Error Correcting Codes: What is Hamming Distance and Minimum Hamming Distance ?

In this video, the basics of the Error Correction Codes and the Concept of Hamming Distance, and the Minimum Hamming Distance is Explained with examples.

Timestamps:
0:00 Error-Correcting Codes (ECC)
1:23 Repetition Code
3:18 Hamming Distance and Minimum Hamming Distance

Error Correcting Codes:
When the data is sent over the noisy channel then the Error-Correcting Codes are used for correcting the errors in received data bits.

The Error Correcting Codes are used in computer memories, in satellite communication, in one-way communication links, and in multicast systems.
The Repetition Code is the very basic type of Error-Correcting Code. In this video, the triple repetition code is explained and the issues of the repetition code are also explained.

What is Hamming Distance?
The Hamming Distance is the number of bit positions at which the two codes differ.

What is Minimum Hamming Distance?
It is the smallest Hamming Distance between all possible codes in the given encoding scheme.

The link for the other useful videos:

1) Error Detecting Code: Parity Explained | Odd Parity and Even Parity

2) Gray Code:

This video will be helpful to all the students of science and engineering in understanding the concept of Hamming Distance and Minimum Hamming Distance.

#ALLABOUTELECTRONICS
#HammingDistance

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[ALLABOUTELECTRONICS]

Timestamps:
0:00 Error-Correcting Codes (ECC)
1:23 Repetition Code
3:18 Hamming Distance and Minimum Hamming Distance

[ritampal]

Sir, you are really a great teacher. 👍
I'm so much interested on your digital electronics lectures.
Happy teachers' day sir. 🙏

[satya_kartik]

Really great explanation brother. It helped me a lot to understand this hard concept. Thank you..

[shadabzahra]

Thanks man, the teacher in class didn't really explain it and I was so trying so hard to make myself understand but didn't succeed but then there I got your video.

[MohsinTahir-ejoe]

Watching 6 hours before exams. respect from Pakistan

[lourduradjou]

Minimum Hamming distance for error detection
To design a code that can detect d single bit errors, the minimum Hamming distance for the set of codewords must be d + 1 (or more). That way, no set of d errors in a single bit could turn one valid codeword into some other valid codeword.

Minimum Hamming distance for error correction
To design a code that can correct d single bit errors, a minimum distance of 2d + 1 is required. That puts the valid codewords so far apart that even after bit errors in d of the bits, it is still less than half the distance to another valid codeword, so the receiver will be able to determine what the correct starting codeword was.

incase you wanna understand the formulaes...from michegan university

[yogeshraj]

Please make a video on linear block code.

[jinyuzhang]

For d bits of error detection, the minimum Hamming Distance is d + 1. I don't really understand it. Take the example from the video:
0000
0001
0010
0011
...
The minimum Hamming Distance is 1 since the number of different bits between 0000 and 0001 is 1. However, it is 5 (4 bit + 1)...did I miss something? Also, where did 2d + 1 is the minimum Hamming Distance for d bits of error correction come from?

[tomassalas]

What kind of english it's that? It's interesting