CAN309

Information Theory and Data Communications

Assessment 2

Assessment Objective

This assessment aims at evaluating students’ understanding and problem solving skills in Channel Coding, Cryptography, Transceiver Design and Data Communications Networking, which are accumulated during lectures, tutorials and after-class study.

Submission Procedure

Please submit the electronic copy on Learning Mall Online.

Marking Scheme

The specific marks assigned are shown on the right column of each question and sub-question. The assessment of Exercise 3 and Exercise 6 includes MATLAB implementation. Please include your MATLAB code script in the context of the report (NOT as a separate .m file) for Exercise 3. The assessment of Exercise 6 is in the form of a short report. It should include:

a)   A   short  analysis  of  the  questions  and  the   equations   used  in  deriving  your results/codes.

b)   Results and plots (if needed).

c)    Discussion and conclusion.

The assignment covering the 6 Exercises should be submitted as a single report in PDF format and  named as ‘Student ID_GivenName_Surname.pdf’. The designed  MATLAB  codes in  .m format for Exercise 6 should beenclosed together with the report as the separate file(s).

Please compress your report and MATLAB codes as a single .zip file and named as ‘Student ID_GivenName_Surname.zip’ for the submission.

Repetition code achieves error correction by repeating the transmitted information bits r additional times. If the transmitted information is 1 bit and the number of the redundant binary bits r = 6, answer the following questions:

i)    Construct the repetition codeword set. (2 points)

ii)   What is the minimum Hamming distancedmin of the code? (2 points)

iii)  How many errors in a block can the code a) detect, b) correct, and c) detect and correct

at the sametime? (4 points)

iv)  Given a noisy channel with symbol error probability of p, p = 0.01, calculate the bit

error rate (BER) with this repetition code. (7 points)

Consider a public-key Rivest–Shamir–Adleman (RSA) system. Given two prime numbers 43 and 71, derive

i)     A valid public key for the RSA algorithm. (5 points)

ii)    The corresponding private key for the RSA algorithm. (10 points)

For the received pulse pr(t),let pr (0) = 1, pr (T) =  −0.3,  pr (2T) = 0.1,   pr (3T) = −0.07,  pr (4T) = 0.02,  pr (−T) = −0.2,  pr (−2T) = 0.05,  pr (−3T) =   −0.01,

pr (−4T) = 0.005. Design a 5-tap (N=2) Zero-forcing (ZF) equaliserand keep the     calculation accurate to the fourth decimal place. Please provide the matrix inverse calculation procedure with TWO methods:

a) manual calculation with Gauss elimination or determinant method (See Appendix A), and b) with MATLAB.

* Hint: For manual calculation, you may skip some of the calculation steps and keep the key steps in your final answer.

i)    Describe the forms of data units for the 5-layer TCP/IP model. (9 points)

ii)   Given the following IP source and destination addresses (in Hexadecimal format) which are identified in the IP Header (as specified in Appendix B):

IP source address: 81 7E 7B 01

IP destination address: 81 7E 7B 24,

convert the addresses to standard dotted-decimal format. (6 points)

Identify protocols involved in email communication and interpret the procedure.

* Hint: Use block diagrams or flowcharts as necessary for better clarity. (20 points)

The theorems and principles in Channel Coding and Cryptography could be quite mathematical and difficult to comprehend. Using MATLAB to visualize specific theorems, concepts and properties helps to strengthen our understanding on the challenging part   of the knowledge. Please select ONE theorem/concept that was introduced in Channel Coding and Cryptography, and design the MATLAB code to visualize the related formulation/properties.

Note: The MATLAB codes in .m format should be typeset properly and be included together with Assignment 2 (in PDF) as a single compressed document for submission.

Quick Guidance on the Open Ended Question:

The solution should be in the form. of a short report covering the following three sections; the section marks are given below.

Section 1: A description of the theorem or concept with formulation. (5 points)

Section 2: MATLAB codes and Graphs to visualize the theorem/concept. (10 points) Section 3: Detailed comments and discussion. (5 points)

Appendix A: Matrix Inverse Calculation

1.   Gauss elimination method

Let A bean × n matrix, the inverse of A, if it exists, can be computed, by row reduction via the following steps:

Step 1: Then × n identity matrix is augmented to the right of A, forming an × 2n block matrix [A  | I].

Step 2: Through application of elementary row operations, find the reduced echelon form of this n × 2n matrix, [I  | B].

Step 3: There is BA = I, and therefore, B = A −1 which is the inverse matrix of A.

Note: The matrix A is invertible if and only if the left block can be reduced to the identity matrix I; in this case the right block of the final matrix is A−1 .

2.   The determinant method

Given a square matrix A, the inverse of A can be calculated via the following steps:

Step 1:  Find determinant of A, |A|.

If |A| = 0, A−1 does not exist.

If |A| ≠ 0,  one can proceed to find the inverse of the matrix.

Step 2: Replace each element of A by its cofactor.

Step 3: Transpose the result to form. the adjoint matrix, adj(A).

Step 4: The matrix inverse is then given by A−1 = |A|/1 adj(A)