Joint Source-Channel Coding Revisited: Information-Spectrum Approach

Given a general source V = {V n } ∞ n=1 with countably infinite source alphabet and a general channel W = {W n } ∞ n=1 with arbitrary abstract channel input/channel 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 V to be reliably transmissible over the channel W with asymptotically vanishing probability of error. It is shown that our sufficient condition is equivalent to the sufficient condition derived by Vembu, Verdú and Steinberg [9], whereas our necessary condition is shown to be stronger than or equivalent to the necessary condition derived by them. It turns out, as a direct consequence, that " separation principle " in a relevantly generalized sense holds for a wide class of sources and channels, as was shown in a quite dfifferent manner by Vembu, Verdú and Steinberg [9]. It should also be remarked that a nice duality is found between our necessary and sufficient conditions, whereas we cannot fully enjoy such a duality between the necessary condition and the sufficient condition by Vembu, Verdú and Steinberg [9]. In addition, we demonstrate a sufficient condition as well as a necessary condition for the ε-transmissibility (0 ≤ ε < 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.