Introduction to Information Theory

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Questions and Answers

Who is regarded as the father of digital communication?

  • Alan Turing
  • Claude Elwood Shannon (correct)
  • John von Neumann
  • Norbert Wiener

What does Shannon's definition of communication emphasize?

  • The speed of data transmission
  • The emotional impact of messages
  • The meaning conveyed by the messages
  • The technical accuracy of reproduced messages (correct)

What year did Claude Elwood Shannon publish his groundbreaking paper on communication theory?

  • 1968
  • 1938
  • 1948 (correct)
  • 1958

What problem does Shannon aim to address in his communication model?

<p>Reliable transmission of data at maximal rate (B)</p> Signup and view all the answers

In the communication model, what does the 'Encoder' do?

<p>Changes English symbols into a binary sequence (C)</p> Signup and view all the answers

What does the term 'Data Compression' refer to in Shannon’s theory?

<p>Data Encoding (C)</p> Signup and view all the answers

In Shannon’s theory, what is the purpose of adding a CRC?

<p>Error Correction (A)</p> Signup and view all the answers

What does 'CC' stand for in the context of cellular phone communication?

<p>Convolutional Code (C)</p> Signup and view all the answers

Which part of Shannon's original theory deals with the transmission of information through various channels?

<p>Channel Coding Theory (A)</p> Signup and view all the answers

What can be inferred about the measurement of information in Shannon’s theory?

<p>It involves determining expected bits based on probabilistic events. (B)</p> Signup and view all the answers

What does 'Unzip' signify in the context of data processing?

<p>Data Decompression (A)</p> Signup and view all the answers

What is one primary function of the MPEG encoder in the context of video distribution?

<p>Data Encoding (A)</p> Signup and view all the answers

Which coding method is associated with error protection in WLAN IEEE 802.11b?

<p>Convolutional Code (B)</p> Signup and view all the answers

What does the entropy function H(X) represent in probability theory?

<p>The measure of uncertainty or information content (D)</p> Signup and view all the answers

What major impairment is discussed in relation to computer network communications?

<p>Packet Loss (A)</p> Signup and view all the answers

What is the outcome regarding the number of bits needed to store information about a die toss according to Shannon's theorem?

<p>2.585 bits are needed for each outcome (C)</p> Signup and view all the answers

How is the optimal compression ratio calculated based on Shannon's findings compared to the original file size?

<p>By dividing original file size by compressed file size (B)</p> Signup and view all the answers

In the Binary Erasure Channel example, what does 'p' represent?

<p>The packet loss rate (B)</p> Signup and view all the answers

What happens when symbols are erased during transmission?

<p>They are lost during transmission (A)</p> Signup and view all the answers

What did David Huffman contribute to information theory in 1952?

<p>A coding technique that achieves the optimal compression ratio (A)</p> Signup and view all the answers

What is the significance of the number 2.585 in the context of storing outcomes of a die toss?

<p>It represents the base 2 logarithm of 6 outcomes (B)</p> Signup and view all the answers

What method does Alice use to reduce the effects of packet loss in her communication with Bob?

<p>Sending each symbol multiple times (B)</p> Signup and view all the answers

If Alice's original network has a packet loss rate of p=0.25 and she repeats each symbol four times, what is the new packet loss rate?

<p>0.00390625 (A)</p> Signup and view all the answers

What represents the difference between Shannon's compressed file size and traditional ASCII representation for storing die outcomes?

<p>Shannon's size is significantly smaller than ASCII size (C)</p> Signup and view all the answers

What is the maximum data transmission rate Alice can achieve after using repetition?

<p>2 Mbps (D)</p> Signup and view all the answers

What percentage corresponds to the optimal compression ratio reported by Shannon?

<p>32.31% (C)</p> Signup and view all the answers

In what applications are Huffman codes commonly used?

<p>In various digital data compression and transmission contexts (D)</p> Signup and view all the answers

According to Shannon’s Channel Coding Theorem, what can be computed for a given channel?

<p>The channel capacity, C (A)</p> Signup and view all the answers

What is the channel capacity calculated in the example where Alice sends data at a rate of 8 Mbps with a packet loss rate of p=0.25?

<p>0.75 Mbps (A)</p> Signup and view all the answers

What is the formula for channel capacity in terms of Signal to Noise Ratio?

<p>$C = B imes log_2 (S/N)$ (C)</p> Signup and view all the answers

Which of the following coding techniques is NOT mentioned as a known code developed over 50 years?

<p>Quantum Codes (D)</p> Signup and view all the answers

In what year did the Mariner 4 mission communicate with a data rate of 8.33 bps?

<p>1965 (B)</p> Signup and view all the answers

Which compression technique was used by the Mars Reconnaissance Orbiter for lossless data?

<p>FELICS Compression (D)</p> Signup and view all the answers

How many bps was the data rate for the Mars Exploration Rovers in 2004?

<p>168 bps (D)</p> Signup and view all the answers

Which application has NOT utilized Shannon Theory?

<p>Nutrition Science (C)</p> Signup and view all the answers

Which of the following statements about the Source Coding Theorem is true?

<p>It is used in MPEG compression. (C)</p> Signup and view all the answers

What was the frequency used by Mars Exploration Rovers in 2004?

<p>8.4 GHz (C)</p> Signup and view all the answers

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Study Notes

Introduction to Information Theory

  • Claude Elwood Shannon published “A Mathematical Theory of Communication” in 1948, establishing the foundation for digital communication.
  • A digital communication system consists of integral components: Source, Encoder, Communication Channel, Decoder, and Destination.

Shannon’s Definition of Communication

  • Communication’s fundamental problem is accurately reproducing a selected message at a different point, focusing on the engineering aspects rather than semantic meaning.

Shannon's Objectives

  • Shannon aimed to develop methods for reliably transmitting data over communication channels at maximal rates, leading to the emergence of Information Theory.

Information Theory Key Concepts

  • Information measurement is defined using bits; Shannon introduced the entropy function: H(X) = −Σ p(x) log₂ p(x).
  • Entropy quantifies the level of uncertainty or information content in a random variable.

Source Coding and Compression

  • Shannon’s First Source Coding Theorem indicates that, on average, H(X) bits are required for storing each outcome from a random source.
  • For example, tossing a die results in an entropy of approximately 2.585 bits per outcome, enabling optimal compression strategies.

Compression Techniques

  • Huffman coding, developed by David Huffman in 1952, provides systematic methods for achieving optimal compression ratios and is widely used in digital data transmission.

Communication Challenges

  • Packet loss in network communications can be modeled as erasures, complicating data recovery.
  • The Binary Erasure Channel represents loss where symbols may become unreadable.

Shannon’s Channel Coding Theorem

  • Reliable communication is possible only if the data rate is below a calculated channel capacity C, which considers factors like signal loss.

Channel Capacity Formula

  • The channel capacity can be expressed as C = B log₂(S/N), where B is bandwidth and S/N is the signal-to-noise ratio.

Advances in Coding Techniques

  • Over the decades, numerous coding methods have been developed, including Hamming codes, Convolutional codes, Reed-Solomon codes, Turbo codes, and others, enhancing communication reliability.

Applications of Shannon Theory

  • Information Theory principles apply broadly across JPEG 2000, MPEG compression, wireless communications, and optical communication.
  • In space communication, advancements illustrate the application of Shannon's theories, with progressively increasing data transmission rates and compression methods.

Broader Implications of Information Theory

  • The principles of Information Theory extend into various fields, including economics, game theory, cryptography, quantum physics, biology, and genetics, underscoring its interdisciplinary significance.

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