On Bi-Modal Constrained Coding

TL;DR

This paper investigates bi-modal fixed-length constrained encoders, establishing conditions for their existence and demonstrating that under certain conditions, such encoders can have finite decoding delay, aiding storage system design.

Contribution

It provides necessary and sufficient conditions for the existence of bi-modal fixed-length constrained encoders and shows how to achieve finite decoding delay under stronger conditions.

Findings

Conditions for existence of bi-modal encoders are derived.

Finite decoding delay can be guaranteed under certain conditions.

The study advances encoding strategies for storage applications like optical disks.

Abstract

Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal coding allows to achieve DC control, in addition to satisfying the runlength limited (RLL) constraint specified by the recording channel. In this work, a study is initiated on bi-modal fixed-length constrained encoders. Necessary and sufficient conditions are presented for the existence of such encoders for a given constraint. It is also shown that under somewhat stronger conditions, one can guarantee a bi-modal encoder with finite decoding delay.