Title: On the Necessity of Structured Codes for Communications over MAC with Feedback,
Abstract: The problem of three-user multiple-access channel (MAC) with noiseless
feedback is investigated. A new coding strategy is presented. The coding scheme
builds upon the natural extension of the Cover-Leung (CL) scheme; and uses
quasi-linear codes. A new single-letter achievable rate region is derived. The
new achievable region strictly contains the CL region. This is shown through an
example. In this example, the coding scheme achieves optimality in terms of
transmission rates. It is shown that any optimality achieving scheme for this
example must have a specific algebraic structure. Particularly, the codebooks
must be closed under binary addition.