An Enumerative Method for Encoding Spectrum Shaped Binary Run-Length Constrained Sequences

TL;DR

This paper presents an enumerative encoding and decoding method for spectrum shaped binary run-length constrained sequences, utilizing recurrence relations based on Cover's scheme to efficiently handle sequences with specified exponential sum ranges.

Contribution

It introduces a novel enumerative approach for encoding and decoding spectrum shaped binary sequences with predefined exponential sum constraints, extending Cover's scheme.

Findings

Derived recurrence relations for sequence enumeration

Implemented encoding and decoding procedures

Validated the method's effectiveness for constrained sequences

Abstract

A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence relations for calculating the number of these sequences are derived. Implementation of encoding and decoding procedures is also shown.