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Published June 2004 | Published
Book Section - Chapter Open

Miscorrection probability beyond the minimum distance

Abstract

The miscorrection probability of a list decoder is the probability that the decoder will have at least one non-causal codeword in its decoding sphere. Evaluating this probability is important when using a list-decoder as a conventional decoder since in that case we require the list to contain at most one codeword for most of the errors. A lower bound on the miscorrection is the main result. The key ingredient in the proof is a new combinatorial upper bound on the list-size for a general q−ary block code. This bound is tighter than the best known on large alphabets, and it is shown to be very close to the algebraic bound for Reed-Solomon codes. Finally we discuss two known upper bounds on the miscorrection probability and unify them for linear MDS codes.

Additional Information

© Copyright 2004 IEEE. Reprinted with permission. Publication Date: 27 June-2 July 2004. Current Version Published: 2005-01-10. This work was supported in part by the Lee Center for Advanced Networking at the California Institute of Technology.

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