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Random linear network coding (RLNC) in theory achieves the max-flow capacityof multicast networks, at the cost of high decoding complexity. To improve theperformance-complexity tradeoff, we consider the design of sparse networkcodes. A generation-based strategy is employed in which source packets aregrouped into overlapping subsets called generations. RLNC is performed onlyamongst packets belonging to the same generation throughout the network so thatsparseness can be maintained. In this paper, generation-based network codeswith low reception overheads and decoding costs are designed for transmittingof the order of $10^2$-$10^3$ source packets. A low-complexityoverhead-optimized decoder is proposed that exploits "overlaps" betweengenerations. The sparseness of the codes is exploited through local processingand multiple rounds of pivoting of the decoding matrix. To demonstrate theefficacy of our approach, codes comprising a binary precode, random overlappinggenerations, and binary RLNC are designed. The results show that our designscan achieve negligible code overheads at low decoding costs, and outperformexisting network codes that use the generation based strategy.

On Efficient Decoding and Design of Sparse Random Linear Network Codes