Lecture of Error Detect and Correct

Let us first discuss some issues related, directly or indirectly, to error detection and correction.

Types of Errors
Redundancy
Detection Versus Correction
Forward Error Correction Versus Retransmission
Coding

Modular Arithmetic

BLOCK CODING

In block coding, we divide our message into blocks, each of k bits, called datawords. We add r redundant bits to each block to make the length n = k + r. The resulting n-bit blocks are called codewords.

Error Detection
Error Correction
Hamming Distance

Minimum Hamming Distance

Example.1

The 4B/5B block coding is a good example of this type of coding. In this coding scheme,
k = 4 and n = 5. As we saw, we have 2k = 16 datawords and 2n = 32 codewords. We saw that 16 out of 32 codewords are used for message transfer and the rest are either used for other purposes or unused.