Optimal code rates for Lorentzian channel models

In this paper, we take an information-theoretic approach to obtaining optimal code rates for error-control codes on a magnetic storage channel approximated by the Lorentzian channel. Code rate optimality is in the sense of maximizing the information-theoretic user density along a track. To arrive at such results, we compute the achievable information rates for the Lorentzian channel as a function of SNR and channel density, and then use these information rate calculations to obtain optimal code rates and maximal user densities. The achievable information rate calculations exploit the pioneering work of Arnold and Loeliger (2001) (see also H.D. Pfister and P.H. Siegel, 2001) who recently presented a technique for accurately estimating achievable information rates for binary-input intersymbol interference channels with additive white Gaussian noise.