Error Correcting Codes 1: Introduction + Hamming (7,4) Code

New video series. Not expecting it to be very long. Maybe 5-10 videos, depending on how I split them up.

[jonasdaverio]

I'm so happy. I came for your tensor calculus series and now I'm addicted

[blazingsniper]

Thank you so much for explaining the reasoning behind the equations I was taught this in way that was basically forcing me to memorize . I truly believe that the best way to learn is by understanding the reasoning behind what your doing as it makes it easier to memorize and more enjoyable

[TORGIXGaming]

I study media engineering in Germany. Since there are no good videos in my language about this topic, you are my hero. Thank you! :D

[PC-witk]

Glad to see you back. Code theory has very interesting ties with field theory and algebraic geometry, and it's not easy to find instructional videos about it. Keep up the great work!

[alibaba]

Thank you very much for explaining clearly and not including too many unnecessary and complex words!

[prajwolgyawali]

Repetition Code - 2:30
Hamming Code - 6:55
Syndromes - 17:03
Check-bit states and Error States - 17:10

[JgM-iejy]

Absolutely amazing !

I was eagerly awaiting the upcoming series on GR which I thought would be the end of your production. But instead, a totally unexpected series on error correction coding, which I also am very interested in. So excited, I wrote this comment even before I began watching the lecture. The first screen seems to relate linear algebra to error correction ...

How is the tip jar coming along ? I hope I don't have to use an intermediary to process a credit card transaction.

[NoNameAtAll]

interesring to compare this explanation of Hamming code with 3blue1brown's one

I guess I like 3b1b's version more, because it shows "set intersection" aspect visually, but pure "make equations do the work" approach deserves respect

and I guess that "one can mix what error states correspond to which error bits" idea is eye-opening, but probably just corresponds to taking different bits in 3b1b rectangle...

[OliviaDanes-ux]

Your videos seem to be the best ones to understand ECC by far. Its a shame the series isn't finished but I was wondering if you have made any notes on the rest of the topic that I could buy?

[Sharikkhursheed]

Hello eigen why dont you upload video on tensor analysis.. We are waiting to go for General theory of Relativity

[neomuks]

it's a vary good video so easily explained, good work.

[eleazaralmazan]

Great video! I already love this channel!

[emmanueladebiyi]

I would like to know the reason why we have those exact equations for x, y and z. It's it a random selection?

[eatonashton]

Thanks a lot. Your lecture is very awesome and helps me understand hamming codes!!!

[SzechSauce]

Excellent video thank you so much for this!

[sandeep]

Students are liberated after seeing this !

[ВиталийОвчаренко-ин]

Error Correcting Codes 1: Introduction + Hamming (7, 4) Code Decoding Problems Stages

In the field of data transmission and storage, error-correcting codes play a crucial role in ensuring the reliable transfer of information. The Hamming (7, 4) code is a specific example of an error-correcting code that can detect and correct errors in a data transmission. Let's break down the stages involved in understanding and solving problems related to this code.

1. Introduction to Error Correcting Codes:

Error-correcting codes are mathematical algorithms that encode digital data in a way that allows the receiver to detect and, in some cases, correct errors that may occur during transmission. These codes work by adding redundant information to the original data, which helps the receiver identify and correct errors without the need for retransmission.

2. Understanding Hamming (7, 4) Code:

The Hamming (7, 4) code is a popular example of an error-correcting code. It is a linear code that can correct a single error in the transmitted data. The code is named after its inventor, Richard Hamming. This code uses 7-bit blocks to encode 4-bit information, with the remaining 3 bits serving as parity checks for error detection and correction.

3. Decoding Problems:

Decoding problems in error-correcting codes involve determining the original data from the received data, which may contain errors. In the case of the Hamming (7, 4) code, the decoding process involves the following steps:

a. Syndrome Calculation: The receiver calculates the syndrome, which is the sum of the product of the received bits and a set of fixed coefficients. This syndrome helps determine the location and type of error(s) in the received data.

b. Error Location: Using the syndrome, the receiver identifies the location(s) of the error(s) in the received data.

c. Error Correction: Once the location of the error(s) is known, the receiver can correct the error(s) by flipping the bit(s) at the identified location(s).

4. Stages in Solving Decoding Problems:

To solve decoding problems related to the Hamming (7, 4) code, you can follow these stages:

a. Understand the code structure and its ability to correct errors.
b. Learn how to calculate the syndrome for a given set of received data.
c. Develop strategies to identify the location of errors based on the syndrome.
d. Implement methods to correct the errors by flipping the appropriate bits in the received data.

By mastering these stages, you will be well-equipped to understand and solve problems related to the Hamming (7, 4) code and other error-correcting codes.

[signorellil]

Hi Chris not wanting to sound like a broken record, and this new series is great... but when will we get the final videos on Tensor Calculus?

[maran_]

Is that we can use Hamming(5, 4) or Hamming(6, 4) code

[malcolmvernon]

Hey I googled ricci to know how to pronounce it and saw some of your videos. Good stuff