Asymptotic Transmission Capacity of Channels with a Countable Alphabet and Application to Asynchronous Channels

Discrete memoryless communications channels are considered with a countable number of symbols at input and output. It is assumed that the signal distortion at the input is subject to the restriction
$$ \sum^\infty_{k=1}\varphi(k)p_k\leq\mu, $$
where $\varphi(\cdot)$ is some positive function satisfying fairly general conditions. For such channels with low noise, for fairly general conditions, formulas are obtained asymptotic (with respect to a small parameter characterizing the noise power) for the transmission capacity. The method described is used to calculate the asymptotic transmission capacity of asynchronous channels with synchrosymbol and low noise.