22 research outputs found
Representations of the Multicast Network Problem
We approach the problem of linear network coding for multicast networks from
different perspectives. We introduce the notion of the coding points of a
network, which are edges of the network where messages combine and coding
occurs. We give an integer linear program that leads to choices of paths
through the network that minimize the number of coding points. We introduce the
code graph of a network, a simplified directed graph that maintains the
information essential to understanding the coding properties of the network.
One of the main problems in network coding is to understand when the capacity
of a multicast network is achieved with linear network coding over a finite
field of size q. We explain how this problem can be interpreted in terms of
rational points on certain algebraic varieties.Comment: 24 pages, 19 figure
Network coding as a coloring problem (Invited paper)
We consider a multicast configuration with two sources, and translate the network code design problem to vertex coloring of an appropriately defined graph. This observation enables to derive code design algorithms and alphabet size bounds, as well as establish a connection with a number of well-known results from discrete mathematics that increase our insight in the different trade-offs possible for network coding
Spinal codes
Spinal codes are a new class of rateless codes that enable wireless networks to cope with time-varying channel conditions in a natural way, without requiring any explicit bit rate selection. The key idea in the code is the sequential application of a pseudo-random hash function to the message bits to produce a sequence of coded symbols for transmission. This encoding ensures that two input messages that differ in even one bit lead to very different coded sequences after the point at which they differ, providing good resilience to noise and bit errors. To decode spinal codes, this paper develops an approximate maximum-likelihood decoder, called the bubble decoder, which runs in time polynomial in the message size and achieves the Shannon capacity over both additive white Gaussian noise (AWGN) and binary symmetric channel (BSC) models. Experimental results obtained from a software implementation of a linear-time decoder show that spinal codes achieve higher throughput than fixed-rate LDPC codes, rateless Raptor codes, and the layered rateless coding approach of Strider, across a range of channel conditions and message sizes. An early hardware prototype that can decode at 10 Mbits/s in FPGA demonstrates that spinal codes are a practical construction.Massachusetts Institute of Technology (Irwin and Joan Jacobs Presidential Fellowship)Massachusetts Institute of Technology (Claude E. Shannon Assistantship)Intel Corporation (Intel Fellowship
Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy
We develop information-theoretic measures of spatial structure and pattern in
more than one dimension. As is well known, the entropy density of a
two-dimensional configuration can be efficiently and accurately estimated via a
converging sequence of conditional entropies. We show that the manner in which
these conditional entropies converge to their asymptotic value serves as a
measure of global correlation and structure for spatial systems in any
dimension. We compare and contrast entropy-convergence with mutual-information
and structure-factor techniques for quantifying and detecting spatial
structure.Comment: 11 pages, 5 figures,
http://www.santafe.edu/projects/CompMech/papers/2dnnn.htm
On achievable information rates in single-source non-uniform demand networks
A non-uniform demand network consists of a source and a set of receivers that have different min-cut values from the source. We look at the case where the receivers would like to receive from the source a rate that is (approximately) equal to their min-cut value. We formulate this problem and its relaxations and present preliminary results