Non-Asymptotic and Second-Order Achievability Bounds for Coding With Side-Information [article]

Shun Watanabe, Shigeaki Kuzuoka, Vincent Y. F. Tan
2014 arXiv   pre-print
We present novel non-asymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include (i) the Wyner-Ahlswede-Korner (WAK) problem of almost-lossless source coding with rate-limited side-information, (ii) the Wyner-Ziv (WZ) problem of lossy source coding with side-information at the decoder and (iii) the Gel'fand-Pinsker (GP) problem of channel coding with noncausal state information available at the encoder. The bounds are
more » ... ved using ideas from channel simulation and channel resolvability. Our bounds for all three problems improve on all previous non-asymptotic bounds on the error probability of the WAK, WZ and GP problems--in particular those derived by Verdu. Using our novel non-asymptotic 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-Esseen theorem to our new non-asymptotic bounds. Numerical results show that the second-order coding rates obtained using our non-asymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds.
arXiv:1301.6467v5 fatcat:oaeiwum32zg5dlhejnkyrdpzyq