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arXiv 1105.6115cs.ITmath.IT
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乘性非线性矩阵信道的容量

On the Capacity of Multiplicative Finite-Field Matrix Channels

Roberto W. Nóbrega, Danilo Silva, Bartolomeu F. Uchôa-Filho

摘要:

本文研究了乘性有限域矩阵信道,这是一种离散的无记忆信道,其输入和输出是由乘性传递矩阵相关的矩阵(在有限域上)。这里考虑的模型假设所有具有相同秩的传输矩阵是等概率的,因此信道完全由传输矩阵的秩分布来表征。这个模型被认为是更灵活的比以前提出的描述随机线性网络编码系统的链路擦除,同时仍然是足够简单,允许易处理。该模型也是保守的意义上说,它的容量提供了一个下界的容量的任何渠道具有相同的秩分布。一个主要的贡献是表示的信道容量的凸优化问题,可以很容易地通过数值计算解决的解决方案。对于常秩输入的特殊情况,得到了容量的封闭表达式。渐近大字段大小或数据包长度的信道的行为进行了研究,它表明,在这种情况下,常数秩输入足够。最后,它被证明是众所周知的方法,将输入和输出作为子空间是信息无损的,即使在这个更一般的模型。

英文摘要:

This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes that all transfer matrices with the same rank are equiprobable, so that the channel is completely characterized by the rank distribution of the transfer matrix. This model is seen to be more flexible than previously proposed ones in describing random linear network coding systems subject to link erasures, while still being sufficiently simple to allow tractability. The model is also conservative in the sense that its capacity provides a lower bound on the capacity of any channel with the same rank distribution. A main contribution is to express the channel capacity as the solution of a convex optimization problem which can be easily solved by numerical computation. For the special case of constant-rank input, a closed-form expression for the capacity is obtained. The behavior of the channel for asymptotically large field size or packet length is studied, and it is shown that constant-rank input suffices in this case. Finally, it is proved that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general model.

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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