Data Communications Module III

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Questions and Answers

What is the minimum number of check bits required for a Hamming code that protects 4 bits of data?

3 (correct)

In Hamming codes, what does the check bit P1 represent in relation to bits 1, 3, 5, and 7?

XOR of bits 1, 3, 5, and 7 (correct)

XOR of bits 2, 3, and 5

XOR of bits 2 and 4

XOR of bits 1, 2, 3, and 4

When a Hamming code 0110001 is received, which position indicates the error based on the checksum bits calculated?

6 (correct)

What allows for some chunks of data to be missing in multimedia transmission while using Forward Error Correction?

Chunk Interleaving Signup and view all the answers

What must the minimum Hamming distance be in a block code to guarantee the detection of up to 2 errors?

3 Signup and view all the answers

What type of code is a simple parity-check code classified as?

Single-bit error-detecting code Signup and view all the answers

If a codeword of 11101 is received, what must be determined in the context of Hamming code?

The dataword corresponding to the codeword. Signup and view all the answers

In a cyclic code, what happens when a codeword is cyclically shifted?

It results in another valid codeword. Signup and view all the answers

What is the equation for the minimum Hamming distance required to correct up to 1 error in a block code?

dmin = 2t + 1 Signup and view all the answers

What is the primary purpose of adding a redundant bit to a block of data in longitudinal redundancy check?

To detect errors in transmission. Signup and view all the answers

Which property characterizes cyclic redundancy check (CRC) codes?

They are polynomial-based error-detecting codes. Signup and view all the answers

Given a message of 11001001, which polynomial could be used to protect it using CRC?

x^3 + 1 Signup and view all the answers

What result occurs when the receiver checks data for errors using Longitudinal Redundancy Check?

Accepts the data and discards the redundant row. Signup and view all the answers

What is the primary function of Forward Error Correction (FEC)?

To correct errors without requiring a reverse channel Signup and view all the answers

In checksum error detection, what indicates that the received data is accepted?

The sum equals zero after adding the segments Signup and view all the answers

What is required for the Hamming Code to successfully correct a single-bit error?

The number of redundancy bits must satisfy $2^r ext{≥} m+r+1$ Signup and view all the answers

In which scenario is re-transmission of corrupted data considered unacceptable?

Real-time multimedia transmissions Signup and view all the answers

What do redundancy bits in data transmission help achieve?

Allow detection and correction of errors Signup and view all the answers

What happens during error detection using the CRC technique when a bit is corrupted?

The error is detected at the receiver end Signup and view all the answers

What is the result of adding segments using 1's complement arithmetic in checksum error detection?

A sum that can lead to a reset condition Signup and view all the answers

Which of the following methods can be used for Forward Error Correction?

Hamming distance utilization Signup and view all the answers

Study Notes

Data Link Layer Overview

The minimum Hamming distance requirement for error detection and correction is critical for block codes.
To detect up to s errors, the minimum Hamming distance (dmin) must satisfy the equation: dmin = s + 1.
To correct up to t errors, the equation is: dmin = 2t + 1.

Error Detection Techniques

XOR Property: In linear block codes, the XOR of any two valid codewords produces another valid codeword.
Parity-check Code: A simple single-bit error detection method with parameters n = k + 1 and dmin = 2.
Longitudinal Redundancy Check (2D-parity check): Method organizes data into a matrix format and adds redundant bits per row for error detection.

Cyclic Codes

Cyclic codes are a subset of linear block codes where cyclically shifting a codeword results in another valid codeword.
Example of bit shifting: If 1011000 is a codeword, left-shifting gives 0110001.
Cyclic Redundancy Check (CRC): Commonly used in networking (LANs and WANs) for error detection, represented through polynomial division.

Checksum Method

Involves dividing data into segments, summing them using 1's complement arithmetic to derive a checksum.
The sender complements the sum, and the checksum is sent alongside data segments.
At the receiver, if the complemented sum equals zero, the data is accepted; otherwise, it is discarded.

Forward Error Correction (FEC)

Technique to minimize errors in data transmission over communication channels without requiring retransmissions.
Important for real-time multimedia transmission, as re-transmission introduces delays.

Hamming Codes

Constructed by adding parity bits to identify and locate errors in transmitted messages.
The number of redundancy bits (r) must satisfy: 2r ≥ m + r + 1, where m = data bits.
Example usage with a codeword reveals the position of an error through calculated parity bits.

Chunk Interleaving

Allows selective error recovery by missing small chunks at the receiver, rather than losing entire packets.
Aims to maximize data integrity without full retransmission of lost packets.

Key Exercises

Calculation of CRC messages for specific polynomial encoding.
Usage of polynomial long division for error checking in transmitted messages.
Ability to detect single-bit errors in a received Hamming code through parity checks.
Understanding dataword recovery based on received codewords.

Example Scenarios

For Hamming code correction, an example codeword (0110001) is decoded to identify the exact originally transmitted code.
Encoding messages using CRC polynomials demonstrates error protection prior to transmission.

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Description

This quiz focuses on the Data Link Layer as part of the Data Communications and Computer Networks course. Understanding Hamming distance and error detection and correction principles are crucial for ensuring reliable data transmission. Test your knowledge and grasp the fundamental concepts related to block codes.