Improved Slepian-Wolf exponents via Witsenhausen´s rate

We provide new achievable error exponents for the problem of source coding with full side information at the decoder. In some instances our exponent strictly improves upon the previous applicable results of Csiszar; Oohama and Han; and the ldquoexpurgatedrdquo exponent of Csiszar and Korner. Our improvement follows from studying the growth rate of the chromatic number of strong (and) product graphs via a new information-theoretic functional on a graph. We also give an upper bound on Witsenhausen´s rate, i.e. the zero error rate for the problem of source coding with full side information at the decoder. An application of our functional to zero-error channel capacity is also given.