Proceedings of the 1999 IEEE Information Theory and Communications Workshop (Cat. No. 99EX253)
DOI: 10.1109/itcom.1999.781434
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Abstract: Abstract-We derive a new upper bound on the exponent of error probability of decoding for the best possible codes in the Gaussian channel. This bound is tighter than the known upper bounds (the sphere-packing and minimum-distance bounds proved in Shannon's classical 1959 paper and their low-rate improvement by Kabatiansky and Levenshtein). The proof is accomplished by studying asymptotic properties of codes on the sphere 1 ( ). First we prove a general lower bound on the distance distribution of codes of large… Show more

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“…The preceding theorem can, in particular, be used with the family (μ, C) taken to be either (Poi, L( )) or (Mat, L( )), for which π (μ, C, α , ) has been studied in detail in this paper. An excellent survey of the known upper and lower bounds for the error exponent function in the power-constrained AWGN case is given in [3].…”
Section: Lemma 2 Under the Foregoing Assumptionsmentioning
confidence: 99%
“…The preceding theorem can, in particular, be used with the family (μ, C) taken to be either (Poi, L( )) or (Mat, L( )), for which π (μ, C, α , ) has been studied in detail in this paper. An excellent survey of the known upper and lower bounds for the error exponent function in the power-constrained AWGN case is given in [3].…”
Section: Lemma 2 Under the Foregoing Assumptionsmentioning
confidence: 99%