Variable-length block-coding schemes are investigated for discrete memoryless
channels with ideal feedback under cost constraints. Upper and lower bounds are
found for the minimum achievable probability of decoding error Pe,minβ as
a function of constraints R, \AV, and ΟΛ on the transmission rate,
average cost, and average block length respectively. For given R and \AV,
the lower and upper bounds to the exponent β(lnPe,minβ)/ΟΛ are
asymptotically equal as ΟΛββ. The resulting reliability
function, limΟΛβββ(βlnPe,minβ)/ΟΛ, as a
function of R and \AV, is concave in the pair (R, \AV) and generalizes
the linear reliability function of Burnashev to include cost constraints. The
results are generalized to a class of discrete-time memoryless channels with
arbitrary alphabets, including additive Gaussian noise channels with amplitude
and power constraints