TY - GEN
T1 - On the dispersions of three network information theory problems
AU - Tan, Vincent Y.F.
AU - Kosut, Oliver
PY - 2012
Y1 - 2012
N2 - We characterize fundamental limits for the Slepian-Wolf problem, the multiple-access channel and the asymmetric broadcast channel in the finite blocklength setting. For the Slepian-Wolf problem (distributed lossless source coding), we introduce a fundamental quantity known as the entropy dispersion matrix. We show that if this matrix is positive-definite, the optimal rate region under the constraint of a fixed blocklength and non-zero error probability has a curved boundary compared to being polyhedral for the asymptotic Slepian-Wolf scenario. In addition, the entropy dispersion matrix governs the rate of convergence of the non-asymptotic region to the asymptotic one. We develop a general universal achievability procedure for finite blocklength analyses of other network information theory problems such as the multiple-access channel and broadcast channel. We provide inner bounds to these problems using a key result known as the vector rate redundancy theorem which is proved using a multidimensional version of the Berry-Essèen theorem. We show that a so-called information dispersion matrix characterizes these inner bounds.
AB - We characterize fundamental limits for the Slepian-Wolf problem, the multiple-access channel and the asymmetric broadcast channel in the finite blocklength setting. For the Slepian-Wolf problem (distributed lossless source coding), we introduce a fundamental quantity known as the entropy dispersion matrix. We show that if this matrix is positive-definite, the optimal rate region under the constraint of a fixed blocklength and non-zero error probability has a curved boundary compared to being polyhedral for the asymptotic Slepian-Wolf scenario. In addition, the entropy dispersion matrix governs the rate of convergence of the non-asymptotic region to the asymptotic one. We develop a general universal achievability procedure for finite blocklength analyses of other network information theory problems such as the multiple-access channel and broadcast channel. We provide inner bounds to these problems using a key result known as the vector rate redundancy theorem which is proved using a multidimensional version of the Berry-Essèen theorem. We show that a so-called information dispersion matrix characterizes these inner bounds.
KW - Dispersion
KW - Finite blocklength
KW - Network information theory
UR - http://www.scopus.com/inward/record.url?scp=84868563432&partnerID=8YFLogxK
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U2 - 10.1109/CISS.2012.6310768
DO - 10.1109/CISS.2012.6310768
M3 - Conference contribution
AN - SCOPUS:84868563432
SN - 9781467331401
T3 - 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012
BT - 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012
T2 - 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012
Y2 - 21 March 2012 through 23 March 2012
ER -