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

• Type: Article in International Conference Proceedings Book
• Date: 2009

Authors

Daniel E. Lucani (Author) FEUP; Muriel Medard (Author) FEUP; Milica Stojanovic (Author) FEUP

Conference proceedings International

Title: IEEE Global Communications Conference (GLOBECOM) 2009

Pages: 1-6

Honolulu, Hawaii, USA, 30 Novembro de 2009 a 4 Dezembro de 2009

Scientific classification

FOS: Engineering and technology > Electrical engineering, Electronic engineering, Information engineering

Other information

Resumo (PT): 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.

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific