Optimal Coding for the Erasure Channel with Arbitrary Alphabet Size

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dc.creatorFashandi, Shervan
dc.creatorGharan, Shahab Oveis
dc.creatorKhandani, Amir K.
dc.date2008-05-28
dc.date2008-06-06
dc.date.accessioned2026-07-07T09:42:47Z
dc.date.available2026-07-07T09:42:47Z
dc.descriptionAn erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming maximum likelihood decoding). Assuming a memoryless erasure channel, the error exponent of MDS codes are compared with that of random codes and linear random codes. It is shown that the envelopes of all these exponents are identical for rates above the critical rate. Noting the optimality of MDS codes, it is concluded that both random codes and linear random codes are exponentially optimal, whether the block sizes is larger or smaller than the alphabet size.
dc.description15 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0805.4440
dc.identifierhttp://arxiv.org/abs/0805.4440
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162311
dc.subjectInformation Theory
dc.titleOptimal Coding for the Erasure Channel with Arbitrary Alphabet Size
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