FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Random linear network coding for time division duplexing: energy analysis
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
IEEE Transactions on Information Theory
A Random Linear Network Coding Approach to Multicast
IEEE Transactions on Information Theory
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We study the effect of the field size on the performance of random linear network coding for time division duplexing channels proposed in [1]. In particular, we study the case of a node broadcasting to several receivers. We show that the effect of the field size can be included in the transition probabilities of the Markov chain model of the system. Also, an improved upper bound on the mean number of coded packets required to decode M original data packets using random linear network coding is presented. This bound shows that even if the field size is 2, i.e. we perform XORs amongst randomly selected packets from the pool of M original ones, we will need on average at most M + 2 coded packets in order to decode. Thus, there will be only a very small degradation in performance if M is large. We present numerical results showing that the mean completion time of our scheme with a field size of 2 is close in performance to our scheme when we use larger field sizes. We also show that as M increases, the difference between using a field size of 2 and larger field sizes decreases. Finally, we show that we can get very close to the optimal performance with small field sizes, e.g. a field size of 4 or 8, even when M is not very large.