Markov encoder-decoder optimized for cyclo-stationary communications channel or storage media

A cyclo-stationary characteristic of a communications channel and/or storage media is determined. The cyclo-stationary characteristic has K-cycles, K>1. Markov transition probabilities are determined that depend on a discrete phase ϕ=t mod K, wherein t is a discrete time value. An encoder to optimize the Markov transition probabilities for encoding data sent through the communications channel and/or stored on the storage media. The optimized Markov transition probabilities are used to decode the data from the communication channel and/or read from the storage media.