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/tit.2008.926449
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发表时间：
2007-03
影响因子：
2.5
通讯作者：
R. Koetter;F. Kschischang
中科院分区：
文献类型：
--
作者：
R. Koetter;F. Kschischang
研究了随机线性网络编码中的差错控制问题。假设一个ldquononcoherentrdquo或ldquochannelobliviousrdquo模型，其中假设发射机和接收机都不知道信道传输特性。受线性网络编码是向量空间保持的性质的启发，信息传输被建模为向量空间V的基到网络中的注入和接收器对向量空间U的基的收集。引入了与分组空间相关的投影几何的度量，并且示出了如果空间V capU的维度足够大，则对于该度量的最小距离解码器实现正确的解码。如果每个码字的维数被限制为一个固定的整数，则该码形成有限域格拉斯曼图的子集，或者等价地，形成相应格拉斯曼图的顶点的子集。球包装和球覆盖的界限，以及推广的单例界提供了这样的代码。最后，Reed-Solomon类码的建设，有关Gabidulin的建设的最大秩距离码，描述和苏丹风格的ldquolist-1 rdquo最小距离译码算法。
The problem of error-control in random linear network coding is considered. A ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear network coding is vector-space preserving, information transmission is modeled 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 metric on the projective geometry associated with the packet space is introduced, and it is shown that a minimum-distance decoder for this metric achieves correct decoding if the dimension of the space V capU is sufficiently large. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or, equivalently, a subset of the vertices of the corresponding Grassmann graph. Sphere-packing and sphere-covering bounds as well as a generalization of the singleton bound are provided for such codes. Finally, a Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ldquolist-1rdquo minimum-distance decoding algorithm is provided.