The stages involved in deciding the minimum distance for linear error correcting codes are as follows: 1. Determine the number of bits in each codeword (n). 2. Calculate the number of message bits transmitted by each codeword (k). 3. Find the minimum Hamming distance between codewords (d). 4. Calculate the code rate, which is the ratio of k to n. For the problem given where management has decided to use 20-bit data blocks in the company's new (n,20,3) error correcting code, the minimum value of n that will permit the code to be used for single bit error correction is 23.
For the Hamming (7,4), if you calculate the syndrome and use that to detect and correct errors (works only for 1 bit error), is that better than having to input the entire codeword map into memory?
If I have a code with hamming distance of 3, then like you said I can correct up to 1 error bit, but this is only true if you assume that only 1 bit has changed. But how do you know in general how many bits have been false?
With a hamming distance of 3, you can correct 1 bit error, but anything more than that renders the code useless. 2 bit errors will detect the error but make the wrong fix, and 3 bit errors will make the jump to another valid codeword, making it seem like there are no errors at all. Every code has its limits. The only way to know for sure which errors occurred is to compare the results with the original message. When we use ECCs, we have to "hope" that our chosen minimum distance is good enough. But if you scratch a CD enough, or tear up a QR code enough, you simply can't read it anymore.
@@TVSuchty oh, I see what you mean. These "best-of" codes have message length k=1 and codeword length n. The minimum distance is always going to be n, since there are only 2 valid codewords, which have a separation of n.
You could if you wanted, but the examples shown in this videos always have ther vertices and edges arranged in a way that matched a cube in some dimension.
I think I explain how to get the generator matrix for Hamming Codes later in the series. The entire point of Error Correcting Codes as a field of study is coming up with good generator matrices and studying their properties, and there are many different types of generator matrices that have been developed over the years. You can see the wikipedia article on Error Correcting Code for more links.
Hamming Weight - 0:35
Hamming Distance - 0:57
Minimum Distance d - 1:50
Distance d vs Errors detected vs Errors corrected - 3:25
I used to count hamiltonians, but this video opened new dimensions to my understanding. Thank you Sir!
would be incredible if you teach my prof that visualising things is possible but for now I'll just watch your amazing vids
The stages involved in deciding the minimum distance for linear error correcting codes are as follows:
1. Determine the number of bits in each codeword (n).
2. Calculate the number of message bits transmitted by each codeword (k).
3. Find the minimum Hamming distance between codewords (d).
4. Calculate the code rate, which is the ratio of k to n.
For the problem given where management has decided to use 20-bit data blocks in the company's new (n,20,3) error correcting code, the minimum value of n that will permit the code to be used for single bit error correction is 23.
Very well presented. Great job!
Amazing explanations, as always. Thank you.
Thank you so much. Very clear, very well explained!
For the Hamming (7,4), if you calculate the syndrome and use that to detect and correct errors (works only for 1 bit error), is that better than having to input the entire codeword map into memory?
a huge help, so great !!
Awesome explanation!
If I have a code with hamming distance of 3, then like you said I can correct up to 1 error bit, but this is only true if you assume that only 1 bit has changed. But how do you know in general how many bits have been false?
With a hamming distance of 3, you can correct 1 bit error, but anything more than that renders the code useless. 2 bit errors will detect the error but make the wrong fix, and 3 bit errors will make the jump to another valid codeword, making it seem like there are no errors at all. Every code has its limits. The only way to know for sure which errors occurred is to compare the results with the original message. When we use ECCs, we have to
"hope" that our chosen minimum distance is good enough. But if you scratch a CD enough, or tear up a QR code enough, you simply can't read it anymore.
keep making these videos
I needed this! Thank you!
So useful thank you
Awesome explanation thanks
Amazingly great♥️
great explanation!
awesome, thank you!
How do you prove that the best (k,n) - Code has minimum distance k?
I'm a bit confused by what you mean by "best" in this question. Can you explain?
@@eigenchris Well you said: best. I will link it in a minute.
I mean 5:43 you said with the best 7,4 correction codes you can correct up to 3 bit errors...
@@TVSuchty oh, I see what you mean. These "best-of" codes have message length k=1 and codeword length n. The minimum distance is always going to be n, since there are only 2 valid codewords, which have a separation of n.
This is genius, thanks so much
Joydeep
I like a good Hamming sandwich from time to time.
Can't see the movie, just hearing the sound track.
You call them cubes. Is it incorrect to call them graphs?
You could if you wanted, but the examples shown in this videos always have ther vertices and edges arranged in a way that matched a cube in some dimension.
@@eigenchris alright, thanks😁
how do I generate the generator matrix?
I think I explain how to get the generator matrix for Hamming Codes later in the series. The entire point of Error Correcting Codes as a field of study is coming up with good generator matrices and studying their properties, and there are many different types of generator matrices that have been developed over the years. You can see the wikipedia article on Error Correcting Code for more links.
@@eigenchris ok thanks
Tanks a lot