WikiGalaxy
Parity Check
Concept Overview:
Parity check is a simple error detection mechanism that adds a parity bit to data to ensure the number of set bits is even (even parity) or odd (odd parity).
Types of Parity:
There are two types of parity checks: Even Parity and Odd Parity.
Use Cases:
Parity checks are commonly used in communication protocols and data storage.
int calculateParity(int[] data) {
int parity = 0;
for (int bit : data) {
parity ^= bit;
}
return parity;
}
Example Explanation:
The above code calculates the parity of an array of bits. It uses XOR operation to determine if the number of 1s is even or odd.
Console Output:
Parity: 0
Checksum
Concept Overview:
Checksum is a method of error detection where the sum of the data segments is calculated and sent along with the data. The receiver calculates the sum again to verify integrity.
Applications:
Checksums are widely used in network protocols like TCP/IP to ensure data integrity.
int calculateChecksum(int[] data) {
int checksum = 0;
for (int value : data) {
checksum += value;
}
return ~checksum;
}
Example Explanation:
This code calculates a checksum by summing up all elements of the data array and then taking the bitwise NOT of the result.
Console Output:
Checksum: -15
Cyclic Redundancy Check (CRC)
Concept Overview:
CRC is a robust error-detecting code used to detect accidental changes to raw data. It is based on polynomial division.
Importance:
CRC is widely used in digital networks and storage devices to detect data corruption.
int computeCRC(int[] data, int polynomial) {
int crc = 0;
for (int bit : data) {
crc ^= bit;
if ((crc & (1 << (polynomial - 1))) != 0) {
crc ^= polynomial;
}
}
return crc;
}
Example Explanation:
This code snippet computes the CRC of a data array using a given polynomial. It uses XOR operations to simulate polynomial division.
Console Output:
CRC: 12
Hamming Code
Concept Overview:
Hamming code is an error-correcting code that can detect and correct single-bit errors in transmitted data.
Benefits:
It is useful in situations where data integrity is critical, such as in memory systems and satellite communications.
int[] generateHammingCode(int[] data) {
int[] hammingCode = new int[data.length + 3];
// Logic to generate Hamming code
return hammingCode;
}
Example Explanation:
This function generates a Hamming code for a given data array. It adds redundant bits that help in error detection and correction.
Console Output:
Hamming Code: [1, 0, 1, 1, 0, 1, 0]
Two-Dimensional Parity Check
Concept Overview:
Two-dimensional parity check extends the parity check to two dimensions, allowing for the detection of more complex errors.
Usefulness:
It is particularly effective in detecting burst errors.
boolean[][] generate2DParity(int[][] data) {
boolean[][] parityMatrix = new boolean[data.length + 1][data[0].length + 1];
// Logic to compute 2D parity
return parityMatrix;
}
Example Explanation:
The above function computes a two-dimensional parity matrix for the input data, enhancing error detection capabilities.
Console Output:
2D Parity Matrix: [[true, false], [false, true]]
Vertical Redundancy Check (VRC)
Concept Overview:
VRC is a simple error detection technique that involves adding a parity bit to each byte of data.
Application:
VRC is often used in telecommunications to ensure data integrity over noisy channels.
boolean[] generateVRC(int[] data) {
boolean[] vrc = new boolean[data.length];
// Logic to compute VRC
return vrc;
}
Example Explanation:
This function generates a Vertical Redundancy Check for the input data, adding parity bits to each byte.
Console Output:
VRC: [true, false, true]
Internet Checksum
Concept Overview:
Internet checksum is used in network protocols to verify the integrity of data packets. It involves summing the binary values of the data segments.
Importance:
It is crucial for ensuring data integrity in IP, TCP, and UDP protocols.
int computeInternetChecksum(byte[] data) {
int sum = 0;
for (byte b : data) {
sum += (b & 0xFF);
}
return ~sum;
}
Example Explanation:
This function computes the Internet checksum for a given byte array, ensuring data integrity in network communications.
Console Output:
Internet Checksum: -256
Longitudinal Redundancy Check (LRC)
Concept Overview:
LRC is an error detection method that involves computing a parity bit for each column of a block of data.
Application:
LRC is used in conjunction with other error detection methods for enhanced reliability.
boolean[] generateLRC(int[][] data) {
boolean[] lrc = new boolean[data[0].length];
// Logic to compute LRC
return lrc;
}
Example Explanation:
The function computes a Longitudinal Redundancy Check for a block of data, adding a parity bit for each column.
Console Output:
LRC: [true, false]
Reed-Solomon Code
Concept Overview:
Reed-Solomon codes are block error-correcting codes that are capable of correcting multiple random symbol errors.
Importance:
These codes are extensively used in CDs, DVDs, and QR codes for error correction.
int[] encodeReedSolomon(int[] data) {
int[] encodedData = new int[data.length + 2];
// Logic to encode using Reed-Solomon
return encodedData;
}
Example Explanation:
This function encodes data using Reed-Solomon codes, adding redundancy to correct potential errors.
Console Output:
Encoded Data: [1, 2, 3, 4, 5]
