Conquering the Map

Abstract

A thorough analysis of convolutional turbo codes requires the well-understanding of its decoding algorithm. Two options are normally considered: the Maximum A Posteriori (MAP) algorithm published by Bahl et al. in 1974 [1] and the soft-output Viterbi decoding algorithm [2]. The complete derivation of the MAP is presented, making clear some points that are not thoroughly described in the available literature. Some simplifications normally applied to the MAP algorithm are also seen. Those simplifications are made in order to allow the efficient implementation of MAP decoders as the SISO modules required in convolutional turbo decoding. Trade-offs that have to be tackled when designing turbo decoders are made clear when a complete understanding of the decoding algorithm is achieved; that is the main purpose of Sections 3.2 and 3.3. Section 3.4 deals with different termination schemes for the turbo encoder, pointing out that termination is normally costly from the implementation point of view. Section 3.5 introduces the main bottlenecks when dealing with the log-max MAP algorithm and details several optimization steps that transform the slow recursion inherent to the MAP in a full parallel architecture with a special memory organization targeted at saving energy consumption.