On the capacity of burst noise-erasure channels with and without feedback

A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is shown to satisfy a so-called “quasi-symmetry” condition under certain invertibility conditions. As a result, it is proved that a uniformly distributed input process maximizes the channel's block mutual information, resulting in a closed-form formula for its nonfeedback capacity in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary erasure process. The feedback channel capacity is also characterized, showing that feedback does not increase capacity and generalizing prior related results.

[1]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[2]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[3]  Robert J. McEliece,et al.  The theory of information and coding : a mathematical framework for communication , 1977 .

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

[5]  F. Alajaji,et al.  Effect of feedback on the capacity of discrete additive channels with memory , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[6]  Sergio Verdú,et al.  A general formula for channel capacity , 1994, IEEE Trans. Inf. Theory.

[7]  Sergio Verdú,et al.  The source-channel separation theorem revisited , 1995, IEEE Trans. Inf. Theory.

[8]  Fady Alajaji.  Feedback does not increase the capacity of discrete channels with additive noise , 1995, IEEE Trans. Inf. Theory.

[9]  Toby Berger,et al.  The capacity of finite-State Markov Channels With feedback , 2005, IEEE Transactions on Information Theory.

[10]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[11]  Haim H. Permuter,et al.  Capacity of the Trapdoor Channel With Feedback , 2006, IEEE Transactions on Information Theory.

[12]  Sekhar Tatikonda,et al.  The Capacity of Channels With Feedback , 2006, IEEE Transactions on Information Theory.

[13]  Fady Alajaji,et al.  Feedback Capacity of a Class of Symmetric Finite-State Markov Channels , 2009, IEEE Transactions on Information Theory.

[14]  Andrea J. Goldsmith,et al.  Finite State Channels With Time-Invariant Deterministic Feedback , 2006, IEEE Transactions on Information Theory.

[15]  Jon Hamkins.  Optimal Codes for the Burst Erasure Channel , 2010 .

[16]  Farrokh Etezadi,et al.  Zero-Delay Sequential Transmission of Markov Sources Over Burst Erasure Channels , 2014, IEEE Transactions on Information Theory.

[17]  Haim H. Permuter,et al.  Capacity and Coding for the Ising Channel With Feedback , 2012, IEEE Transactions on Information Theory.

[18]  Haim H. Permuter,et al.  Can feedback increase the capacity of the energy harvesting channel? , 2015, 2015 IEEE Information Theory Workshop (ITW).

[19]  Haim H. Permuter,et al.  The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint , 2016, IEEE Transactions on Information Theory.

[20]  Charalambos D. Charalambous,et al.  Feedback does not increase the capacity of compound channels with additive noise , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[21]  Guangyue Han,et al.  Asymptotics of Input-Constrained Erasure Channel Capacity , 2016, IEEE Transactions on Information Theory.