On Channel Capacity per Unit Cost

Memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered. The maximum number of bits that can be transmitted reliably through the channel per unit cost is studied. It is shown that if the input alphabet contains a zero-cost symbol, then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions. The direct part of this coding theorem admits a constructive proof via Stein’s lemma on the asymptotic error probability of binary hypothesis tests. Single-user, multiple-access and interference channels are studied.