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Understanding Data Compression and Error Detection: Lecture Summary and Homework

This lecture covers critical concepts in data compression and error detection. We delve into Huffman coding, a method to optimize the representation of data through variable-length codewords based on frequency of occurrence. The discussion includes error detection methods like parity bits, essential for ensuring data integrity during transmission. Relevant homework assignments include problems from the text focusing on these topics. Students are required to explore sections that cover theory, application, and real-world scenarios in data compression and error codes.

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Understanding Data Compression and Error Detection: Lecture Summary and Homework

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  1. Todays Lecture (Feb 15, 2000) • Reading and Homework Assignments • Summary of Last Lecture • Start Computers • Data Compression • Huffman Code • More on Encryption

  2. H/W and Reading • Homework Assignment #1 • Problems 7.1, 7.2, 7.3, 7.7 • Due Thursday Feb 17th • Text Sections to Date • Chapter 1 • Section 2.5 (part about UPC scanner) • Sections 7.1, 7.2, 7.3, 7.7, 7.12 • Text Sections for today’s lecture • Section 7.9, 7,10

  3. Current Events

  4. Summary of Last Lecture • Redundancy can be introduced in a code to detect inevitable bit errors which may result from imperfect communication or sensor scan. This is called error detection and correction coding. • Bit errors can be detected and/or corrected by: • Bit repetition • Parity • All schemes presented work ONLY if one bit is in error

  5. Even and Odd Parity • There are two type of parity • Even • Parity bit is 1 if an odd number of ones are present in the original codeword • Odd • Parity bit is 0 if an odd number of ones are present in the original codeword • Note in example 7.4 of text, “odd” parity is used on the columns

  6. Two Types of Codes • Variable Length • Codewords are a variable number of bits • Fixed length • Codewords are a fixed number of bits • The UPC and ASCII codes are examples of fixed length codes

  7. Huffman Coding • Goal: Develop a code to reduce the total number of bits required to encode information. This is called Compression • Idea: Assign most frequently occurring symbols short codewords and less frequently occurring symbols long codewords

  8. Tree Structure Root (Starting Point) Branches Node Leaves

  9. Huffman Code Tree Example 1 0 1 0 A (1) 1 0 B (01) C (001) D (000) • Symbols are leaves of the tree • Codeword is identified by starting at root and branching to leaf

  10. Huffman Encoding Example • Consider the Symbol Sequence AABAD • Problem: Encode the Symbol Sequence using the Huffman Code just presented

  11. Solution A 1 B 01 C 001 D 000 Huffman Code Encode AABAD 11011000 Thus, AABAD is represented by 8 bits

  12. Compare to Fixed Length Code A 00 B 01 C 10 D 11 Code Encode AABAD 0000010011 Thus, AABAD is represented by 10 bits

  13. Huffman Decoding Example

  14. Real World Histograms • Figure 7.19 in Text

  15. Do Problem 7.19

  16. Do Problem 7.20

  17. Data Compression • Lossless Compression • Techniques retain all the information present in the original data • Example: Huffman encoding, run-length encoding • Lossy Compression • techniques allow some loss of the original data • Example: MPEG video compression

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