Abstract-Consider an arbitrarily connected broadcast network of N nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and broadcasts messages to its neighbors. For the case where nodes must transmit an integer number of packets, this paper provides necessary and sufficient conditions which characterize the set of all transmission schemes that permit universal recovery (in which every node learns all k packets). By relaxing the integer transmission constraint, this paper gives a computable lowerbound on the amount of information required to be broadcast to achieve universal recovery. Furthermore, a network-coding-based scheme (computable in polynomial time) can always achieve this lower bound if packet splitting is permitted. In this way, packet splitting can provide a significant reduction in the amount of communication required for universal recovery. For cliques with N nodes, this paper shows that splitting the packet into N − 1 chunks allows the lower bound to be achieved with high probability.
Abstract-There are numerous notions of symmetry for discrete memoryless channels. A common goal of these various definitions is that the capacity may be easily computed once the channel is declared to be symmetric. In this paper we focus on a class of definitions of symmetry characterized by the invariance of the channel mutual information over a group of permutations of the input distribution. For definitions of symmetry within this class, we give a simple proof of the optimality of the uniform distribution. The fundamental channels are all symmetric with a general enough definition of symmetry. This paper provides a definition of symmetry that covers these fundamental channels along with a proof that is simple enough to find itself on the chalkboard of even the most introductory class in information theory.
Abstract-This paper presents an optimal transmission strategy, with simple encoding and decoding, for the twouser broadcast Z channel. This paper provides an explicitform expression for the capacity region and proves that the optimal surface can be achieved by independent encoding. Specifically, the information messages corresponding to each user are encoded independently and the OR of these two streams is transmitted. Nonlinear turbo codes that provide a controlled distribution of ones and zeros are used to demonstrate a low-complexity scheme that works close to the optimal surface.
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