Linear Block Codes - Encoding and Decoding Mechanisms - The Bit Error Rate (BER) - MATLAB Assignment Help

Assignment Task:

Task:

Goals:
1. To study the encoding and decoding mechanisms of linear block codes.
2. To study the modulation and demodulation in a communication system.
3. To study the method to simulate the bit error rate (BER) and word error rate (WER) of a communication system with the application of a linear block code.
 

Instructions:
1. Project task 1 requests you to develop simple MATLAB programs to conduct the simulation of a coded communication system using linear block codes by applying and extending the fundamental knowledge on encoding and decoding you learnt from the course.

2. You need to submit a short report with simulation results and all the MATLAB programs. The programs should only invoke MATLAB built-in functions and must not call any additional
MATLAB toolbox.

Project Activity
In this task, each student is expected to implement MATLAB programs to simulate a coded communication system using linear block codes and evaluate their error probability performance in a binary symmetric channel (BSC) resulted from the additive white Gaussian noise (AWGN) channel with a hard output demodulator.

Overview
(1) Linear block codes
The two most common ways to present a linear block code are with either a generator matrix or a parity check matrix. For an (n, k) systematic linear block code with the message bits forming the first k bits of a codeword, the code can be represented by a generator matrix G of the form [I$| P], where I$ is the k × kidentity matrix. The corresponding parity check matrix representation is H = [P*|I+,$]. A t-error syndrome decoding algorithm can recover the transmitted message by correcting up to t bit errors corrupting any bit positions of the transmitted codeword, where t is the error correction capability of this code.

Required tasks
(1) Build a modulator and demodulator for BPSK by writing the MATLAB functions, BPSK_modulator(.) and BPSK_demodulator(.), respectively, stored in the corresponding named .m files. For the demodulator, it produces hard decision output, 0 or 1. The input/output parameters of the aforementioned functions are specified as follows.

x = BPSK_modulator(c) with parameters
c---- A binary digit to denote a transmitted bit
x---- A modulated symbol

r = BPSK_demodulator(y)with parameters
y---- A received symbol
r---- A demodulated bit

(2) Build an uncoded BPSK communication system over the AWGN channel with a hard output demodulator by writing a MATLAB program, named as Uncoded_main.m. In this program, you are required to plot the simulated BER curve of this uncoded system at least covering the BER range
[10,V, 1] and the analytical BER curve given by the aforementioned formula of the channel BER qI should also be plotted for comparison. (Hint: A rule of thumb to ensure the sufficient accuracy of the estimated BER is to gather at least 500 erroneous bits. E.g. simulate at least 5 million bits in order to get an acceptable estimate of BER at 10-4.)

(3) Write a MATLAB function to compute the error correction capability t, named as Capability_check.m. You can find the minimum Hamming weight of the code, and then compute t accordingly. The parameters are

t = Capability_check(G) with parameters
G---- A k × n matrix to denote the generator matrix
t---- A scalar to denote the error correction capability

You should verify its correctness using the example in Lecture note 2.

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