Novel Bounds on the Capacity of the Binary Deletion Channel

We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined random processes. Since some of the proposed bounds involve infinite series, we also introduce provable inequalities that lead to more manageable results. For most values of the deletion probability, these bounds improve the existing ones and significantly narrow the gap with the available lower bounds. Exploiting the same auxiliary processes, we also derive, as a by-product, two simple lower bounds on the channel capacity, which, for low values of the deletion probability, are almost as good as the best existing lower bounds.

[1]  Richard E. Blahut,et al.  Computation of channel capacity and rate-distortion functions , 1972, IEEE Trans. Inf. Theory.

[2]  Snezana Lawrence.  October , 1855, The Hospital.

[3]  Jeffrey D. Ullman,et al.  On the capabilities of codes to correct synchronization errors , 1967, IEEE Trans. Inf. Theory.

[4]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[5]  Eleni Drinea,et al.  Directly Lower Bounding the Information Capacity for Channels With I.I.D. Deletions and Duplications , 2010, IEEE Transactions on Information Theory.

[6]  Roy D. Yates,et al.  Probability and stochastic processes , 1998 .

[7]  W. Rudin.  Principles of mathematical analysis , 1964 .

[8]  Suguru Arimoto,et al.  An algorithm for computing the capacity of arbitrary discrete memoryless channels , 1972, IEEE Trans. Inf. Theory.

[9]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[10]  Michael Mitzenmacher,et al.  Capacity Bounds for Sticky Channels , 2008, IEEE Transactions on Information Theory.

[11]  Suhas N. Diggavi,et al.  Capacity Upper Bounds for the Deletion Channel , 2007, 2007 IEEE International Symposium on Information Theory.

[12]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[13]  R. Gallager.  SEQUENTIAL DECODING FOR BINARY CHANNELS WITH NOISE AND SYNCHRONIZATION ERRORS , 1961 .

[14]  Michael Mitzenmacher,et al.  Improved Lower Bounds for the Capacity of i.i.d. Deletion and Duplication Channels , 2007, IEEE Transactions on Information Theory.

[15]  Michael Mitzenmacher,et al.  A Simple Lower Bound for the Capacity of the Deletion Channel , 2006, IEEE Transactions on Information Theory.

[16]  Dario Fertonani,et al.  Bounds on the Capacity of Channels with Insertions, Deletions and Substitutions , 2011, IEEE Transactions on Communications.