High-rate self-synchronizing codes

TL;DR

This paper introduces new constructions for difference systems of sets that improve the information rate of self-synchronizing codes, balancing synchronization robustness with efficiency, especially in low-noise environments.

Contribution

It presents methods to construct difference systems of sets with higher information rates, using optimal systems as building blocks, and provides direct constructions for high-rate, error-tolerant self-synchronizing codes.

Findings

Constructed difference systems with higher information rates.

Achieved asymptotically optimal difference systems.

Developed direct constructions for binary and ternary codes.

Abstract

Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error-tolerance that generate binary and ternary self-synchronizing codes.