Implementation and Performance Analysis of Two Error Detection and Correction Techniques: CRC and Hamming Code

2.1. Parity Bit Codes

Parity bit codes are very simple schemes that can be used to detect single or odd numbers (i.e., three, five, etc.) of errors in the output. An even number of flipped bits will make the parity bit appear correct.

2.2. Hamming Codes

Hamming codes are a set of error-correction codes that detect and correct bit errors that happen while moving or storing computer data. The most widely recognized types of error detection codes utilized as a part of RAM depend on the codes contrived by R. W. Hamming. In the Hamming code, k equality bits are added to an n-bit information word, framing another expression of n^k bits. The bit positions are numbered in arrangement from 1 to n^k. Those positions numbered with powers of two are saved for the equality bits. The rest of the bits are the information bits. The code can be utilized with expressions of any length (Ma, Yu, Zhang, & Cheng, 2015).

The basic Hamming code can detect and correct an error on just a single bit. When multiple bit errors are detected, they are erroneously corrected as single bit errors. By adding another parity bit to the coded word, the Hamming code can be used to correct a single error and detect double errors.