Extending the Shannon Upper Bound Using Spiral Modulation

TL;DR

This paper demonstrates that using non-periodic signals based on complex spirals can extend the classical Shannon upper bound on channel capacity, challenging longstanding assumptions in information theory.

Contribution

It introduces a novel approach using spiral modulation to surpass the traditional Shannon upper bound for non-linear channels.

Findings

Non-periodic spiral signals can extend the Shannon upper bound.

Theoretical and constructive evidence supports the extension.

Challenging the assumption that signals must be periodic for capacity limits.

Abstract

The Shannon upper bound places a limit on the error-free information transmission rate (capacity) of a noisy channel. It has stood for over sixty years, and underlies both theoretical and practical work in the telecommunications industry. This upper bound arises from the Shannon-Hartley law, which has two parameters: the available bandwidth and the signal-to-noise power ratio. However, aside from these explicit parameters, the Shannon-Hartley law also rests on certain assumptions. One of these is that the channel is linear: recent work has shown that nonlinear channels are not limited by the Shannon upper bound. A second assumption, arising from the mathematical tools used in its proof, is that signals are periodic. Surprisingly, the capacity limit associated with non-periodic signals has not previously been examined. Here we show, both theoretically and by construction, that the use of non-periodic signals, based on complex spirals, allows the Shannon upper bound to be extended.