Universal coding for memoryless sources with countably infinite alphabets

We present an asymptotically efficient coding strategy for a stationary countably infinite source determined over a set of nonnegative integers. If the $k$th moment $\mu_k$ of the source data is finite, then asymptotic average coding redundancy for length-$n$ blocks, $n\to\infty$ is upper bounded by $C(\log n/n)^{k/(k+1)}$, where $C$ is a nonnegative constant. The coding efficiency is demonstrated via an example of scalar quantization of random variables with generalized Gaussian distribution.