On Efficient Decoding and Design of Sparse Random Linear Network Codes
  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. 
Ye Li, Wai-Yip Chan, Steven D. Blostein
cs.IT math.IT