Function-Correcting Codes

02/05/2021
by   Andreas Lenz, et al.
0

Motivated by applications in machine learning and archival data storage, we introduce function-correcting codes, a new class of codes designed to protect a function evaluation on the data against errors. We show that function-correcting codes are equivalent to irregular distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and we show that function-correcting codes can achieve significantly less redundancy than standard error-correcting codes which protect the whole data.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/16/2018

Error correcting codes from sub-exceeding fonction

In this paper, we present error-correcting codes which are the results o...
03/11/2019

Clustering-Correcting Codes

A new family of codes, called clustering-correcting codes, is presented ...
09/16/2018

Sequence-Subset Distance and Coding for Error Control in DNA Data Storage

The process of DNA data storage can be mathematically modelled as a comm...
08/30/2018

Asymptotically Optimal Codes Correcting Fixed-Length Duplication Errors in DNA Storage Systems

A (tandem) duplication of length k is an insertion of an exact copy of...
01/21/2019

Anchor-Based Correction of Substitutions in Indexed Sets

Motivated by DNA-based data storage, we investigate a system where digit...
03/29/2020

On the decoding of 1-Fibonacci error correcting codes

The study of new error correcting codes has raised attention in the last...
09/18/2021

Ensemble Learning using Error Correcting Output Codes: New Classification Error Bounds

New bounds on classification error rates for the error-correcting output...