TY - JOUR

T1 - Exact random coding exponents for erasure decoding

AU - Somekh-Baruch, Anelia

AU - Merhav, Neri

PY - 2011/10

Y1 - 2011/10

N2 - Random coding of channel decoding with an erasure option is studied. By analyzing the large deviations behavior of the code ensemble, we obtain exact single-letter formulas for the error exponents in lieu of Forney's lower bounds. The analysis technique we use is based on an enhancement and specialization of tools for assessing the statistical properties of certain distance enumerators. We specialize our results to the setup of the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which, unlike Forney's bounds, does not involve optimization over two parameters. We also establish the fact that for this setup, the difference between the exact error exponent corresponding to the probability of undetected decoding error and the exponent corresponding to the erasure event is equal to the threshold parameter. Numerical calculations indicate that for this setup, as well as for a Z-channel, Forney's bound coincides with the exact random coding exponent.

AB - Random coding of channel decoding with an erasure option is studied. By analyzing the large deviations behavior of the code ensemble, we obtain exact single-letter formulas for the error exponents in lieu of Forney's lower bounds. The analysis technique we use is based on an enhancement and specialization of tools for assessing the statistical properties of certain distance enumerators. We specialize our results to the setup of the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which, unlike Forney's bounds, does not involve optimization over two parameters. We also establish the fact that for this setup, the difference between the exact error exponent corresponding to the probability of undetected decoding error and the exponent corresponding to the erasure event is equal to the threshold parameter. Numerical calculations indicate that for this setup, as well as for a Z-channel, Forney's bound coincides with the exact random coding exponent.

KW - Distance enumerator

KW - erasure

KW - error exponent

KW - list

KW - random coding

UR - http://www.scopus.com/inward/record.url?scp=80053980985&partnerID=8YFLogxK

U2 - 10.1109/TIT.2011.2165826

DO - 10.1109/TIT.2011.2165826

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AN - SCOPUS:80053980985

SN - 0018-9448

VL - 57

SP - 6444

EP - 6454

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 10

M1 - 6034743

ER -