Alignment based Network Coding for Two-Unicast-Z Networks

In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side information of the first message. We make three contributions in this paper: 1. We describe a new linear network coding algorithm for two-unicast-Z networks over directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For graphs of a bounded degree, our algorithm has linear complexity in terms of the number of vertices, and polynomial complexity in terms of the number of edges. 2. We prove that our algorithm achieves the rate-pair (1, 1) whenever it is feasible in the network. Our proof serves as an alternative, albeit restricted to two-unicast-Z networks over directed acyclic graphs, to an earlier result of Wang et al. which studied necessary and sufficient conditions for feasibility of the rate pair (1, 1) in two-unicast networks. 3. We provide a new proof of the classical max-flow min-cut theorem for directed acyclic graphs.Comment: The paper is an extended version of our earlier paper at ITW 201

Effects of the Generation Size and Overlap on Throughput and Complexity in Randomized Linear Network Coding

To reduce computational complexity and delay in randomized network coded content distribution, and for some other practical reasons, coding is not performed simultaneously over all content blocks, but over much smaller, possibly overlapping subsets of these blocks, known as generations. A penalty of this strategy is throughput reduction. To analyze the throughput loss, we model coding over generations with random generation scheduling as a coupon collector's brotherhood problem. This model enables us to derive the expected number of coded packets needed for successful decoding of the entire content as well as the probability of decoding failure (the latter only when generations do not overlap) and further, to quantify the tradeoff between computational complexity and throughput. Interestingly, with a moderate increase in the generation size, throughput quickly approaches link capacity. Overlaps between generations can further improve throughput substantially for relatively small generation sizes.Comment: To appear in IEEE Transactions on Information Theory Special Issue: Facets of Coding Theory: From Algorithms to Networks, Feb 201

Recursive partitioning multicast: a bandwidth-efficient routing for networks-on-chip

Chip Multi-processor (CMP) architectures have become mainstream for designing processors. With a large number of cores, Networks-on-Chip (NOCs) provide a scalable communication method for CMP architectures. NOCs must be carefully designed to meet constraints of power consumption and area, and provide ultra low latencies. Existing NOCs mostly use Dimension Order Routing (DOR) to determine the route taken by a packet in unicast traffic. However, with the development of diverse applications in CMPs, one-to-many (multicast) and one-to-all (broadcast) traffic are becoming more common. Current unicast routing cannot support multicast and broadcast traffic efficiently. In this paper, we propose Recursive Partitioning Multicast (RPM) routing and a detailed multicast wormhole router design for NOCs. RPM allows routers to select intermediate replication nodes based on the global distribution of destination nodes. This provides more path diversities, thus achieves more bandwidth-efficiency and finally improves the performance of the whole network. Our simulation results using a detailed cycle-accurate simulator show that compared with the most recent multicast scheme, RPM saves 25 % of crossbar and link power, and 33 % of link utilization with 50 % network performance improvement. Also RPM is more scalable to large networks than the recently proposed VCTM. 1