Beyond the Bound: A New Performance Perspective for Identification via Channels

Abstract

Identification via channels (ID) is a goal-oriented (Post-Shannon) communications paradigm that verifies the matching of message (identity) pairs at source and sink. To date, ID research has focused on the upper bound λ for the probability of a false-positive (FP) identity match, mainly through ID tagging codes that represent the identities through ID codeword sets consisting of position-tag tuples. We broaden the ID research scope by introducing novel ID performance metrics: the expected FP-error probability <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fp</sub> which considers distance properties of ID codeword sets in conjunction with the probability for selecting ID pairs, the threshold probabilities <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ϵ</sub> that characterize quantiles of FP-probabilities, and the distance tail uplift ratio DiTUR giving the fraction of ID pairs whose distance is increased above the minimum distance (which corresponds to λ). We define a No-Code (NC) approach that directly conducts the ID operations with the messages (identities) without any additional coding as a baseline for ID. We investigate a concatenated Reed-Solomon ID code and a Reed-Muller ID code, and find that they do not always yield advantages over using no ID code. We analytically characterize the reduction of error-prone ID pairs through sending multiple tags. Overall, our insights point to investigating the distance distribution of ID codes and incorporating the ID pair distributions of real ID systems in future ID research.