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The problem of three-user multiple-access channel (MAC) with noiselessfeedback is investigated. A new coding strategy is presented. The coding schemebuilds upon the natural extension of the Cover-Leung (CL) scheme; and usesquasi-linear codes. A new single-letter achievable rate region is derived. Thenew achievable region strictly contains the CL region. This is shown through anexample. In this example, the coding scheme achieves optimality in terms oftransmission rates. It is shown that any optimality achieving scheme for thisexample must have a specific algebraic structure. Particularly, the codebooksmust be closed under binary addition.

On the Necessity of Structured Codes for Communications over MAC with Feedback