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Extremality Between Symmetric Capacity and Gallager’s Reliability Function <span class="MathJax_Preview">E_{0}</span><script type="math/tex">E_{0}</script> for Ternary-Input Discrete Memoryless Channels | IEEE Journals & Magazine | IEEE Xplore

Extremality Between Symmetric Capacity and Gallager’s Reliability Function E_{0} for Ternary-Input Discrete Memoryless Channels


Abstract:

This paper examines the exact ranges between the symmetric capacity and Gallager's reliability function E0 for ternary-input discrete memoryless channels (T-DMCs) under a...Show More

Abstract:

This paper examines the exact ranges between the symmetric capacity and Gallager's reliability function E0 for ternary-input discrete memoryless channels (T-DMCs) under a uniform input distribution. We first derive the two extremal ternary-input strongly symmetric channels taking the maximum and minimum values of the E0 function among all ternary-input strongly symmetric channels with a fixed capacity. Extending the results of ternary-input strongly symmetric channels, we second derive the exact ranges between capacity and the E0 function for ternary-input Gallager-symmetric channels. We third show that the exact ranges between the symmetric capacity and the E0 function of T-DMCs coincide with the ranges of ternaryinput Gallager-symmetric channels. In particular, we identify the extremal channels taking the maximum and minimum of E0 among all T-DMCs with a fixed symmetric capacity. As applications of the results, we describe some bounds of error exponents for T-DMCs with a fixed symmetric capacity.
Published in: IEEE Transactions on Information Theory ( Volume: 64, Issue: 1, January 2018)
Page(s): 163 - 191
Date of Publication: 12 September 2017

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