Theory and Performance of ML Decoding for Turbo Codes using Genetic Algorithm

Abstract

Although yielding the lowest error probability, ML decoding of turbo codes has been considered unrealistic so far because efficient ML decoders have not been discovered. In this paper, we propose the Genetic Decoding Algorithm (GDA) for turbo codes. GDA combines the principles of perturbed decoding and genetic algorithm. In GDA, chromosomes are random additive perturbation noises. A conventional turbo decoder is used to assign fitness values to the chromosomes in the population. After generations of evolution, good chromosomes that correspond to decoded codewords of very good likelihood emerge. GDA can be used as a practical decoder for turbo codes in certain contexts. It is also a natural multiple-output decoder. The most important aspect of GDA, in our opinion, is that one can utilize GDA to empirically determine a lower bound on the error probability with ML decoding. Our results show that, at a word error probability of 10-4, GDA achieves the performance of ML decoding. Using GDA, we establish that an ML decoder only slightly outperforms a MAP-based iterative decoder at this word error probability for the block size we used and the turbo code defined for WCDMA.