Markov Information Binary Sequences Based on Piecewise Linear Chaotic Maps

0. Note

This is the third assignment from my Masters Applied Digital Information Theory Course which has never been published anywhere and I, as the author and copyright holder, license this assignment customized CC-BY-SA where anyone can share, copy, republish, and sell on condition to state my name as the author and notify that the original and open version available here.

1. Introduction

On the first assignment we produced a chaotic sequence based skew tent map by showing that output sequence is uncontrollable as on the chaos theory. A large sequence produced by skew tent map is uniformly distributed. On the second assignment we produce a memoryless binary sequence based on the first assignment’s skew tent map based chaotic sequence. The probability of 0, 1, 00, 01, 10, 11, and the Markov chain is analyze. Finally the entropy is calculated based on the critical points of each data and find the correlation between the entropy and expected compression ratio. This time the same method on assignment 2 is used but change the assignment 1 of not using skew tent map but piecewise linear map.

2. Piecewise Linear Chaotic Map