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In this paper, a time-variant decoding model of a convolutional network code (CNC) is proposed. New necessary and sufficient conditions are established for the decodability of a CNC at a node r with delay L. They only involve the first L+1 terms in the power series expansion of the global encoding kernel matrix at r. Concomitantly, a time-variant decoding algorithm is proposed with a decoding matrix...
Over acyclic networks, it is well known that the global encoding kernels are uniquely determined by the local encoding kernels. But it is not in the case over cyclic networks. To study this problem, we employ matrix power series to describe the encoding kernels. This arrangement not only makes the physical meaning explicitly, but also makes it easy to obtain the conditions of determining the global...
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