, we then jointly optimize irregular codes and irregular soft decoders for minimizing the decoding complexity. More specifically, for a given set of soft algorithms, a given channel, and a given code-rate, we find an irregular code-decoder pair which is capable of achieving a desired error performance with minimal decoding complexity. Robustness of irregular decoders when there exist channel estimation errors is also shown via an example
Over the past two decades, irregular low-density parity-check (LDPC) codes have been hardly able to decode information corrupted by insertion and deletion (ID) errors without markers. Surprisingly, in this paper, we bring to light the existence of irregular LDPC codes that approach the theoretical limit of the channel with ID errors even without markers. These codes contain high fractions of low-degree check nodes that do not appear in irregular codes for other channels. This motivates us to investigate the contribution of low-degree check nodes to correcting ID errors. The investigation provides the following interesting result: degree-2 check nodes are critical to approaching the theoretical limit even without markers, codes with only degree-3, 4, or more check nodes provide moderate decoding performance, and codes with only degree-5 or more check nodes can hardly correct ID errors. Finally, we present simulation results that confirm the excellent decoding performance of the irregular codes without markers.
Time-invariant hybrid (HTI) decoding of irregular low-density parity-check (LDPC) codes is studied. Focusing on HTIalgorithms with majority-based (MB) binary message-passing constituents, we use density evolution and finite-length simulation to analyze the performance and the convergence properties of these algorithms. Tight upper bounds on the threshold of MB HTIalgorithms are derived, and it is proven that the asymptotic error probability for these algorithms tends to zero at least exponentially with the number of iterations. We devise optimal MB HTIalgorithms for irregular LDPC codes, and show that these algorithms outperform Gallager's algorithm A applied to optimized irregular LDPC codes. We also show that compared to switch-type algorithms, such as Gallager's algorithm B, where a comparable improvement is obtained by switching between different MB algorithms, MB HTIalgorithms are more robust, and can better cope with unknown channel conditions, and thus can be practically more attractive
The optimal performance-complexity tradeoff for error-correcting codes at rates strictly below the Shannon limit is a central question in coding theory. This paper proposes a numerical approach for the minimization of decoding complexity for long-block-length irregular low-density parity-check (LDPC) codes. The proposed design methodology is applicable to any binary-input memoryless symmetric channel and any iterative message-passing decoding algorithm with a parallel-update schedule. A key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence. This paper shows that the proposed complexity measure can be accurately estimated from a density-evolution and extrinsic-information transfer chart analysis of the code. A sufficient condition is presented for convexity of the complexity measure in the variable edge-degree distribution; when it is not satisfied, numerical experiments nevertheless suggest that the local minimum is unique. The results presented herein show that when the decoding complexity is constrained, the complexity-optimized codes significantly outperform threshold-optimized codes at long block lengths, within the ensemble of irregular codes.
Recently, the concept of layered decoding schedule for Low-Density Parity-Check codes has been introduced. But the advantage of layered decoding schedule for irregular LDPC codes is not as obvious as regular LDPC codes. The major drawback of the layered irregular LDPC codes versus the layered regular LDPC codes is its comparative low convergence decoding speed. Simulation results show that different bit node degrees of irregular LDPC codes significantly contribute to the decoding performance. The decoding performance of bit nodes with different degrees is of great difference. Bit nodes with small degrees always converge slower than larger ones. In this paper, we propose an optimized decoding schedule for irregular LDPC codes to accelerate the decoding convergence rate. Meanwhile, for the irregular LDPC decoder, the faster decoding speed means a higher throughput and almost the same error performance.