Zero-Error Coding with a Generator Set of Variable-Length Words

We propose a new approach to construct optimal zero-error codes, based on the concatenation of words of variable length, taken from a generator set. Two zero-error variable-length coding algorithms, referred to as "variable-length coding" and "intermingled coding" are under study. We characterize their asymptotic performances via linear difference equations, in terms of simple properties of the generator set, e.g. the roots of the characteristic polynomial or the spectral radius of an adjacency matrix. For a specific example, we construct an "intermingled" coding scheme that achieves asymptotically the zero-error capacity of a specific channel graph. A full version of this paper is accessible on ArXiv at: https: //arxiv.org/abs/2001.03523.