Codes for Constrained Periodicity

TL;DR

This paper introduces efficient, low-redundancy constructions for codes that prevent periodicity in all windows, addressing reliability issues in racetrack memories with novel algorithms and theoretical guarantees.

Contribution

It presents the first efficient, low-redundancy constructions for avoiding periodicity in all windows, with proven convergence and near-optimal redundancy.

Findings

Algorithms achieve average-linear time complexity.

Constructions successfully avoid periodicity in all windows.

Studied the size and limits of such constrained codes.

Abstract

Reliability is an inherent challenge for the emerging nonvolatile technology of racetrack memories, and there exists a fundamental relationship between codes designed for racetrack memories and codes with constrained periodicity. Previous works have sought to construct codes that avoid periodicity in windows, yet have either only provided existence proofs or required high redundancy. This paper provides the first constructions for avoiding periodicity that are both efficient (average-linear time) and with low redundancy (near the lower bound). The proposed algorithms are based on iteratively repairing windows which contain periodicity until all the windows are valid. Intuitively, such algorithms should not converge as there is no monotonic progression; yet, we prove convergence with average-linear time complexity by exploiting subtle properties of the encoder. Overall, we both provide constructions that avoid periodicity in all windows, and we also study the cardinality of such constraints.