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arXiv 1204.4249cs.ITmath.IT
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高斯多址信道反馈后验匹配算法

Posterior Matching Scheme for Gaussian Multiple Access Channel with Feedback

Lan V. Truong

摘要:

后验匹配是由Ofer Shayevitz和Meir Feder提出的一种方法,用于设计具有反馈的一般点对点无记忆信道的容量实现编码方案。本文提出了一种基于后验匹配的时变后验匹配编码和变速率译码方案,并分析了该方案的可达速率域和错误概率。时变后验匹配方案是Shayevitz和Feder的后验匹配方案的推广,当输入消息给定输出的后验分布在传输时隙上不固定时。事实证明,众所周知的Ozarow的编码方案,它获得了两个用户高斯信道的容量,是我们的扩展后验匹配框架的一个特例,因为Schalkwijk-Kailath的方案是上述点对点后验匹配的一个特例。此外,我们设计的后验匹配也获得了对称多用户高斯MAC的线性反馈和容量。此外,本文中的编码方案是为实高斯MAC设计的,以获得该性能,这与以前的方法不同,其中编码方案是为复高斯MAC设计的。更重要的是,本文显示了潜在的后验匹配设计最佳编码方案的多用户信道反馈。

英文摘要:

Posterior matching is a method proposed by Ofer Shayevitz and Meir Feder to design capacity achieving 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 the Gaussian MAC 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 posterior matching also obtains the linear-feedback sum-capacity for the symmetric multiuser Gaussian MAC. Besides, the encoding scheme in this paper is designed for the real Gaussian MAC to obtain that performance, which is different from previous approaches where encoding schemes are designed for the complex Gaussian MAC. More importantly, this paper shows potential of posterior matching in designing optimal coding schemes for multiuser channels with feedback.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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