In network communication, the source often transmits messages at severaldifferent information rates within a session. How to deal with informationtransmission and network error correction simultaneously under different ratesis introduced in this paper as a variable-rate network error correctionproblem. Apparently, linear network error correction MDS codes are expected tobe used for these different rates. For this purpose, designing a linear networkerror correction MDS code based on the existing results for each informationrate is an efficient solution. In order to solve the problem more efficiently,we present the concept of variable-rate linear network error correction MDScodes, that is, these linear network error correction MDS codes of differentrates have the same local encoding kernel at each internal node. Further, wepropose an approach to construct such a family of variable-rate network MDScodes and give an algorithm for efficient implementation. This approach savesthe storage space for each internal node, and resources and time for thetransmission on networks. Moreover, the performance of our proposed algorithmis analyzed, including the field size, the time complexity, the encodingcomplexity at the source node, and the decoding methods. Finally, a randommethod is introduced for constructing variable-rate network MDS codes and weobtain a lower bound on the success probability of this random method, whichshows that this probability will approach to one as the base field size goes toinfinity.
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