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INT338 — Network-Based Multimedia

Assignment 2

Question 1: What is the distinction between lossy and lossless data compression?

• Lossless Compression: After decompression, it provides an exact copy of the original data (e.g., ZIP files, PNG images).
• Lossy Compression: After decompression, it gives a close approximation of the original data — often perceptually similar but not identical (e.g., MP3 audio, JPEG images).

Question 2: Give one application each suitable for lossy and lossless compression.

• Lossy compression: Streaming services like YouTube use lossy compression to reduce video size while maintaining watchable quality.
• Lossless compression: Archiving important documents or code repositories using ZIP ensures data integrity.

Question 3: Describe the difference between lossless and lossy compression techniques for encoding information and give an example of each in image coding.

• Lossless: Maintains original quality — e.g., PNG uses DEFLATE algorithm.
• Lossy: Removes less noticeable data — e.g., JPEG compresses images by discarding subtle color details.

Question 4: Define the term "run length coding."

• Run Length Encoding (RLE): Compresses data by storing consecutive repeated values as a single value and count (e.g., AAAAABBB → 5A3B).

Question 5: Give the principle of "differential encoding."

• Differential Encoding: Encodes the difference between successive values instead of the values themselves, reducing redundancy (e.g., 5, 7, 9, 10 → 5, +2, +2, +1).

Question 6: Given the following Differential Pulse Code Modulated (DPCM) sequence, reconstruct the original signal:

+4 +2 +3 -2 +3 -1 +1 +1

• Solution: Start with 0 and add each number cumulatively:
  • 4, 6, 9, 7, 10, 9, 10, 11

Question 7: Find the Huffman codeword for the given text "AAAAAAAAAABBBBBCCCSS" using a static Huffman tree. Calculate entropy and derive the average number of bits per character.

• Solution:
  • Frequencies: A (10), B (5), C (3), S (2)
  • Huffman Tree gives codes: A: 0, B: 10, C: 110, S: 111
  • Entropy:( H = - \sum p_i \log_2(p_i) )
  • Average bits per character: Weighted average based on frequencies.

Question 8: Audio encoding at 8 bits/sample, 8000 samples/sec — how many bits per second?

• 8 bits × 8000 samples = 64,000 bits/sec (64 kbps)

Question 9: Video encoding at 1000×1000 pixels, 24 bits/pixel, 30 frames/sec — how many bits per second?

• 1000 × 1000 × 24 × 30 = 720,000,000 bits/sec (720 Mbps)

Question 10: Describe LZW encoding algorithm using "ABABBABCABABBA" as an example.

• LZW (Lempel-Ziv-Welch) builds a dictionary of repeating patterns:
  • A, B, AB, BA, BB, ABC, C, ABBA

Question 11: Describe four basic types of data redundancy for audio, image, and video signals.

1. Temporal: Redundant data over time (e.g., unchanged video frames).
2. Spatial: Correlation between neighboring pixels.
3. Spectral: Exploits color/brightness frequency patterns.
4. Psycho-visual/acoustic: Leverages human perception limits.

Question 12: One example each of lossless and lossy compression techniques:

• Lossless: Huffman Coding
• Lossy: Discrete Cosine Transform (JPEG)

Question 13: Basic approach of entropy coding algorithms. Two examples:

• Steps:
  1. Measure entropy (amount of information).
  2. Sort data into a binary tree.
  3. Traverse tree assigning 0/1 at each branch.
  4. Codes are paths from root to leaves.
• Examples: Shannon-Fano, Huffman Coding

Question 14: Briefly state the Huffman coding algorithm. Encode "AAABDCEFBBAADCDF":

• Steps:
  • Count frequencies, build a tree, assign shorter codes to frequent symbols.
  • Example codes: A: 0, B: 10, D: 110, C: 1110, E: 11110, F: 11111

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