Huge Size Codes for Identification Via a Multiple Access Channel Under a Word-Length Constraint

Abstract

It is well-known from pioneering papers published since 1989 that, for identification via a communication channel of given Shannon capacity ${\cal C}$, the number N(n) of messages which can be reliably identified using an identification code grows doubly exponentially with the wordlength n, as n→∞. This paper provides contributions to the study of identification plus transmission (IT) codes under a wordlength constraint n≤n ₀ for sending an identifier and message content over a noiseless one-way channel. While the false identification probability no longer vanishes under such constraint, it can be drastically suppressed both by serial and parallel versions of an appropriately defined non-algebraic forward error control (FEC). The main result of this paper consists of exact and approximate expressions for the huge size N(n), and the corresponding second-order rate, of an asymptotically optimal IT code sequence under a wordlength constraint, both with and without either of the two proposed FEC schemes. Also, upper bounds are obtained on the false identification probability under such wordlength constraint for both FEC versions, showing the drastic reduction possible when applying FEC. Furthermore, it is outlined in this paper how the simultaneous transfer of identifiers and message contents by several active users via a noiseless multiple access channel (MAC) could be handled, using the concept of a least length single control sequence. Huge size identifier sets might be of design interest for certain prospective remote alarm services, such as when occasional alarm services are to be conveyed via a simple MAC which is controlled by the same single common cyclically permutable sequence at all nodes involved. It is pointed out under which circumstances the use of huge IT codes might be worth further detailed investigation by designers interested in such prospective services.