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A Capacity-Achieving Feedback Scheme of the Gaussian Multiple-Access Channel with Degraded Message Sets
Haoheng Yuan1,2, Bin Dai1,2
1School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China.
Abstract:
The classical Schalkwijk-Kailath (SK) scheme for the point-to-point white Gaussian channel with noiseless feedback plays an important role in information theory due to the fact that it is capacity-achieving and the complexity of its encoding-decoding procedure is extremely low. In recent years, it has been shown that an extended SK feedback scheme also achieves the capacity region of the two-user Gaussian multiple-access channel with noiseless feedback (GMAC-NF), where two independent messages are, respectively, encoded by two intended transmitters. However, for the two-user GMAC-NF with degraded message sets (one common message for both users and one private message for an intended user), the capacity-achieving feedback scheme remains open. In this paper, we propose a novel two-step SK-type feedback scheme for the two-user GMAC-NF with degraded message sets and show that this scheme is capacity-achieving.
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