Random Linear Network Coding for Time-Division Duplexing: Field Size Considerations

Abstract— 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 ...

• Type: Conference
• Year: 2009
• Where: GLOBECOM
• Authors: Daniel Enrique Lucani, Muriel Médard, Milica Stojanovic
• Keywords: GLOBECOM 2009, Linear Network Coding, Random Linear Network, Telecommunications , field Size