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###### 日期：2019-12-15 10:32

MSc in Communications Systems and Signal Processing

(2019-2020)

Communication Systems M (EENGM2100) - Information theory coursework

Instructor: Robert Piechocki, TA: Ioannis Papoutsidakis

1. A ternary memoryless channel is discribed by the following probability transition matrix,

where Y in rows denotes the output, and X in columns denotes the input.

(a) What is the capacity of this channel?

(b) Assume that a series of N such channels are concatenated (so that output of n channel

becomes input to n + 1). What is the capacity for N = 3, 5, 10.

2. Arithmetic coding is an optimal technique for lossless source coding that is used in several

modern applications. Use MATLAB code and the build-in function arithenco to encode

the string of a thousand bytes found in source.mat (available on Blackboard).

(a) What are the empirical marginal probabilities of the symbols?

(b) What is the compression rate you expect and why?

(c) Construct the Huffman code for this source, which encodes one symbol at a time.

What compression rate is achieved?

(d) What compression rate is achieved by the arithmetic coding? Compare it with the

Huffman code and the fundamental limit. Is the limit achieved by any of the two

techniques? If not, give your explanation why.

Submission via blackboard (pdf), deadline Wednesday 18th December, 17:00.

Making scheme

Total for this coursework is 40 marks (Q1: 20 marks; Q2: 20 marks). Submit your Matlab

codes (1 ”M file” for each question) along with a technical note with your answers and

commentary.