Residual Error Rate of Binary Linear Block Codes
We consider two decoders: an incomplete decoder,Di, as defined in , which corrects up to t errors, and a complete one, D, derived from Di (see section 4). In section 2 the decoding probability corresponding to Di, Pd, is expanded in series up to the two first orders. We then compute an exact expression for the residual error rate Rre for both Di, and D, and derive a straightforward upper bound for Rre 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  is used.
KeywordsBlock Code Code Word Weight Enumerator Transitive Permutation Group Binary Symmetric Channel
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