Evaluation of standard approximation to log-likelihood ratio addition in the MAP algorithm, and its application in block code (‘Turbo’) iterative decoding algorithms

Abstract

This paper examines the log-likelihood addition aspects of the Turbo Decoding of product codes. Simple Parity Check (SPC) codes are used as the Constituent Codes (CCs) of the Turbo encoder in an array code format. The general approximation used in the log-likelihood addition of the soft values of the code bits is evaluated and some results are presented. Two iterative (‘Turbo’) decoding algorithms for block codes are compared, only one of which uses the previously mentioned approximation. The first is set out in Hagenauer (1994), which uses the dual code method to implement the MAP decoder, and the second was developed in Pyndiah (1994), which uses an algorithm presented in Chase (1972). The results presented show the affect of the approximation on decoder performance. The outcome differs somewhat from that which was expected.