A general method for the development of constrained codes

TL;DR

This paper introduces a unified polynomial-time method for constructing both local and global constrained codes, enabling flexible code design for various applications without relying on precomputed combinatorial formulas.

Contribution

It presents a novel, general algorithm based on Cover's enumerative code that computes all parameters dynamically, simplifying and unifying the code construction process.

Findings

The method operates with polynomial complexity.

It can handle combined local and global constraints.

It eliminates the need for precomputed combinatorial formulas.

Abstract

Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be encoded by binary sequences containing no sub-words 00 and 111. The second class contains codes with global constraints; for example, the code-words must be binary sequences of certain even length with half zeros and half ones. It is important to note that often the necessary codes must fulfill some requirements of both classes. In this paper we propose a general polynomial complexity method for constructing codes for both classes, as well as for combinations thereof. The proposed method uses the enumerative Cover's code, but the main difference between known applications of this code is that the known algorithms require the use of combinatorial formulae when applied, whereas the proposed method calculates all parameters on-the-fly using a polynomial complexity algorithm.