Walsh Sampling with Incomplete Noisy Signals

TL;DR

This paper introduces a novel sampling method for incomplete noisy signals based on Walsh coefficients and Shannon's channel coding theorem, with applications in cryptanalysis and system optimization.

Contribution

It establishes the first necessary and sufficient conditions for sampling incomplete noisy signals using Walsh coefficients and Shannon's theorem.

Findings

Walsh coefficients characterize discrete statistical signals.

Necessary and sufficient sampling conditions are derived.

Applications include cryptanalysis and system performance optimization.

Abstract

With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources as well. Under the general assumption of discrete statistical signal sources, we propose a practical problem of sampling incomplete noisy signals for which we do not know a priori and the sampling size is bounded. We approach this sampling problem by Shannon's channel coding theorem. Our main results demonstrate that it is the large Walsh coefficient(s) that characterize(s) discrete statistical signals, regardless of the signal sources. By the connection of Shannon's theorem, we establish the necessary and sufficient condition for our generic sampling problem for the first time. Our generic sampling results find practical and powerful applications in not only statistical cryptanalysis, but software system performance optimization.