Efficient Feedback-Based Scheduling Policies for Chunked Network Codes over Networks with Loss and Delay

The problem of designing efficient feedback-based scheduling policies for chunked codes (CC) over packet networks with delay and loss is considered. For networks with feedback, two scheduling policies, referred to as random push (RP) and local-rarest-first (LRF), already exist. We propose a new scheduling policy, referred to as minimum-distance-first (MDF), based on the expected number of innovative successful packet transmissions at each node of the network prior to the "next" transmission time, given the feedback information from the downstream node(s) about the received packets. Unlike the existing policies, the MDF policy incorporates loss and delay models of the link in the selection process of the chunk to be transmitted. Our simulations show that MDF significantly reduces the expected time required for all the chunks (or equivalently, all the message packets) to be decodable compared to the existing scheduling policies for line networks with feedback. The improvements are particularly profound (up to about 46% for the tested cases) for smaller chunks and larger networks which are of more practical interest. The improvement in the performance of the proposed scheduling policy comes at the cost of more computations, and a slight increase in the amount of feedback. We also propose a low-complexity version of MDF with a rather small loss in the performance, referred to as minimumcurrent-metric-first (MCMF). The MCMF policy is based on the expected number of innovative packet transmissions prior to the "current" transmission time, as opposed to the next transmission time, used in MDF. Our simulations (over line networks) demonstrate that MCMF is always superior to RP and LRF policies, and the superiority becomes more pronounced for smaller chunks and larger networks.Comment: 12 pages, 13 tables; Submitted to IEEE Trans. on Networkin

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