Code Constructions and Bounds for Identification via Channels

Onur Gunlu, Jorg Kliewer, Rafael F. Schaefer, Vladimir Sidorenko

Research output: Contribution to journalArticlepeer-review

Abstract

Consider the identification (ID) via channels problem, where a receiver decides whether the transmitted identifier is its identifier, rather than decoding it. This model allows to transmit identifiers whose size scales doubly-exponentially in the blocklength, unlike common transmission codes with exponential scaling. Binary constant-weight codes (CWCs) suffice to achieve the ID capacity. Relating parameters of a binary CWC to the minimum distance of a code and using higher-order correlation moments, two upper bounds on binary CWC sizes are proposed. These bounds are also upper bounds on identifier sizes for ID codes constructed by using binary CWCs. We propose two constructions based on optical orthogonal codes (OOCs), which are used in optical multiple access schemes, have constant-weight codewords, and satisfy cyclic cross-correlation and auto-correlation constraints. These constructions are modified and concatenated with outer Reed-Solomon codes to propose new binary CWCs being optimal for ID. Improvements to the finite-parameter performance are shown by using outer codes with larger minimum distance vs. blocklength ratios. We illustrate ID regimes for which our ID code constructions perform significantly better than existing constructions.

Original languageEnglish (US)
Pages (from-to)1486-1496
Number of pages11
JournalIEEE Transactions on Communications
Volume70
Issue number3
DOIs
StatePublished - Mar 1 2022

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Keywords

  • Identification via channels
  • binary constant weight codes
  • constant composition codes
  • hypothesis testing
  • optical orthogonal codes

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