Finite-blocklength channel coding rate under a long-term power constraint

This paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability ε, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-n expansion of the maximal channel coding rate is characterized both for AWGN channels and for quasi-static fading channels with perfect channel state information at the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to √(log n)/n.