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On the pseudocodeword redundancy of binary linear codes
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, 2012
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On ML Redundancy of Codes
"... Abstract — The ML redundancy of a code is defined as the smallest number of rows in its paritycheck matrix such that a messagepassing decoder working in the corresponding Tanner graph achieves maximumlikelihood (ML) performance on an erasure channel. General upper bounds on ML redundancy are obta ..."
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Abstract — The ML redundancy of a code is defined as the smallest number of rows in its paritycheck matrix such that a messagepassing decoder working in the corresponding Tanner graph achieves maximumlikelihood (ML) performance on an erasure channel. General upper bounds on ML redundancy are obtained. In particular, it is shown that the ML redundancy of a qary code is at most the number of minimal codewords in its dual code, divided by q −1. Special upper bounds are derived for codes whose dual code contains a covering design. For example, the ML redundancy of a Simplex code of length n is shown to be no greater than (n 2 − 4n +9)/6. I.