Encoding Semiconstrained Systems

TL;DR

This paper explores the properties of semiconstrained systems, a generalization of constrained systems, focusing on their capacity and the relationships with contained or containing constrained systems, with implications for encoding strategies.

Contribution

It introduces new insights into the containment and approximation of semiconstrained systems by constrained systems, including encoder constructions and theoretical limitations.

Findings

Sequences contained in semiconstrained systems enable constant-to-constant bit-rate encoding.

Most semiconstrained systems are not contained within any proper fully-constrained system.

The study provides a theoretical framework for encoding and analyzing semiconstrained systems.

Abstract

Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply techniques from constrained systems, we study sequences of constrained systems that are contained in, or contain, a given semiconstrained system, while approaching its capacity. In the case of contained systems we describe to such sequences resulting in constant-to-constant bit-rate block encoders and sliding-block encoders. Surprisingly, in the case of containing systems we show that a "generic" semiconstrained system is never contained in a proper fully-constrained system.