Entropy rate of hidden markov chains and capacity and coding for input-constrained channels

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In many practical noisy channels, input sequences are constrained in order to enable the channel to operate effectively. For instance, in magnetic and optical recording channels input sequences are constrained in a variety of ways to ensure accurate timing and reduce the likelihood of certain kinds of error events. Input constraints also model memory that is typically present in data recording channels and band-limited communication channels.For many of the most important input-constrained channels, there is no explicit formula known for capacity, which is defined as the maximal rate at which information can be transmitted without error. We plan to focus on two main themes for input-constrained channels: 1) estimates and asymptotics for capacity of input-constrained channels and 2) construction of good codes for such channels.   For 1), we will investigate estimates and asymptotics for entropy rate of Hidden Markov chains, and apply this to capacity of input-constrained channels.For 2), we will focus on coding schemes that limit error propagation and coding schemes that combine input constraints with error correction.