—We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity… (More)
—We develop methods for analyzing and constructing combined modulation/error-correctiong codes (ECC codes), in particular codes that employ some form of reversed concatenation and whose ECC decoding scheme requires easy access to soft information (e.g., turbo codes, low-density parity-check (LDPC) codes or parity codes). We expand on earlier work of Immink… (More)
We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117–122], we derive an asymptotic formula (when the… (More)
Given a stationary Z d-Markov random field µ that satisfies a spatial mixing property, known as strong spatial mixing, we give general upper and lower bounds to the entropy of µ. In the case of a stationary nearest-neighbor Z d-Gibbs measure, we use these to get computable sequences of upper and lower approximations that converge to the entropy. In the case… (More)
This paper provides a self-contained exposition of k modulation code design methods based upon the state splitting algorithm. The techniques are applied to the design of several codes of interest in digital data recording.