Coding schemes for multi-level channels with unknown gain and/or offset

We will present coding techniques for transmission and storage channels with unknown gain and/or offset. It will be shown that a codebook of length-n q-ary codewords, S, where all codewords in S have equal balance and energy show an intrinsic resistance against unknown gain and/or offset. Generating functions for evaluating the size of S will be presented. We will present an approximate expression for the code redundancy for asymptotically large values of n.