Consider a lossy communication channel for unicast with zero-delay feedback. For this communication scenario, a simple retransmission scheme is optimum with respect to delay. An alternative approach is to use random linear coding in automatic repeat-request (ARQ) mode. We extend the work of Shrader and Ephremides in [1], by deriving an expression for the delay of random linear coding over a field of infinite size. Simulation results for various field sizes are also provided.
Random linear coding @cite_11 is known to work particularly well in the multicast case @cite_8 , and multicast problems similar to the ones we discuss here are investigated in @cite_5 @cite_10 .
@cite_8 @cite_5 @cite_10 @cite_11
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We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code length. We also demonstrate that random linear coding performs compression when necessary in a network, generalizing error exponents for linear Slepian-Wolf coding in a natural way. Benefits of this approach are decentralized operation and robustness to network changes or link failures. We show that this approach can take advantage of redundant network capacity for improved success probability and robustness. We illustrate some potential advantages of random linear network coding over routing in two examples of practical scenarios: distributed network operation and networks with dynamically varying connections. Our derivation of these results also yields a new bound on required field size for centralized network coding on general multicast networks In this work we address the stability and delay performance of a multicast erasure channel with random arrivals at the source node. We consider both a standard retransmission (ARQ) scheme as well as random linear coding. Our results show that while random linear coding may outperform re-transmissions for heavy traffic, the delay incurred by the use of random linear codes is significantly higher when the source is lightly loaded Network coding shows that the data rate can be increased if information is allowed to be encoded in the network nodes. The recent work of S.-Y.R. (see IEEE Trans. Inform. Theory, vol.49, no.2, p.371-81, 2003) and R. Koetter and M. Medard (see Proc. INFOCOM, 2002) shows that linear network coding is sufficient for a single source multicast network. The restrictiveness of the use of linear code is still an unknown in the general multisource multicast network. We characterize the achievable information rate region for a single source node multi-source multicast network with two sinks. We further show that linear coding is sufficient for achieving the maximum network capacity. For a network with one sender, n receivers (users) and m possible messages (files), caching side information at the users allows to satisfy arbitrary simultaneous demands by sending a common (multicast) coded message. In the worst-case demand setting, explicit deterministic and random caching strategies and explicit linear coding schemes have been shown to be order optimal. In this work, we consider the same scenario where the user demands are random i.i.d., according to a Zipf popularity distribution. In this case, we pose the problem in terms of the minimum average number of equivalent message transmissions. We present a novel decentralized random caching placement and a coded delivery scheme which are shown to achieve order-optimal performance. As a matter of fact, this is the first order-optimal result for the caching and coded multicasting problem in the case of random demands.