Nonasymptotic and Second-Order Achievability Bounds for Coding With Side-Information

We present a novel nonasymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include: 1) the Wyner-Ahlswede-Körner (WAK) problem of almost-lossless source coding with rate-limited side-information; 2) the Wyner-Ziv (WZ) problem...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 61; no. 4; pp. 1574 - 1605
Main Authors: Watanabe, Shun, Kuzuoka, Shigeaki, Tan, Vincent Y. F.
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
channel coding
Coding theory
Decoding
Error probability
finite blocklength
Gel'fand-Pinsker
Information theory
Joints
non-asymptotic
Optimization
Probability
Rate-distortion
second-order coding rates
side-information
Simulation
Source coding
Theorems
Wyner-Ahlswede-Korner
Wyner-Ziv
Wyner-Ziv
Source coding
channel coding
non-asymptotic
Wyner-Ahlswede-Körner
side-information
Gel’fand-Pinsker
finite blocklength
second-order coding rates
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We present a novel nonasymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include: 1) the Wyner-Ahlswede-Körner (WAK) problem of almost-lossless source coding with rate-limited side-information; 2) the Wyner-Ziv (WZ) problem of lossy source coding with side-information at the decoder; and 3) the Gel'fand-Pinsker (GP) problem of channel coding with noncausal state information available at the encoder. The bounds are proved using ideas from channel simulation and channel resolvability. Our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the WAK, WZ, and GP problems-in particular those derived by Verdú. Using our novel nonasymptotic bounds, we recover the general formulas for the optimal rates of these side-information problems. Finally, we also present achievable second-order coding rates by applying the multidimensional Berry-Esséen theorem to our new nonasymptotic bounds. Numerical results show that the second-order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2400994