  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 $P_{e,\min}$ as
a function of constraints $R, \AV$, and $\bar \tau$ on the transmission rate,
average cost, and average block length respectively. For given $R$ and $\AV$,
the lower and upper bounds to the exponent $-(\ln P_{e,\min})/\bar \tau$ are
asymptotically equal as $\bar \tau \to \infty$. The resulting reliability
function, $\lim_{\bar \tau\to \infty} (-\ln P_{e,\min})/\bar \tau$, 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.
