Residual Error Rate of Binary Linear Block Codes

Abstract

We consider two decoders: an incomplete decoder,D_i, as defined in [1], which corrects up to t errors, and a complete one, D, derived from D_i (see section 4). In section 2 the decoding probability corresponding to D_i, P_d, is expanded in series up to the two first orders. We then compute an exact expression for the residual error rate R_re for both D_i, and D, and derive a straightforward upper bound for R_re of D. Series expansions of these quantities are given, based on the results of section 2. Basically, a classical result on the decoding probability due to J. Mac Williams [1] is used.