Error Exponents for Variable-length block codes with feedback and cost constraints

Variable-length block-coding schemes are investigated for discrete memoryless channels (DMC) with perfect feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error P_epsi,min as a function of transmission rate R, cost constraint P, and expected block length taumacr. For given P and R, the lower and upper bounds to the exponent -(InP_epsi,min)/taumacr are asymptotically equal as taumacr rarrinfin. The reliability function, lim_{tau rarrinfin}(-ln P_epsi,min)/taumacr, as a function of P and R, is concave in the pair (P, R) and generalizes the linear reliability function of Burnashev (M.V. Burnashev, 1976) to include cost constraints