Using the Chinese Remainder Theorem for the Grouping of RFID Tags

In this paper, we propose a novel scheme for the design of grouping of radio-frequency identification (RFID) tags, based on the Chinese remainder theorem (CRT). Grouping allows verifying the integrity of a collection of objects without the requirement for accessing external systems, and can be extended to identify missing objects. Motivated by the redundancy property of the Chinese remainder representation, we propose grouping of RFID tags via the CRT. The proposed scheme not only provides designated decoding guarantees, but also offers flexibility in constructing group generation matrices. We also characterize the key objects needed to study decoding guarantees of grouping and its extended counterpart, called rank-deficient and dead-end sets, respectively, which enable theoretical analyses of error rates. The two key objects are related to the minimum and stopping distances of a linear code, respectively. As such, the characterization offers direct connection with coding theory that helps in the understanding of the verification/identification problems being studied. Theoretical and simulation results are presented, demonstrating that the proposed scheme is an efficient approach to the design of grouping of RFID tags.