We address the problem of finite-state code construction for thecostly channel. Adler et al. developed powerful state-splittingalgorithm for use in the construction of finite-state codes forhard-constrained channels. We extend the state-splitting algorithm tothe costly channel. We present several examples of costly channelsrelated to magnetic recording, the telegraph channel, and shaping gainmodulation. We design a number of synchronous and asynchronous codes,some of which come very close to achieving capacity
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