Digital Communication - DMS, DMC, LZ77, LZ78, LZW problem

This should be a fairly easy problem set for digital communication engineer. My budget is >$30. I need it done within 4 days. Please check attachment for more details.

1. Consider a discrete memoryless source (DMS) with alphabet A={a1, a2, a3, a4, a5, a6, a7, a8} and respective probabilities {p1, p2, p3, p4, p5, p6, p7, p8} = {0.2, 0.2, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1}. Construct a Huffman code such that the probabilities are arranged in descending order after each iteration and the newly combined symbol probability is placed (i) as high as possible or (ii) as low as possible, when there are equal probabilities. In each case, determine the average codeword length and the variance of the code word length.

2. A DMS has three output symbols {a1, a2, a3}with probabilities {p1, p2, p3} = {0.5, 0.4, 0.1}.

(i) Determine the Huffman code for this source and find the efficiency η (average codeword/entropy).

(ii) Determine the Huffman code for this source taking two symbols at a time and find the efficiency.

3. Consider a discrete memoryless source with alphabet A={a, b, c} and respective probabilities {pa, pb, pc} = {0.5, 0.25, 0.25}. The codeword of a 4 symbols sequence using Arithmetic code is 0.6015625 (binary .1001001).

(a) Decode the 4 symbols in the sequence.

(b) Determine the range [L,H) to encode the sequence in (a).

4. Consider the binary sequence {101011011010101011}.

(a) Encode the sequence using LZ77 algorithm.

(b) Encode the sequence using LZ78 algorithm.

(c) Encode the sequence using LZW algorithm.

5. Assuming binary source, decode the followings:

(a) Use the LZ77 procedure to decode the following codeword sequence:

(0,0)1, (0,0)0, (2,1)1, (3,1)0, (2,2)1, (8,3)1, (4,1)1

(b) Use the LZ78 procedure to decode the following codeword sequence:

(0,1), (0,0), (1,1), (2,0), (4,1), (2,1), (3,0), (2,-)

(c) Use the LZW procedure to decode the following codeword sequence:

122341387699

6. For the channel shown below, determine H(A), H(B), H(A|B), H(B|A), and I(A,B).

Electrical Engineering

Project ID: #537009

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