A Modified Step-By-Step Decoding for Binary BCH Codes

Abstract — This study presents a modified and conceptually simple step-by-step decoding algorithm for binary cyclic BCH codes. Step-by-step decoding temporarily changes one information bit value at a time and then checks weather the weight of the error pattern decreases by computing the corresponding syndrome matrix determinant. Based on the channel information, this study propose a modified step-by-step decoding, which locates a test set and checks the weight of the error pattern in the decoding procedure. Rather than testing all information bits, the bit positions listed in the test set are examined in the proposed step-by-step decoding. The error performance of the proposed decoding is very close to that of the conventional step-by-step decoding with a low decoding complexity, as in simulations of a BPSK coherent system over AWGN channels. Key Words —step-by-step decoding, BCH codes. I