Finite-length extrinsic information transfer (EXIT) analysis for coded and precoded ISI channels

In this paper, we consider the classic problem of accessing coded and precoded intersymbol interference (ISI) channels, and particularly partial response (PR) channels, which are widely used in modeling magnetic recording systems. Previous work has either treated the binary precoder as an exclusive function of the channel characteristics, disregarding possible impact from the channel code, or, in performing the iterative analysis of this concatenated system, assumed an unbounded length. Our approach here is to extend the conventional infinite-length extrinsic information transfer (EXIT) charts to ISI systems of limited lengths, and to explicitly account for the effect of the channel nonergodicity. We found that short-length channel codes may exhibit distinctively different EXIT behaviors in different rate regions, and it is important to couple the precoder and the channel code. We show that infinite- and finite-length EXIT behaviors do not always agree, and hence the results obtained from the infinite-length analysis may not hold for practical short-length systems.