Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Average Throughput with Linear Network Coding over Finite Fields: The Combination Network Case | Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2008 Article ID 329727 7 pages doi 2008 329727 Research Article Average Throughput with Linear Network Coding over Finite Fields The Combination Network Case Ali Al-Bashabsheh and Abbas Yongacoglu School of Information Technology and Engineering University of Ottawa Ottawa Canada K1N 6N5 Correspondence should be addressed to Ali Al-Bashabsheh aalba059@ Received 4 November 2007 Revised 17 March 2008 Accepted 27 March 2008 Recommended by Andrej Stefanov We characterize the average linear network coding throughput Tavg for the combination network with min-cut 2 over an arbitrary finite field. We also provide a network code completely specified by the field size achieving Tfvs for the combination network. Copyright 2008 A. Al-Bashabsheh and A. Yongacoglu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION For a set of sinks in a directed multicast network it was shown in 1 that if the network can achieve a certain throughput to each sink individually then it can achieve the same throughput to all sinks simultaneously by allowing coding at intermediate nodes. Such argument is possible since information is an abstract entity rather than a physical one. Thus in addition to repetition and forwarding nodes can manipulate the symbols available from their in-edges and apply functions of such symbols to their out-edges. The collection of edge functions can be referred to as the network code. The work in 1 shows that a natural bound on the achievable coding rate is the least of the min-cuts between the source and each of the sinks. We refer to a code achieving the min-cut rate as a solution. It is known that every multicast network has a linear solution over a sufficiently large finite .
