Title :
On Witsenhausen´s zero-error rate for multiple sources
Author_Institution :
Alfred Renyi Inst. of Math., Hungarian Acad. of Sci., Budapest, Hungary
Abstract :
We investigate the problem of minimum rate zero-error source coding when there are several decoding terminals having different side information about the central source variable and each of them should decode in an error-free manner. For one decoder this problem was considered by Witsenhausen. The Witsenhausen rate of the investigated multiple source is the asymptotically achievable minimum rate. We prove that the Witsenhausen rate of a multiple source equals the Witsenhausen rate of its weakest element. The proof relies on a powerful result of Gargano, Korner, and Vaccaro about the zero-error capacity of the compound channel.
Keywords :
channel capacity; decoding; error statistics; graph theory; minimisation; probability; set theory; source coding; Witsenhausen rate; central source variable; chromatic number; compound channel; decoding terminal; minimum rate zero-error source coding; multiple source; zero-error capacity; Block codes; Broadcasting; Decoding; Graph theory; Information theory; Mathematics; Random variables; Source coding; Transmitters;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2003.820048