Improving the redundancy of Knuth's balancing scheme for packet transmission systems

TL;DR

This paper enhances Knuth's binary balancing scheme by reducing redundancy and introducing an efficient, lookup-table-free method for full balancing of encoded data, improving transmission efficiency.

Contribution

It presents a novel approach to decrease redundancy in Knuth's balancing scheme and offers an efficient full balancing method without lookup tables or enumerative coding.

Findings

Reduces redundancy compared to Knuth's original scheme

Provides an efficient full balancing method

Eliminates the need for lookup tables in balancing process

Abstract

A simple scheme was proposed by Knuth to generate binary balanced codewords from any information word. However, this method is limited in the sense that its redundancy is twice that of the full sets of balanced codes. The gap between Knuth's algorithm's redundancy and that of the full sets of balanced codes is significantly considerable. This paper attempts to reduce that gap. Furthermore, many constructions assume that a full balancing can be performed without showing the steps. A full balancing refers to the overall balancing of the encoded information together with the prefix. We propose an efficient way to perform a full balancing scheme that does not make use of lookup tables or enumerative coding.