The time-varying nature of wireless channels poses a challenge for using soft-decision iterative decoders on such channels. Even if the channel gain is perfectly known to the receiver, inaccurate estimation of the additive noise power, results in incorrect log-likelihood computation at the receiver and hence significant performance degradation in the decoder. Through a detailed study of the effects of channel estimation errors on the performance of soft-decision iterative decoders in uncorrelated block-fading channels, we propose a solution which does not need a knowledge of the power of the additive noise. We show that this solution performs almost identical to the case for which a perfect knowledge of the power of the additive noise exists at the receiver. The choice of the block-fading channel reflects a situation where the equivalent variance of the additive Gaussian noise can change in a wide range and thus the decoder performance seriously relies on the knowledge of the noise power at the receiver.

Time-invariant hybrid (HscrTI) decoding of irregular low-density parity-check (LDPC) codes is studied. Focusing on HscrTIalgorithms with majority-based (MB) binary message-passing constituents, we use density evolution (DE) and finite-length simulation to analyze the performance and the convergence properties of these algorithms over (memoryless) binary symmetric channels. To apply DE, we generalize degree distributions to have the irregularity of both the code and the decoding algorithm embedded in them. A tight upper bound on the threshold of MB HscrTIalgorithms is 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 HscrTIalgorithms 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 HscrTIalgorithms are more robust and can better cope with unknown channel conditions, and thus can be practically more attractive.

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

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

Hybrid decoding is to combine different iterative decoding algorithms with the aim of improving error performance or decoding complexity. In this work, we introduce "time-invariant" hybrid (HTI) algorithms, and show that for regular low-density parity-check codes and binary message-passing algorithms, HTIalgorithms perform remarkably better than their constituent algorithms. We also show that compared to "switch-type" hybrid algorithms, such as Gallager's algorithm B, where a comparable improvement is obtained by switching between different iterative decoding algorithms, HTIalgorithms are far less sensitive to channel conditions and thus can be practically more attractive.

This work presents a detailed study of a family of binary message-passing decoding algorithms for low-density parity-check (LDPC) codes, referred to as "majority-based algorithms." Both Gallager's algorithm A (G/sub A/) and the standard majority decoding algorithm belong to this family. These algorithms, which are, in fact, the building blocks of Gallager's algorithm B (G/sub B/), work based on a generalized majority-decision rule and are particularly attractive for their remarkably simple implementation. We investigate the dynamics of these algorithms using density evolution and compute their (noise) threshold values for regular LDPC codes over the binary symmetric channel. For certain ensembles of codes and certain orders of majority-based algorithms, we show that the threshold value can be characterized as the smallest positive root of a polynomial, and thus can be determined analytically. We also study the convergence properties of majority-based algorithms, including their (convergence) speed. Our analysis shows that the stand-alone version of some of these algorithms provides significantly better performance and/or convergence speed compared with G/sub A/. In particular, it is shown that for channel parameters below threshold, while for G/sub A/ the error probability converges to zero exponentially with iteration number, this convergence for other majority-based algorithms is super-exponential.