Computer Science > Information Theory
[Submitted on 21 Jul 2013 (v1), last revised 28 Aug 2013 (this version, v2)]
Title:The Random Coding Bound Is Tight for the Average Linear Code or Lattice
View PDFAbstract:In 1973, Gallager proved that the random-coding bound is exponentially tight for the random code ensemble at all rates, even below expurgation. This result explained that the random-coding exponent does not achieve the expurgation exponent due to the properties of the random ensemble, irrespective of the utilized bounding technique. It has been conjectured that this same behavior holds true for a random ensemble of linear codes. This conjecture is proved in this paper. Additionally, it is shown that this property extends to Poltyrev's random-coding exponent for a random ensemble of lattices.
Submission history
From: Yuval Domb [view email][v1] Sun, 21 Jul 2013 12:45:05 UTC (26 KB)
[v2] Wed, 28 Aug 2013 11:47:57 UTC (26 KB)
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