Spectral lines of codes given as functions of finite Markov chains

Spectral lines of signals that are given by functions of finite Markov chains are investigated. A problem of characterizing encoders in such a manner that the messages emitted from these encoders have some amount of information about clock, independent of the source statistics, is considered. Necessary and sufficient conditions are established for the encoded message to have a spectral line of a given amplitude for every transition probability matrix of the underlying Markov chain. Several other related results about spectral lines are given. A biased coboundary condition is defined at a frequency f, and it is shown that this condition is necessary and sufficient for the encoded message to have a spectral density null at f.