Improved cardinality bounds on the auxiliary random variables in Marton's inner bound

Marton's region is the best known inner bound for a general discrete memoryless broadcast channel. We establish improved bounds on the cardinalities of the auxiliary random variables. We combine the perturbation technique along with a representation using concave envelopes to achieve this improvement. As a corollary of this result, we show that a randomized time division strategy achieves the entire Marton's region for binary input broadcast channels, extending the previously known result for the sum-rate and validating a previous conjecture due to the same authors.

[1]  Venkat Anantharam,et al.  Evaluation of Marton's Inner Bound for the General Broadcast Channel , 2009, IEEE Transactions on Information Theory.

[2]  Amin Gohari,et al.  On Marton ’ s inner bound for two receiver broadcast channels , 2011 .

[3]  Katalin Marton,et al.  A coding theorem for the discrete memoryless broadcast channel , 1979, IEEE Trans. Inf. Theory.

[4]  Chandra Nair,et al.  An Information Inequality and Evaluation of Marton's Inner Bound for Binary Input Broadcast Channels , 2013, IEEE Trans. Inf. Theory.

[5]  Abbas El Gamal,et al.  Network Information Theory , 2021, 2021 IEEE 3rd International Conference on Advanced Trends in Information Theory (ATIT).

[6]  Chandra Nair,et al.  The capacity region for two classes of product broadcast channels , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[7]  H. Vincent Poor,et al.  On the Equivalence of Two Achievable Regions for the Broadcast Channel , 2011, IEEE Transactions on Information Theory.

[8]  Venkat Anantharam,et al.  On an outer bound and an inner bound for the general broadcast channel , 2010, 2010 IEEE International Symposium on Information Theory.

[9]  Venkat Anantharam,et al.  On Marton's inner bound for broadcast channels , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.