Weighted generalizations of Hoffman’s ratio bound on the independence number of a regular graph are surveyed. Several known bounds are reviewed as special cases of modest extensions. Comparisons are made with the Shannon capacity Θ, Lovász’ parameter θ, Schrijver’s parameter θ, and the ultimate independence ratio for categorical products. The survey concludes with some observations on graphs th...

A fundamental problem in wireless networks is to develop communication protocols that achieve high throughput in the face of noise, interference, and fading, all of which vary with time. An ideal solution is a rateless wireless system, in which the sender encodes data without any explicit estimation or adaptation, implicitly adapting to the level of noise or interference. In this paper, we pres...

In this paper, we analytically investigate Gallager’s exponent for space-time block codes over multiple-input multipleoutput block-fading channels with Gaussian input distribution. As a suitable metric of the fundamental tradeoff between communication reliability and information rate, Gallager’s exponent can be used to determine the required codeword length to achieve a prescribed error probabi...

We show that the Gaussian multiple-access channel and the Gaussian broadcast channel are fundamentally related and are essentially duals of each other. The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of a broadcast channel (both constant and fading) can be written in terms of the capacity region of the dual mu...

In this paper, we study the limitations imposed by the laws of electromagnetism on achievable MIMO channel capacity in its general form. Our approach is a two-fold one. First, we use the channel correlation argument to demonstrate that the minimum antenna spacing under any scattering conditions is at least half a wavelength. Secondly, using a plane-wave spectrum expansion of a generic electroma...

We define classical–quantum multiway channels for transmission of classical information, after recent work by Allahverdyan and Saakian. Bounds on the capacity region are derived in a uniform way, which are analogous to the classically known ones, simply replacing Shannon entropy with von Neumann entropy. For the single receiver case (multiple access channel) the exact capacity region is determi...

In this exposition we prove an existence theorem for a quantum mechanical dynamical entropy based on von-Neumann’s measurement theory. To that end we introduced a Shannon type of information associated with a quantum channel or measurement based on Araki’s relative entropy. This is an invariance for the dynamics which generalizes Kolmogorov-Sinai ’s notion of dynamical entropy of a measure pres...

This paper concerns the capacity of the discrete noiseless channel introduced by Shannon. A sufficient condition is given for the capacity to be well-defined. For a general discrete noiseless channel allowing non-integer valued symbol weights, it is shown that the capacity—if well-defined—can be determined from the radius of convergence of its generating function, from the smallest positive pol...

The quantum capacity of thermal noise channel (which is addressed as Gaussian quantum channel before) is studied, it turns out to be the maximum of the coherent information of a single use of the channel. The quantum capacity is achieved when the input state is a thermal noise state with infinitive energy. The capacity is achievable with quantum error-correction code. The quantum capacities of ...

Recently the author introduced a semidefinite upper bound on the square of the stability number of a graph, the inverse theta number, which is proved here to be multiplicative with respect to the strong graph product, hence to be an upper bound for the square of the Shannon capacity of the graph. We also describe a heuristic algorithm for the stable set problem based on semidefinite programming...