Coding Theory Overview

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Questions and Answers

What is the primary purpose of the Viterbi algorithm?

To minimize Hamming distance in signal transmission

To encode data for TCM

To estimate the most likely sequence of hidden states (correct)

To generate random sequences in communication systems

Which of the following technologies has NOT commonly used the Viterbi algorithm?

Speech recognition and synthesis

Wi-Fi 802.11 wireless LAN

CDMA and GSM digital cellular

Optical fiber communication (correct)

When decoding TCM code, what is the first step in the Viterbi decoding process?

Draw the trellis diagram for the code

Write the path for the received code

Determine the Hamming Distance for every state transition (correct)

Assign probabilities to each state

Who proposed the Viterbi algorithm?

Andrew J. Viterbi Signup and view all the answers

Which of the following best describes a trellis diagram?

A visual representation of the decoding process for linear codes Signup and view all the answers

What is the primary purpose of using encryption and decryption in cryptography?

To ensure confidentiality of information Signup and view all the answers

Which of the following concepts ensures that data has not been tampered with or corrupted?

Data Integrity Signup and view all the answers

What does non-repudiation in cryptography imply?

The sender cannot deny sending the message Signup and view all the answers

In the context of GSM security management, what does the term 'Kc' refer to?

Cipher key used for encryption Signup and view all the answers

Which of the following statements best describes 'secret sharing' in cryptography?

Utilizing multiple keys to access a single piece of information Signup and view all the answers

What is the average bits per symbol for the string 'ISAT!'?

4 bits/symbol Signup and view all the answers

In arithmetic coding, what must each code word include to signify the end of transmission?

An end-of-message marker Signup and view all the answers

What does entropy encoding refer to in data compression?

Lossless encoding schemes Signup and view all the answers

What type of information does the code '10000111100110110001' represent in decimal?

0.52970981597900390625 Signup and view all the answers

Which of the following symbols has the highest assumed probability in the given probability table?

I Signup and view all the answers

What mathematical structure is utilized in trellis coding?

Lattices Signup and view all the answers

What does the term 'end of file' (EOF) signify in data transmission?

The end of data transmission Signup and view all the answers

Which of the following steps is NOT part of arithmetic encoding?

Compressing data into fixed-length strings Signup and view all the answers

What is the primary purpose of the Huffman code?

To create a minimum-length lossless data-compression code Signup and view all the answers

How is the average bits per symbol calculated in Huffman coding for the example given?

By dividing total bits by total symbols Signup and view all the answers

Which of the following describes a key difference between Huffman coding and arithmetic coding?

Huffman coding encodes only one symbol at a time Signup and view all the answers

In the provided text string example, what is the total number of symbols used?

46 Signup and view all the answers

What is Hartley’s Equation used for in the context of data compression?

To calculate entropy based on the number of symbols Signup and view all the answers

What is the range of the number 'q' in arithmetic coding?

0 ≤ q < 1.0 Signup and view all the answers

What is the calculated average bits per symbol from the Huffman tree example?

2.5 bits Signup and view all the answers

What is a characteristic of lossless data compression methods such as Huffman coding?

The original data can be perfectly reconstructed from the compressed data Signup and view all the answers

What is the main purpose of encryption?

To convert data into a code for protection Signup and view all the answers

Which of the following is a symmetric encryption algorithm?

AES Signup and view all the answers

What characterizes symmetric encryption?

The same key is used for both encryption and decryption Signup and view all the answers

Which algorithm is known for its public-key cryptography?

RSA Signup and view all the answers

What is considered a disadvantage of the Data Encryption Standard (DES)?

Its key length of 56 bits is too insecure Signup and view all the answers

What term describes the encrypted message in symmetric encryption?

Ciphertext Signup and view all the answers

How are public and private keys related in asymmetric encryption?

They are mathematically related but not interchangeable Signup and view all the answers

Which of the following options best describes asymmetric encryption?

Utilizes a pair of keys for the encryption and decryption process Signup and view all the answers

What is the primary goal of cryptography?

To ensure secure communication between sender and recipient Signup and view all the answers

In the context of the trellis diagram, what does the Hamming Distance measure?

The difference between two code words Signup and view all the answers

Which state transition represents the least Hamming Distance according to the diagram?

11 to 01 Signup and view all the answers

What algorithm is used for decoding the received TCM code word?

Viterbi decoding algorithm Signup and view all the answers

What is represented by the '11' at the top of the trellis diagram?

An initial state Signup and view all the answers

Which step follows the calculation of Hamming Distance in the decoding process?

