A systematic approach to modified BCJR MAP algorithms for convolutional codes

Abstract

Since Berrou, Glavieux and Thitimajshima published their landmarkpaper in 1993, different modified BCJR MAP algorithms haveappeared in the literature. The existence of a relatively largenumber of similar but different modified BCJR MAP algorithms,derived using the Markov chain properties of convolutional codes,naturally leads to the following questions. What is therelationship among the different modified BCJR MAP algorithms?What are their relative performance, computational complexities,and memory requirements? In this paper, we answer these questions.We derive systematically four major modified BCJR MAP algorithmsfrom the BCJR MAP algorithm using simple mathematicaltransformations. The connections between the original and thefour modified BCJR MAP algorithms are established. A detailedanalysis of the different modified BCJR MAP algorithms shows thatthey have identical computational complexities and memoryrequirements. Computer simulations demonstrate that the fourmodified BCJR MAP algorithms all have identical performance to theBCJR MAP algorithm.