A Framework for Information-Theoretic Converses
Publication Date
1-1-2023
Document Type
Conference Proceeding
Publication Title
IEEE International Symposium on Information Theory - Proceedings
Volume
2023-June
DOI
10.1109/ISIT54713.2023.10206647
First Page
1190
Last Page
1195
Abstract
A new approach to information-theoretic converses is proposed based on Shannon's original sphere-packing argument. Typical sequence arguments are hardened with decoding sets to include structured codewords. Each decoding set is shown to have a minimum volume of 2nH(Y|X) typical y-sequences in the point-to-point discrete-memoryless channel if the probability of decoding error vanishes. Since a codebook of type p(x) generates at most 2nH(Y) typical y-sequences, the error probability is non-vanishing when R > maxp(x)I(X;Y). Kolmogorov's zero-one law is applied to prove the error probability also goes to one, unifying the weak and strong converses. In preparation for the capacity of the relay channel, i.i.d codebooks are shown via the zero-one law and a sphere-absorption argument, to exhibit a clustering property where their orbits in the y-space asymptotically coincide or separate into clusters of indistinguishable codewords. The capacity of the relay channel is shown to be max p (xs, xr) min {{I (Xs, Xr; Yd), I(Xs; Yr Yd|Xr) - d} where d: = min {| I Yr; Yr|Xr Yd) - C0 | +, I (Xs;Yd|Xr Yr)}, C0 := I(Xr;Yd), and Yr emulates Xs in a virtual source-relay channel.
Department
Electrical Engineering
Recommended Citation
Jonathan Ponniah and Liang Liang Xie. "A Framework for Information-Theoretic Converses" IEEE International Symposium on Information Theory - Proceedings (2023): 1190-1195. https://doi.org/10.1109/ISIT54713.2023.10206647
