On Coding over Sliced Information

TL;DR

This paper investigates the minimal redundancy needed for binary codes in unordered set channels with substitution errors, revealing that redundancy requirements are similar to classical error correction despite data slicing.

Contribution

It provides new constructions for codes in unordered set channels and proves their asymptotic optimality, bridging the gap between classical and unordered data error correction.

Findings

Redundancy in unordered set channels matches classical error correction requirements.

Several code constructions are asymptotically optimal.

Redundancy order is independent of data slicing.

Abstract

The interest in channel models in which the data is sent as an unordered set of binary strings has increased lately, due to emerging applications in DNA storage, among others. In this paper we analyze the minimal redundancy of binary codes for this channel under substitution errors, and provide several constructions, some of which are shown to be asymptotically optimal up to constants. The surprising result in this paper is that while the information vector is sliced into a set of unordered strings, the amount of redundant bits that are required to correct errors is order-wise equivalent to the amount required in the classical error correcting paradigm.