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首页> 外文期刊>Information Theory, IEEE Transactions on >Capacity Analysis of Linear Operator Channels Over Finite Fields
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Capacity Analysis of Linear Operator Channels Over Finite Fields

机译：有限域上线性算子通道的容量分析

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摘要

Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity (C) and the subspace coding capacity (C_{ text {SS}}) are analyzed. By establishing and comparing lower bounds on (C) and upper bounds on (C_{ text {SS}}) , various necessary conditions and sufficient conditions such that (C= C_{text {SS}}) are obtained. A new class of LOCs such that (C=C_{text {SS}}) is identified, which includes LOCs with uniform-given-rank transfer matrices as special cases. It is also demonstrated that (C_{text {SS}}) is strictly less than (C) for a broad class of LOCs. In general, an optimal subspace coding scheme is difficult to find because it requires to solve the maximization of a nonconcave function. However, for an LOC with a unique subspace degradation, (C_{ text {SS}}) can be obtained by solving a convex optimization problem over rank distribution. Classes of LOCs with a unique subspace degradation are characterized. Since LOCs with uniform-given-rank transfer matrices have unique subspace degradations, some existing results on LOCs with uniform-given-rank transfer matrices are explained from a more general way.
机译：通过通过使用线性网络编码的网络进行通信的动机，研究了在有限域上具有任意分布的传输矩阵的线性算子信道（LOC）的容量。分析了香农容量（C）和子空间编码容量（C_ {text {SS}}）。通过建立和比较（C）的下限和（C_ {文本{SS}}）的上限，可以获得各种必要条件和充分条件，使得（C = C_ {text {SS}}）。确定了新的LOC类，例如（C = C_ {text {SS}}），其中包括具有统一给定秩转移矩阵的LOC作为特例。还证明了（C_ {text {SS}}）对于广泛的LOC严格小于（C）。通常，难以找到最优子空间编码方案，因为它需要解决非凹函数的最大化。但是，对于具有唯一子空间退化的LOC，可以通过解决秩分布上的凸优化问题来获得（C_ {text {SS}}}。表征具有独特子空间退化的LOC类。由于具有统一给定秩传递矩阵的LOC具有独特的子空间退化，因此，从更一般的角度来解释具有统一给定秩传递矩阵的LOC的一些现有结果。

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