arXiv subjects

Te Sun Han

Publications and source records attributed to Te Sun Han.

21 records · Page 2Linked to original sources

arXiv2000

An information-spectrum approach to joint source-channel coding

Given a general source $\sV=\{V^n\}\noi$ with {\em countably infinite} source alphabet and a general channel $\sW=\{W^n\}\noi$ with arbitrary {\em abstract} channel input and output alphabets, we study the joint source-channel coding problem from the information-spectrum point of view. First, we generalize Feinstein's lemma (direct part) and Verdú-Han's lemma (converse part) so as to be applicable to the general joint source-channel coding problem. Based on these lemmas, we establish a sufficient condition as well as a necessary condition for the source $\sV$ to be reliably transmissible over the channel $\sW$ with asymptotically vanishing probability of error. It is shown that our sufficient condition coincides with the sufficient condition derived by Vembu, Verdú and Steinberg, whereas our necessary condition is much stronger than the necessary condition derived by them. Actually, our necessary condition coincide with our sufficient condition if we disregard some asymptotically vanishing terms appearing in those conditions. Also, it is shown that {\em Separation Theorem} in the generalized sense always holds. In addition, we demonstrate a sufficient condition as well as a necessary condition for the $\vep$-transmissibility ($0\le \vep <1$). Finally, the separation theorem of the traditional standard form is shown to hold for the class of sources and channels that satisfy the (semi-) strong converse property.

math.PR↗

arXiv2000

The identification capacity and resolvability of channels with input cost constraint

Given a general channel, we first formulate the idetification capacity problem as well as the resolvability problem with input cost constraint in as the general form as possible, along with relevant fundamental theorems. Next, we establish some mild sufficient condition for the key lemma linking the identification capacity with the resolvability to hold for the continuous input alphabet case with input cost constraint. Under this mild condition, it is shown that we can reach the {\em continuous}-input fundamental theorem of the same form as that for the fundamental theorem with {\em finite} input alphabet. Finally, as important examples of this continuous-input fundamental theorem, we show that the identification capacity as well as the resolvability coincides with the channel capacity for stationary additive white (and also non-white) Gaussian noise channels.

math.PR↗

arXiv2000

Hypothesis Testing with the General Source

The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in doing so is first to convert all of the hypothesis testing problems completely to the pertinent computation problems in the large deviation-probability theory. It turns out that this kind of methodologically new approach enables us to establish quite compact general formulas of the optimal exponents of the second kind of error and correct testing probabbilities for the general sources including all nonstationary and/or nonergodic sources with arbitrary abstract alphabet (countable or uncountable). Such general formulas are presented from the information-spectrum point of view.

math.PR↗