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BOUNDS ON THE BENEFIT OF NETWORK CODING FOR WIRELESS
MULTICAST AND UNICAST
ABSTRACT:
In this paper, we explore fundamental limitations of the benefit of network coding in multihop
wireless networks. We study two well-accepted scenarios in the field: single multicast session
and multiple unicast sessions. We assume arbitrary but fixed topology and traffic patterns for the
wireless network. We prove that the gain of network coding in terms of throughput and energy
saving of a single multicast session is at most a constant factor. Also, we present a lower bound
on the average number of transmissions of multiple unicast sessions under any arbitrary network
coding. We identify scenarios under which network coding provides no gain at all, in the sense
that there exists a simple flow scheme that achieves the same performance.
We prove that the gain of network coding in terms of the maximum transport capacity is
bounded by a constant factor of at most _ in any arbitrary wireless network under all traditional
Gaussian channel models. As a corollary, we find that the gain of network coding on the
throughput of large homogeneous wireless networks is asymptotically bounded by a constant.
Furthermore, we establish theorems which relate a network coding scheme to a simple routing
scheme for multiple unicast sessions. The theorems can be used as criteria for evaluating the
potential gain of network coding in a given wired or wireless network. Based on these criteria,
we find more scenarios where network coding has no gain on throughput or energy saving.