  A key problem in random network coding (NC) lies in the complexity and energy
consumption associated with the packet decoding processes, which hinder its
application in mobile environments. Controlling and hence limiting such factors
has always been an important but elusive research goal, since the packet degree
distribution, which is the main factor driving the complexity, is altered in a
non-deterministic way by the random recombinations at the network nodes. In
this paper we tackle this problem proposing Band Codes (BC), a novel class of
network codes specifically designed to preserve the packet degree distribution
during packet encoding, ecombination and decoding. BC are random codes over
GF(2) that exhibit low decoding complexity, feature limited and controlled
degree distribution by construction, and hence allow to effectively apply NC
even in energy-constrained scenarios. In particular, in this paper we motivate
and describe our new design and provide a thorough analysis of its performance.
We provide numerical simulations of the performance of BC in order to validate
the analysis and assess the overhead of BC with respect to a onventional NC
scheme. Moreover, peer-to-peer media streaming experiments with a random-push
protocol show that BC reduce the decoding complexity by a factor of two, to a
point where NC-based mobile streaming to mobile devices becomes practically
feasible.
