Cryptology ePrint Archive: Report 2021/876

Code Constructions and Bounds for Identification via Channels

Onur Gunlu and Joerg Kliewer and Rafael F. Schaefer and Vladimir Sidorenko

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 of both our and existing code constructions 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. An extensive list of other modified OOCs that can be used as binary CWCs is provided.

Category / Keywords: foundations / identification via channels, optical orthogonal codes, binary constant weight codes, hypothesis testing, constant composition codes.

Date: received 25 Jun 2021

Contact author: onur guenlue at uni-siegen de

Available format(s): PDF | BibTeX Citation

Version: 20210629:114326 (All versions of this report)

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