Factor graphs and iterative decoding: new developments

Author(s)

Alexandre de Andrade

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2010-03-25

Examining board members

Jaime Portugheis; Daniel Carvalho da Cunha; Richard Demo Souza; Sueli Irene Rodrigues Costa; Celso de Almeida

• Advisor: Jaime Portugheis

Abstract

The present thesis deals with probabilistic inference methods for communication systems described by the unifying framework of factor graphs and the general elimination algorithm, the so called sum-product algorithm. These exceedingly general tools are understood as a state of the art environment to build many decoding schemes, and to model typical components for a joint efficient inference at reception. More generally, is a suitable framework to unified receiver designs. Additionally, some joint source channel decoding schemes can also be proper modeled under this context. We start with a review of this framework and related mathematical topics. Thereafter, we particularize to cases of interest, like typical communication systems. This framework gives powerful insights into the structures of multivariate constrained systems and shows how distributed probabilistic inferences can be performed, as shown for typical communication systems with a standard channel encoder. Systems represented by fator graphs with cycles are the most relevant. For the iterative version of the sum-product algorithm, a calculation schedule has to be efficiently chosen. We review the turbo decoding scheme for the classical turbo code using a normal and causal factor graph realization, providing an environment for scheduling descriptions. Then, we approach the non-block turbo decoding version (stream-oriented turbo codes), where general periodic and causal interleavers can be used and continuous decoding schemes are required. We present a full decoding sum-product schedule for this case, with pratical improvements over the usual non-graphical decoding scheme. In the last part of this thesis, we address the joint source channel decoding problem using the factor-graph framework. Starting from a general source model, linear discrete time series, we consider straight vectorial quantization. Instead of trying to remove redundancy, we go in the direction of building decoding schemes that explore this redundancy from source model and quantizer map.We analyse cases when iterative decoding can be performed taking these elements into account in a proper way. Some simulation on the proposed schemes are presented (AU)