TY - GEN

T1 - An upper bound on the capacity of non-binary deletion channels

AU - Rahmati, Mojtaba

AU - Duman, Tolga M.

PY - 2013

Y1 - 2013

N2 - We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser in [1] are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability d, denoted by C2K(d), and the capacity of the binary deletion channel with the same deletion probability, C2(d), that is, C2K(d) ≤ C2(d)+(1-d) log(K). Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as d → 0.

AB - We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser in [1] are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability d, denoted by C2K(d), and the capacity of the binary deletion channel with the same deletion probability, C2(d), that is, C2K(d) ≤ C2(d)+(1-d) log(K). Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as d → 0.

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U2 - 10.1109/ISIT.2013.6620764

DO - 10.1109/ISIT.2013.6620764

M3 - Conference contribution

AN - SCOPUS:84890405553

SN - 9781479904464

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2940

EP - 2944

BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013

T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013

Y2 - 7 July 2013 through 12 July 2013

ER -