Channels With Cost Constraints: Strong Converse and Dispersion

This paper shows the strong converse and the dispersion of memoryless channels with cost constraints and performs a refined analysis of the third-order term in the asymptotic expansion of the maximum achievable channel coding rate, showing that it is equal to (1/2)((log n)/n) in most cases of interest. The analysis is based on a nonasymptotic converse bound expressed in terms of the distribution of a random variable termed the b-tilted information density, which plays a role similar to that of the d-tilted information in lossy source coding. We also analyze the fundamental limits of lossy joint-source-channel coding over channels with cost constraints.