A Cross-Layer Perspective on Rateless Coding for Wireless Channels

Abstract—Rateless coding ensures reliability by providing everincreasing redundancy, traditionally at the packet level (i.e. the application layer) through erasure coding. This paper explores whether additional redundancy for wireless channels is most helpful at the packet level through erasure coding or at the physical layer through lower-rate channel coding. This cross-layer trade-off is explored in a traditional wireless setting where the communication of a message consisting of a fixed number of packets takes place over a Rayleigh fading channel. The examined scenarios include both a single receiver and multiple cooperating receivers allowing the results to be extended to situations where selection diversity is available in the system. For several interesting scenarios, this paper determines the optimal trade-off between the amount of packet-level erasure coding and physical-layer channel coding required to provide reliable communication over the widest range of operating SNR’s. Our results indicate that packet-level erasure coding can provide a significant benefit when no other form of diversity is available. In many cases, the amount of redundancy that should be allocated to such erasure coding is nearly constant, and further redundancy (i.e. any rateless coding) should be applied to the physical layer. I

Weighted Universal Recovery, Practical Secrecy, and an Efficient Algorithm for Solving Both

Abstract—In this paper, we consider a network of n nodes, each initially possessing a subset of packets. Each node is permitted to broadcast functions of its own packets and the messages it receives to all other nodes via an error-free channel. We provide an algorithm that efficiently solves the Weighted Universal Recovery Problem and the Secrecy Generation Problem for this network. In the Weighted Universal Recovery Problem, the goal is to design a sequence of transmissions that ultimately permits all nodes to recover all packets initially present in the network. We show how to compute a transmission scheme that is optimal in the sense that the weighted sum of the number of transmissions is minimized. For the Secrecy Generation Problem, the goal is to generate a secret-key among the nodes that cannot be derived by an eavesdropper privy to the transmissions. In particular, we wish to generate a secret-key of maximum size. Further, we discuss private-key generation, which applies to the case where a subset of nodes is compromised by the eavesdropper. For the network under consideration, both of these problems are combinatorial in nature. We demonstrate that each of these problems can be solved efficiently and exactly. Notably, we do not require any terms to grow asymptotically large to obtain our results. This is in sharp contrast to classical information-theoretic problems despite the fact that our problems are informationtheoretic in nature. Finally, the algorithm we describe efficiently solves an Integer Linear Program of a particular form. Due to the general form we consider, it may prove useful beyond these applications. I

On the capacity of network coding for random networks

We study the maximum flow possible between a single-source and multiple terminals in a weighted random graph (modeling a wired network) and a weighted random geometric graph (modeling an ad-hoc wireless network) using network coding. For the weighted random graph model, we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals. Specifically, for a network with a single source, l terminals, and n relay nodes such that the link capacities between any two nodes is independent and identically distributed (i.i.d.) similar to X, the maximum flow between the source and the terminals is approximately nE[X] with high probability. For the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area