Power Spectra of Constrained Codes with Level-Based Signaling: Overcoming Finite-Length Challenges

TL;DR

This paper develops a method to derive the power spectrum of constrained codes with level-based signaling, including finite-length sequences, enhancing analysis for storage and transmission systems.

Contribution

It introduces a generalized framework for calculating the power spectrum of finite-length constrained codes, specifically applied to LOCO and A-LOCO codes, with closed-form solutions.

Findings

Derived power spectra for infinite-length constrained sequences.

Extended the method to finite-length codewords.

Provided closed-form spectral expressions for LOCO and A-LOCO codes.

Abstract

Constrained codes are used to eliminate error-prone patterns in various practical systems. Recently, we introduced efficient binary symmetric lexicographically-ordered constrained (LOCO) codes and asymmetric LOCO (A-LOCO) codes to increase density in magnetic recording systems and lifetime in Flash systems by eliminating the relevant detrimental patterns. Due to their application, LOCO and A-LOCO codes are associated with level-based signaling. Studying the power spectrum of a random signal with certain properties is principal for any storage or transmission system. In this paper, we first modify a framework from the literature in order to introduce a method to derive the power spectrum of a sequence of constrained data associated with level-based signaling. We apply our method to infinitely long sequences satisfying symmetric and asymmetric constraints. Next, we show how to generalize the method such that it works for a stream of finite-length codewords. We use the generalized method to devise closed forms for the spectra of finite-length LOCO and A-LOCO codes from their transition diagrams. Our LOCO and A-LOCO spectral derivations can be performed for any code length and can be extended to other constrained codes. We plot these power spectra, and discuss various important spectral properties for both LOCO and A-LOCO codes.