MIMO MAC-BC Duality With Linear-Feedback Coding Schemes
MIMO MAC-BC Duality With Linear-Feedback Coding Schemes
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DOI：
10.1109/tit.2015.2473838
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发表时间：
2015-11-01
影响因子：
2.5
通讯作者：
Wigger, Michele
中科院分区：
文献类型：
--
作者：
Amor, Selma Belhadj;Steinberg, Yossef;Wigger, Michele
我们表明，通过线性反馈编码方案在双多天线高斯多址信道（MAC）和广播信道（BC）与独立噪声的速率区域相一致。这里的对偶是指：MAC和BC的信道矩阵是彼此的转置，并且在两个信道上施加相同的总输入功率约束P。我们还提出了两个通道的线性反馈容量区域的多字母表达式，即，对于利用线性反馈编码方案可实现的所有速率的集合。我们确定了实现相应线性反馈容量区域的MAC和BC线性反馈编码方案的子类，并且在这些子类内，我们确定了实现相同速率区域的MAC和BC编码方案对。在两个用户的情况下，当发射机或接收机是单天线时，高斯MAC的容量区域是已知的[20]，[15]并且容量实现方案是线性反馈编码方案。与我们的研究结果，我们可以确定的线性反馈容量区域的两个用户高斯BC时，无论是发射机或接收机是单天线，我们可以确定相应的线性反馈容量实现编码方案。我们的结果表明，Elia [11]，Wu等人[30]和Ardestanizadeh等人[1]的控制理论启发的线性反馈编码方案。对于具有相等信道增益的对称单天线高斯BC，在所有线性反馈编码方案中是和速率最优的。更一般地，我们证明了具有独立噪声的标量高斯BC的线性反馈和容量是使用奥扎罗的MAC编码和解码的简单重排来实现的。在K >= 3用户的情况下，克雷默[16]和Ardestanizadeh等人。[2]确定了具有相等信道增益的对称单天线高斯MAC的线性反馈和容量。利用我们的对偶结果，在本文中，我们确定的线性反馈和容量的K >= 3用户单天线高斯BC具有相等的信道增益。它等于Ardestanizadeh等人实现的总和速率。的线性反馈编码方案[1]。我们的结果也推广到只有一个子集的反馈链路存在的设置。
We show that the rate regions achieved by linear-feedback coding schemes over dual multi-antenna Gaussian multi-access channels (MACs) and broadcast channels (BCs) with independent noises coincide. By dual here we mean:the channel matrices of theMAC and the BC are transposes of each other andthe same total input-power constraint P is imposed on both the channels. We also present multi-letter expressions for the linear-feedback capacity regions of the two channels, i.e., for the set of all rates that are achievable with the linear-feedback coding schemes. We identify a sub-class of MAC and BC linear-feedback coding schemes that achieve the respective linear-feedback capacity regions, and within these subclasses, we identify pairs of MAC and BC coding schemes that achieve the same rate regions.In the two-user case, when the transmitters or the receiver are single-antenna, the capacity region for the Gaussian MAC is known [20], [15] and the capacity-achieving scheme is a linear-feedback coding scheme. With our results, we can thus determine the linear-feedback capacity region of the two-user Gaussian BC when either transmitter or receivers are single-antenna and we can identify the corresponding linear-feedback capacity-achieving coding schemes. Our results show that the control-theory inspired linear-feedback coding scheme by Elia [11], Wu et al. [30], and Ardestanizadeh et al. [1] is sum-rate optimal among all the linear-feedback coding schemes for the symmetric single-antenna Gaussian BC with equal channel gains. More generally, we show that the linear-feedback sum-capacity of the scalar Gaussian BC with independent noises is achieved using a simple rearrangement of Ozarow's MAC encodings and decodings.In the K >= 3-user case, Kramer [16] and Ardestanizadeh et al. [2] determined the linear-feedback sum-capacity for the symmetric single-antenna Gaussian MAC with equal channel gains. Using our duality result, in this paper, we identify the linear-feedback sum-capacity for the K >= 3-user single-antenna Gaussian BC with equal channel gains. It is equal to the sum-rate achieved by Ardestanizadeh et al.'s linear-feedback coding scheme [1].Our results extend also to the setup where only a subset of the feedback links are present.