Coding Delay Analysis of Dense and Chunked Network Codes over Line Networks

In this paper, we analyze the coding delay and the average coding delay of random linear network codes (a.k.a. dense codes) and chunked codes (CC), which are an attractive alternative to dense codes due to their lower complexity, over line networks with Bernoulli losses and deterministic regular or Poisson transmissions. Our results, which include upper bounds on the delay and the average delay, are (i) for dense codes, in some cases more general, and in some other cases tighter, than the existing bounds, and provide a more clear picture of the speed of convergence of dense codes to the (min-cut) capacity of line networks; and (ii) the first of their kind for CC over networks with such probabilistic traffics. In particular, these results demonstrate that a stand-alone CC or a precoded CC provide a better tradeoff between the computational complexity and the convergence speed to the network capacity over the probabilistic traffics compared to arbitrary deterministic traffics which have previously been studied in the literature.Comment: 28 pages, 1 figure, 2 tables; Submitted to IEEE Trans. on Info. Theory. arXiv admin note: substantial text overlap with arXiv:1203.1643, arXiv:1202.034