Optimizing Chien Search Usage in the BCH Decoder for High Error Rate Transmission

Abstract

In hybrid automatic repeat request (HARQ), Bose-Chaudhuri-Hocquenghem (BCH) coders can be used before transmission over noisy channel. A sent message is retrieved correctly via decoding, whenever it is correctable. For uncorrectable message, a retransmission is requested by the receiver. In this paper, the detection time for uncorrectable words is reduced. In particular, Chien search usage is optimized. It is only used when all roots of the error locator polynomial belong to F_{2^m}^* = GF(2^m) {0}. Two binary primitive narrow sense BCH codes are considered; the short length BCH(63,39,9) and the long length BCH(16383,16215,25) codes.