Group coding of RF tags to verify the integrity of group of objects

RFID is an essential technology to uniquely identify physical objects. In many practical business processes using RFID, we check not only individual objects but also check if there is no missing objects and no extra objects in a group of objects. While individual objects identifications are done by using RFID, group verifications are usually done by looking up a shipping list or corresponding EDI data which require a network connection. In this paper, we propose "group coding of RF tags" by which we can verify the integrity of a group of objects just by writing additional data in RF tags' memory. The additional data is computed from unique IDs of objects that belong to the group. We propose fundamental and general group codings. With the fundamental group coding, we can check if the integrity of a group of objects is preserved or not. It is a parity check of hashes of unique IDs in a group. We also propose general group coding by extending the fundamental group coding. With the general group coding, we can estimate the number of missing objects if the integrity of a group is not verified. The strength of the missing number estimation can be controlled by the size of data written to RF tags. It can be considered as a Low Density Parity Check (LDPC) in physical objects. The theory of group coding is confirmed by a numerical simulation and an experiment. It is shown by the simulation and experiment that we can detect 10 missing RF tags out of 20 RF tags with 99.5% reliability by writing 96-bit data into each RF tags besides its 96-bit unique ID.