  We study a hidden Markov process which is the result of a transmission of the
binary symmetric Markov source over the memoryless binary symmetric channel.
This process has been studied extensively in Information Theory and is often
used as a benchmark case for the so-called denoising algorithms. Exploiting the
link between this process and the 1D Random Field Ising Model (RFIM), we are
able to identify the Gibbs potential of the resulting Hidden Markov process.
Moreover, we obtain a stronger bound on the memory decay rate. We conclude with
a discussion on implications of our results for the development of denoising
algorithms.
