Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions

Abstract

The statistical properties of chaotic binary sequences generated by the Bernoulli map and Walsh functions are discussed. The Walsh functions are based on a 2 k × 2 k Hadamard matrix. For general k (= 1 , 2 , ⋯ ), we will prove that 2 k - 1 Walsh functions can generate essentially different balanced and i.i.d. binary sequences that are orthogonal to each other.

Keywords

• Bernoulli map
• orthogonal sequence
• Walsh functions
• chaotic binary sequence
• correlation property
• i.i.d.