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.Comment: V3: capacity statement fixed; V2: published version in proceedings at
International Zurich Seminar on Information and Communication (IZS) 2022 with
wrong capacity statement; V1: wrong capacity statement (wrong proof that the
codes do not achieve capacity while they do), submitted to 2021 IEEE
Globecom: Workshop on Channel Coding beyond 5
