Stationary symbol sequences from variable-length word sequences

Variable-length word sequences (VLWS) and symbol sequences obtained from VLWS are discussed. A VLWS is regarded as a vector-valued stochastic process in which the sequence of vector dimensions is itself a stochastic process. For a given VLWS, the symbol sequence is not uniquely defined because it depends on how the choice of the time origin is made. In particular, a deterministic choice leads to a nonstationary symbol sequence even if the originating VLWS is stationary. A suitable random choice must be made in order to get a stationary symbol sequence from a stationary VLWS. Attention is given to the spectral analysis of both the VLWS and the corresponding stationary symbol sequence. An application to a VLWS consisting of mutually independent words is given.