Reed-Muller Identification

TL;DR

This paper explores Reed-Muller codes for identification, demonstrating they can achieve high rates without significant computational increase, unlike some other code constructions.

Contribution

It generalizes identification schemes to Reed-Muller codes, showing they enable high-rate identification with manageable computational complexity.

Findings

Reed-Muller codes can be used for identification with high rates.

The computational load remains manageable compared to other code-based schemes.

The approach does not achieve identification capacity but offers practical advantages.

Abstract

Ahlswede and Dueck identification has the potential of exponentially reducing traffic or exponentially increasing rates in applications where a full decoding of the message is not necessary and, instead, a simple verification of the message of interest suffices. However, the proposed constructions can suffer from exponential increase in the computational load at the sender and receiver, rendering these advantages unusable. This has been shown in particular to be the case for a construction achieving identification capacity based on concatenated Reed-Solomon codes. Here, we consider the natural generalization of identification based on Reed-Muller codes and we show that, although without achieving identification capacity, they allow to achieve the exponentially large rates mentioned above without the computational penalty increasing too much the latency with respect to transmission.