Code Constructions and Bounds for Identification via Channels

doi:10.1109/TCOMM.2021.3136864

Code Constructions and Bounds for Identification via Channels

2022-03-01

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DOI：10.1109/TCOMM.2021.3136864

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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.

Keyword:

Codes

Upper bound

Optical transmitters

Correlation

Reliability

Noise measurement

Decoding

Identification via channels

optical orthogonal codes

binary constant weight codes

hypothesis testing

constant composition codes

Code Constructions and Bounds for Identification via Channels

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