Design of data width requirement for fixed-point turbo decoders based on modified MAP algorithm

Turbo codes are the most exciting and potentially important development in the coding theory and it has already entered the field of practical application. The most important and foremost design issue prior to the implementation of soft decoder for such turbo code is the estimation of bits required to represent the quantized soft log-likelihood ratio (LLR), internal metrics and extrinsic information. This paper presents the systematic approach to estimate the number of bits and the precision required for these factors, such that the performance of decoder is similar to the ideal bit error rate (BER) performance with an infinite precision. Specifically, we have presented this methodology for turbo decoders based on modified MAP algorithm using Maclaurin series. This paper also presents the mathematical analysis which shows the dependency of precision on the BER performance for such modified MAP algorithm.