(4,3)-Single Parity Check of Binary Sequence Skew Tent and PWL Map

0. Note

This is the fourth 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 Figure 1 of Shannon Communication Model, the previous assignments on memoryless and Markov’s source is on the first block transmitter (source), while this fourth assignment is on the channel coding and decoding. It will be demonstrated a binary source coded with parity check codes , going through a noisy channel with the specified bit error rate, and decoded on with parity check. On the receiver side will compare the theoretical and practical error using parity check.

Figure 1. Shannon Communication Model

A parity (3,4) check coding takes 3 bits + 1 into 1 block with the last bit as the parity bit obtained by performing exclusive or (xor) on the 3 bits. The blocks are then transmitted and xor is again performed on the decoder side on the 4 bits of the block, and if the result is 0 then it’s not regarded as error, but if the…