Questions and Answers
Match the following concepts with their definitions in Shannon's Information Theory:
Entropy = Measure of information in bits Source Coding Theorem = Average bits needed for storing outcomes Channel Coding Theory = Method for reliable transmission over a channel Measurement of Information = Determining how to quantify data
Match the following file sizes with their respective compression ratios:
Original File Size = 8,000,000 bits Shannon Compression = 32.31% Winzip Compression = 36.63% WinRAR Compression = 35.74%
Match the following probabilities with the corresponding outcomes of tossing a die:
Outcome 1 = 1/6 probability Outcome 2 = 1/6 probability Outcome 3 = 1/6 probability Outcome 4 = 1/6 probability
Match the following compression sizes with the corresponding file types:
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Match the following statements with their significance in information storage:
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Study Notes
Introduction to Information Theory
- Information Theory was introduced by Claude Shannon in 1948.
- It encompasses the measurement of information, source coding theory, and channel coding theory.
Measurement of Information
- Shannon aimed to quantify information in bits.
- All events are probabilistic; information measurement relies on probability theory.
- The entropy function is established as the standard metric for measuring information in bits.
Example: Tossing a Dice
- Possible outcomes when tossing a dice: 1, 2, 3, 4, 5, 6.
- Each outcome has an equal probability of 1/6.
- The information from a single dice toss is quantified as approximately 2.585 bits, noted for being non-integer.
Shannon’s First Source Coding Theorem
- Shannon asserts that to reliably store information from a random source (X), the average required storage is H(X) bits per outcome.
- For example, tossing a dice 1,000,000 times, 3 bits are sufficient to represent outcomes (1-6), needing 3,000,000 bits in total.
- Using ASCII representation, each outcome requires 8 bits (1 byte), resulting in an 8,000,000 bits file size.
Compression Insight
- Shannon proposes that only 2.585 bits are needed for each outcome, leading to a total of 2,585,000 bits for a million tosses.
- This illustrates significant compression potential compared to naive storage methods.
Optimal Compression Ratio
- Initial file size without compression: 8,000,000 bits (100%).
- Shannon’s theoretical compression: 2,585,000 bits (32.31% of original).
- Comparisons with other compression tools show:
- Winzip: 2,930,736 bits (36.63%).
- WinRAR: 2,859,336 bits (35.74%).
- Shannon’s predictions remain validated decades later, asserting his foundational role in the field of information theory.
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Description
Explore the foundational concepts of Information Theory as proposed by Shannon in 1948. This quiz covers measurement of information, source coding, and channel coding, helping you understand how to quantify and manage information using bits. Test your knowledge on the key principles that shape modern communications.
