Simple MAP Decoding of Binary Cyclic Codes

Soft decision decoding of block codes has traditionally and in recent times been a problem of great research interest. Though several sub-optimal soft decoders are becoming increasingly popular today, optimal soft decoders such as bitwise maximum a posteriori (MAP) decoders are of great value both for theoretical and practical purposes. In this work, we present a simple implementation of the MAP decoder for binary cyclic codes. The implementation is particularly easy and efficient for codes whose check polynomial is either an irreducible polynomial or a product of two irreducible polynomials. We illustrate the efficiency of the method by simulating the MAP decoder for the length 255 2-error-correcting binary BCH code. We also propose a suboptimal soft decision decoder based on the MAP decoder and present comparisons