Rate-distortion functions of non-stationary Markoff chains and their block-independent approximations

TL;DR

This paper proves that the normalized rate-distortion functions of block-independent approximations of irreducible, aperiodic Markov chains converge to a limit independent of initial distribution, matching the chain's rate-distortion function.

Contribution

It establishes the independence of the limit of normalized rate-distortion functions from initial distributions for certain Markov chains.

Findings

Limit of normalized rate-distortion functions is independent of initial distribution.

The limit equals the rate-distortion function of the original Markov chain.

Results apply to irreducible, aperiodic Markov chains.

Abstract

It is proved that the limit of the normalized rate-distortion functions of block independent approximations of an irreducible, aperiodic Markoff chain is independent of the initial distribution of the Markoff chain and thus, is also equal to the rate-distortion function of the Markoff chain.