Multiple-Access Channel Resolvability with Cribbing

We study channel resolvability for the discrete memoryless multiple access channel with cribbing, i.e., the characterization of the amount of randomness required to approximate an i.i.d. output distribution in terms of Kullback-Leibler divergence. We analyze the cases in which one encoder cribs (i) the input of the other encoder; or the output of the other encoder (ii) noncausally, (iii) causally, or (iv) strictly-causally. For cases (i)-(iii), we exactly characterize the channel resolvability region. For case (iv), we provide inner and outer bounds for the channel resolvability region; our achievability result handles the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden.

[1]  Jörg Kliewer,et al.  Strong coordination over a line network , 2013, 2013 IEEE International Symposium on Information Theory.

[2]  Aaron D. Wyner,et al.  The common information of two dependent random variables , 1975, IEEE Trans. Inf. Theory.

[3]  Yossef Steinberg.  Resolvability Theory for the Multiple-Access Channel , 1998, IEEE Trans. Inf. Theory.

[4]  Mohammad Reza Aref,et al.  Multiple Access Wiretap channels with strong secrecy , 2010, 2010 IEEE Information Theory Workshop.

[5]  Gerhard Kramer,et al.  Informational divergence approximations to product distributions , 2013, 2013 13th Canadian Workshop on Information Theory.

[6]  Matthieu R. Bloch,et al.  Strong Secrecy From Channel Resolvability , 2011, IEEE Transactions on Information Theory.

[7]  Ming Xiao,et al.  Strong secrecy for interference channels from channel resolvability , 2015, 2015 49th Asilomar Conference on Signals, Systems and Computers.

[8]  Frans M. J. Willems,et al.  The discrete memoryless multiple-access channel with cribbing encoders , 1985, IEEE Trans. Inf. Theory.

[9]  Paul W. Cuff,et al.  Distributed Channel Synthesis , 2012, IEEE Transactions on Information Theory.

[10]  Sergio Verdú,et al.  Approximation theory of output statistics , 1993, IEEE Trans. Inf. Theory.

[11]  Sergio Verdú,et al.  Channel simulation and coding with side information , 1994, IEEE Trans. Inf. Theory.

[12]  Masahito Hayashi,et al.  General nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel , 2006, IEEE Transactions on Information Theory.

[13]  Sergio Verdú,et al.  Simulation of random processes and rate-distortion theory , 1996, IEEE Trans. Inf. Theory.

[14]  Sergio Verdú,et al.  $f$ -Divergence Inequalities , 2015, IEEE Transactions on Information Theory.

[15]  Slawomir Stanczak,et al.  The MAC Resolvability Region, Semantic Security and Its Operational Implications , 2017, ArXiv.