Coding for Errors and Erasures in Random Network Coding
Coding for Errors and Erasures in Random Network Coding
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DOI：
10.1109/isit.2007.4557321
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
Ralf Koetter;F. Kschischang
中科院分区：
文献类型：
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作者：
Ralf Koetter;F. Kschischang
研究了“非相干”随机网络编码信道中的差错控制问题。将信息传输建模为将向量空间V的基注入网络，并由接收器收集向量空间U的基，定义了合适的子空间编码度量，在该度量下，如果空间V U的维度足够大，则最小距离解码器实现正确的译码。当每个码字的维度被限制为固定整数时，该代码形成Grassmann图的顶点的子集。给出了这种码的球包装、球覆盖界和Singleton界。给出了一种类Reed-Solomon码的构造和译码算法。
The problem of error-control in a "noncoherent" random network coding channel is considered. Information transmission is modelled as the injection into the network of a basis for a vector space V and the collection by the receiver of a basis for a vector space U. A suitable coding metric on subspaces is defined, under which a minimum distance decoder achieves correct decoding if the dimension of the space V U is large enough. When the dimension of each codeword is restricted to a fixed integer, the code forms a subset of the vertices of the Grassmann graph. Sphere-packing, sphere-covering bounds and a Singleton bound are provided for such codes. A Reed-Solomon-like code construction is provided and decoding algorithm given.