Selecting the path with the least Hamming distance Signup and view all the answers

What is the significance of the accumulated Hamming Distance in the Viterbi algorithm?

It is used to find the most reliable path in the trellis Signup and view all the answers

What does TCM stand for in the context of the decoding process?

Trellis Coded Modulation Signup and view all the answers

What is the outcome when the correct path with the least Hamming Distance is found?

The original message can be recovered Signup and view all the answers

Which of the following best describes the purpose of state transitions in the trellis diagram?

To indicate possible state changes based on input sequences Signup and view all the answers

Study Notes

Coding Theory

Coding theory is the study of the properties of "codes" and their suitability for different applications.
Codes are examined by various scientific disciplines, primarily for creating efficient and reliable data transmission methods.
Data transfer involves the removal of redundancy and the identification or correction of errors.

Types of Coding

Data Compression (Source Coding):
- Shannon-Fano Coding
- Huffman Coding
- Arithmetic Coding
Error Control/ECC-FEC (Channel Coding):
- Block Codes (Reed-Solomon, Hamming, Cyclic Redundancy Codes)
- Convolutional Codes (Trellis, Viterbi)
Line Coding:
- Unipolar/Polar/Bipolar (e.g., NRZ, AMI)
- Multilevel/Multi-transition (e.g., 2B1Q, MLT3)
Cryptographic Coding:
- Hash Codes (e.g., MD5, SHA)
- Cipher Codes (e.g., AES, DES, RSA)

Shannon Coding

Shannon Coding is a lossless data compression technique.
It builds a prefix code based on symbol probabilities.
It was the first of its kind and was used to prove Shannon's noiseless coding theorem.

Fano Coding

Fano's method ranks symbols in descending order of probability.
It divides symbols into two equally probable subsets.
The first digit of the code for each symbol is determined based on its subset (0 or 1).
The process repeats recursively for each further subset for successive digits until a code is assigned to each symbol without ambiguity.

Huffman Coding

In 1952, David Huffman developed an algorithm for creating variable length codes.
This algorithm utilizes estimated probabilities or frequencies of occurrence of different symbols to create a unique code for each possible source symbol.

Huffman Encoding Example

The example demonstrated Huffman encoding on the text string "A DEAD DAD CEDED A BAD BABE A BEADED ABACA BED".
It involved finding symbol frequencies/probabilities, creating a Huffman tree, deriving codewords, and calculating the average bits/symbol.

Arithmetic Coding

Arithmetic coding encodes the message as a range of values.
Encoding is a process of selecting a single floating-point value within the range (0 to 1) for the entire message and converting this range into binary code.
Arithmetic coding differs from Huffman coding, encoding the entire message as one number instead of symbol by symbol.

Trellis Coding

A combination of coding and modulation, using concepts of modulation, coding, dynamic programming, lattice structure, and matrices in mathematics.
Trellis Coded Modulation (TCM) uses a convolutional code.

Viterbi Algorithm

A dynamic programming algorithm to derive the maximum a posteriori probability estimate of the most likely sequence of hidden states (Viterbi path).
Proposed by Andrew Viterbi in 1967.
Commonly applied in decoding TCM and convolutional codes, with application in CDMA, GSM cellular technology, dial-up modems, satellite and space communications, Wi-Fi, speech recognition and synthesis, computational linguistics, and bioinformatics.

Cryptography

The study of secure communications techniques to ensure that only the intended sender and receiver can view data or messages.
Key processes are encryption and decryption.
Encryption converts information to code (cipher) to prevent unauthorized access.
Common symmetric (same key for encryption and decryption) algorithms: AES (Advanced Encryption Standard) established by the US National Institute of Standards and Technology; DES (Data Encryption Standard).

Applications of Cryptography

Confidentiality: Encryption and decryption.
Data Integrity: Detection of corruption.
Authentication: Ensuring security and verified identity.
Non-repudiation: Preventing denial of sending a message.
Secret Sharing: Using multiple keys to decode a single message.

GSM (2G) Security Management

Illustrates security management in a 2G GSM network, integrating IMEI checking and encryption components with authentication and data security elements.

Summary

This module covers important coding techniques, including the principles behind error correction; encoding examples from (Huffman, Fano, and arithmetic coding); and an exploration of popular mathematical algorithms for decoding communications such as (Trellis and Viterbi). The module also describes cryptographic methods for secured data transmission.

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Description

This quiz explores the fundamentals of coding theory, focusing on the various types of codes used for data compression and error correction. Topics include Shannon-Fano Coding, Huffman Coding, and cryptographic techniques. Test your knowledge on how these coding methods facilitate efficient data transmission.