Computer Science – Information Theory
Scientific paper
2012-04-19
Computer Science
Information Theory
Scientific paper
Posterior matching is a method proposed by Ofer Shayevitz and Meir Feder to design optimal coding schemes for general point-to-point memoryless channels with feedback. In this paper, we present a way to extend posterior matching based encoding and variable rate decoding ideas for Gaussian MAC channel with feedback, referred to as time-varying posterior matching scheme, analyze the achievable rate region and error probabilities of the extended encoding-decoding scheme. The time-varying posterior matching scheme is a generalization of the Shayevitz and Feder's posterior matching scheme when the posterior distributions of the input messages given output are not fixed over transmission time slots. It turns out that the well-known Ozarow's encoding scheme, which obtains the capacity of two-user Gaussian channel, is a special case of our extended posterior matching framework as the Schalkwijk- Kailath's scheme is a special case of the point-to-point posterior matching mentioned above. Furthermore, our designed poste- rior matching also obtains the linear-feedback sum-capacity for the symmetric multiuser Gaussian MAC channel. Besides, the encoding scheme in this paper is designed for the real Gaussian MAC channel to obtain that performance, which is different from previous approaches where encoding schemes are designed for the complex Gaussian MAC channel. More importantly, this paper shows potential of posterior matching in designing optimal coding schemes for multiuser channels.
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