(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 result is 1 then it’s regarded as error. Looking this checking method it can detect errors when odd numbers of bits error occurs, but it cannot detect when even number of error occurs. This can be demonstrated on the following table.

Table 1. Parity Check Examples

2. Skew Tent Map

The binary sequence on the transmitter is generated by means of 2nd assignment of skew tent map with initial x[1] = 0.1 and c = 0.499999. This time we generated in a million blocks with each blocks contains 3 + 1 bits. On the source we generated the initial bits of normal means on assignment 2, but then we slip a parity bit on every 4th increments of the sequence (on the actual code we made 2 sequence where the first sequence as a reference for the sequence…