Edge-Cut Bounds on Network Coding Rates

Network Coding Bounds 17.1 Network Coding 17.1.1 Upper Bound

Start with a directed acyclic graph (DAG) with a single sender and many receivers, where each receiver has k-edge connectivity from the sender. We assume that each edge has unit capacity, say, 1 bit/second. If our initial DAG does not meet this criterion, we can easily construct one that does: first, divide edge capacities by their greatest common divisor, then replace each c-capacity edge with...

Bounds on rates of variable-basis and neural-network approximation

Tightness of bounds on rates of approximation by feedforward neural networks is investigated in a more general context of nonlinear approximation by variable-basis functions. Tight bounds on the worst case error in approximation by linear combinations of elements of an orthonormal variable basis are derived.

Edge-Enhanced Image Coding for Low Bit Rates

Many current progressive wavelet-based image coders attempt to achieve the greatest reduction in mean squared error (MSE) with each bit sent. In so doing, they tend to send information on the lowest-frequency wavelet coefficients first. At very low bit rates, images compressed by these coders are therefore dominated by low frequency information and blotchy artifacts. These effects combine to ha...

Upper bounds on oarsening rates

Upper bounds on mixing rates

We prove upper bounds on the rate, called ”mixing rate”, at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under nonlocal unitary evolution. For an ensemble consisting of two states, with probabilities of p and 1 − p, we prove that the mixing rate is bounded above by 4 √ p(1− p) for any Hamiltonian of norm 1. For a general ensemble of states...