  Random linear network coding (RLNC) in theory achieves the max-flow capacity
of multicast networks, at the cost of high decoding complexity. To improve the
performance-complexity tradeoff, we consider the design of sparse network
codes. A generation-based strategy is employed in which source packets are
grouped into overlapping subsets called generations. RLNC is performed only
amongst packets belonging to the same generation throughout the network so that
sparseness can be maintained. In this paper, generation-based network codes
with low reception overheads and decoding costs are designed for transmitting
of the order of $10^2$-$10^3$ source packets. A low-complexity
overhead-optimized decoder is proposed that exploits "overlaps" between
generations. The sparseness of the codes is exploited through local processing
and multiple rounds of pivoting of the decoding matrix. To demonstrate the
efficacy of our approach, codes comprising a binary precode, random overlapping
generations, and binary RLNC are designed. The results show that our designs
can achieve negligible code overheads at low decoding costs, and outperform
existing network codes that use the generation based strategy.
