M\'ethode du point proximal: principe et applications aux algorithmes it\'eratifs

TL;DR

This paper revisits the proximal point method and applies it to analyze and improve the convergence of iterative algorithms like Blahut-Arimoto and BICM-ID decoding.

Contribution

It introduces a proximal point framework to interpret and enhance the convergence properties of specific iterative algorithms in information theory.

Findings

Proximal point method provides new insights into algorithm convergence.

Application to Blahut-Arimoto improves capacity computation.

Application to BICM-ID decoding enhances decoding efficiency.

Abstract

This paper recalls the proximal point method. We study two iterative algorithms: the Blahut-Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with probability density estimates and the iterative decoding of the Bit Interleaved Coded Modulation (BICM-ID). For these iterative algorithms, we apply the proximal point method which allows new interpretations with improved convergence rate.