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arXiv 0807.1372cs.ITmath.IT
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基于场矩阵信道的通信

Communication over Finite-Field Matrix Channels

Danilo Silva, Frank R. Kschischang, Ralf Kötter

摘要:

本文的动机是网络编码中的错误控制问题时,错误是随机引入的方式(而不是选择一个对手)。一个加乘矩阵信道被认为是随机网络编码的模型。该模型假设在网络上传输n个长度为m的数据包,并且随机选择多达t个错误数据包并将其注入网络。对于任意信道参数,得到了容量的上界和下界,并在大的域或矩阵大小的限制下给出了容量的渐近表达式。一个简单的编码方案,实现在这两种限制情况下的容量。该方案的解码复杂度为O(n^2 m),并且错误概率在数据包长度和字段大小(以比特为单位)上均呈指数下降。扩展这些结果的相干网络编码。

英文摘要:

This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random network coding. The model assumes that n packets of length m are transmitted over the network, and up to t erroneous packets are randomly chosen and injected into the network. Upper and lower bounds on capacity are obtained for any channel parameters, and asymptotic expressions are provided in the limit of large field or matrix size. A simple coding scheme is presented that achieves capacity in both limiting cases. The scheme has decoding complexity O(n^2 m) and a probability of error that decreases exponentially both in the packet length and in the field size in bits. Extensions of these results for coherent network coding are also presented.

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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