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(Submitted on 5 Apr 2014) Abstract: Posterior matching is a method proposed by Ofer Shayevitz and Meir Feder to design capacity achieving coding schemes for general point-to-point memoryless channel with feedback. The idea of posterior matching is that the transmitter encapsulates the information that receiver does not know up to present time in one random variable and then transmits that random variable to the receiver in the next transmission to refine the receiver's web of science knowledge. The distribution of that variable web of science will be selected in a way such that the input constraint is satisfied. In [1], we proposed a way to extend this encoding-decoding scheme for the Gaussian Multiple Access Channel (AWGN-MAC) with feedback and obtained the same performance as other optimal coding schemes. In this paper, we continue to extend the posterior matching encoding and variable rate decoding idea for the Gaussian broadcast channel (AWGN-BC) with feedback. Our coding strategy web of science for the symmetric AWGN-BC was shown to achieve the same sum-rate as the LQG code [19] and strictly outperform the Kramer code [15]. Moreover, with a more strict input power constraint, a coding web of science scheme similar to the Ozarow-Leung code [4] for the general two-user Gaussian broadcast channel is created with the same achievable rate region.
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