【计算机组成原理】海明校验码(Hamming Code) 在学习计算机组成原理时对海明码不是特别理解,查阅了相关网上的资料也是头昏眼花,大量的字母公式搞得头大,但是为了发扬螺丝钉精神我决定硬着头皮看下去,现在对海明码已经有了一些自己的理解,希望在此用简单的方式记录,方便日后的复习以及帮助对海明码不理解的同学们。 首...
5.3.3 Example: Decoding of a Hamming Code Let us consider the decoding of a simple Hamming code with BPSK modulation over an AWGN channel. Hamming codes are a class of single error-correction codes, characterized by having a codeword length of Kc = 2q − 1 and a message length of Kb...
We make a simple deduction here.The parity code of the k bit can have a value. Obviously, one of the values that the data is correct, and the remaining 1 - value means that the errors in the data, if can meet: - 1>m + K (M + K for the total length of the encoding), in ...
We can try with a simple example: Take the message 1101011011010110. Make space for the parity bits: ??1?101?0110??1?101?0110. Apply the rules: each parity bit equals the sum of the corresponding code bits, modulus 2 (meaning odd parity). First parity bit: (1+1+1+0+1) mod 2...
As an example, let's encode the decimal value 12 (binary 1100) in Hamming code. First, enter the binary values in the data positions. Next, compute the parity values by checking if the sum of the protected bits is even or odd:
The process of encoding a message using a hamming code by the sender includes 3 steps. Step1:The first step is to calculate the no.of redundant bits in a message For example, if a message contains ‘n’ no.of bits and ‘p’ no.of redundant bits are added to the message, then ‘np...
Hamming Code C++: #include <iostream> #include <string> #include <algorithm> int hammingDistance(const std::string& strOne, const std::string& strTwo) { if (strOne.length() != strTwo.length()) { throw std::invalid_argument("Strings must have equal lengths"); } int distance = 0; fo...
For example, the CCITT (International Telegraph and Telephone Consultative Committee) recommendation X.25 for packet-switched data networks adopts a distance-4 cyclic Hamming code with 16 parity-check bits for error detection. The natural length of this code is n = 2(15)-1 = 32,767. In ...
Error detection and correction in Hamming Code If, in the preceding example, the sixth bit is changed from 0 to 1 during data transmission, it results in new parity values in the binary number: We will count the number of 1s in each parity bit is bit position. ...
This triple repetition code is actually the simplest Hamming code withm= 2, since there are 2 parity bits, and22− 2 − 1 = 1data bit. Such codes cannot correctly repair all errors, however. In our example, if the channel flipped two bits and the receiver got "001", the system ...