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IEEE Journal on Selected Areas in Communications

Algorithms for iterative decoding in the presence of strong phase noise

Giulio Colavolpe, Alan Barbieri, Giuseppe Caire

Published Sep 1, 2005• 272 citations

Abstract

We present two new iterative decoding algorithms for channels affected by strong phase noise and compare them with the best existing algorithms proposed in the literature. The proposed algorithms are obtained as an application of the sum-product algorithm to the factor graph representing the joint a posteriori probability mass function of the information bits given the channel output. In order to overcome the problems due to the presence in the factor graph of continuous random variables, we apply the method of canonical distributions . Several choices of canonical distributions have been considered in the literature. Well-known approaches consist of discretizing continuous variables or treating them as jointly Gaussian, thus obtaining a Kalman estimator. Our first new approach, based on the Fourier series expansion of the phase probability density function, yields better complexity/performance tradeoff with respect to the usual discretized-phase method. Our second new approach, based on the Tikhonov canonical distribution, yields near-optimal performance at very low complexity and is shown to be much more robust than the Kalman method to the placement of pilot symbols in the coded frame. We present numerical results for binary LDPC codes and LDPC-coded modulation, with particular reference to some phase-noise models and coded-modulation formats standardized in the next-generation satellite Digital Video Broadcasting (DVB-S2). These results show that our algorithms achieve near-coherent performance at very low complexity without requiring any change to the existing DVB-S2 standard.

DOI: 10.1109/jsac.2005.853813

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Stochastic computation is a new alternative approach for iterative computation on factor graphs. In this approach, the information is represented by the statistics of the bit stream which results in simple high-speed hardware implementation of graph-based algorithms. Despite the first purpose of its invention (i.e., low-precision digital circuits), the stochastic representation has recently been shown to be able to provide near-optimal decoding performance for practical Low-Density Parity- Check (LDPC) codes, with respect to Sum-Product Algorithm (SPA). This paper provides a survey of stochastic methods for graph-based iterative decoding, the state-of-the-art and, their possible new applications.

The DVB-S2 standard has been revealed a reliable standard for data transmission thanks to the LDPC codes. The waterfall of the bit-error rate is very abrupt to reach low values of order 10^(-10) in the error floor. In this paper, we propose a novel investigation on the iterative decoding of these codes by the Belief Propagation algorithm on Gaussian channels. Introducing definitions of persistent and created errors, we analyze them according to the degrees of the Tanner graph nodes and the noise power of the channel. We show that the two-degree bits used to accelerate the encoding process of the DVB-S2 are responsible for most decoding errors. This result could help design DVB-S2 codes in a more appropriate way, for instance avoiding the use of BCH codes to tackle the error floor.

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