Error Correcting Codes 2a: Linear Codes

Error Correcting Codes 2a: Linear Codes - Generator Matrix

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Күн бұрын

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@TheBigWazowski 5 жыл бұрын

You may not realize it, but you’re making awesome videos whether it be coding theory or tensor calc. Theres almost no channels like this with the same high quality as your videos. Keep up the great work

@drevolan 5 жыл бұрын

I just wanted to let you know that this content is incredibly straight forward, clearly explained and made me understand the material way better than what I got from sitting in the lecture hall or trying to understand it myself with the book. Thank you so much for not just making these incredible videos, but making them in a way that is not only easily digestible but entertaining to watch.

@hwangyounsun367 Жыл бұрын

I just want to thank you for your hard work making this wonderful video. This video delivers clear, coherent lectures about the basic concepts of coding theory so that every watcher can grasp the concepts very easily.

@eigenchris Жыл бұрын

Thanks. Unfortunately this series is currently in an unfinished state. But I'm hoping you can still get value out of it.

@TheNixoo 3 жыл бұрын

Best ECC courses you can find on the internet! Thank you!

@prajwolgyawali6770 4 жыл бұрын

Linear Codes use special matrix called Generator Matrix to project binary message into higher dimensional space. This allows us to correct errors. Valid and invalid words - 0:50 Moving to higher dimension - 4:15 Generator Matrix - 6:00

@2262sandeep Жыл бұрын

Cant find such explanation anywhere, this is just unbeleivable.

@dnsala Жыл бұрын

Morning of the Exam, you explained the last piece I didn't understand, thank you! And thank you KZbin for recommending this to ne last second haha

@introductiontocryptography4223 Жыл бұрын

Excellent lecture, much appreciated!!

@klevisimeri607 Жыл бұрын

Thank you for making these kind of videos!

@abhinavsaket1194 7 ай бұрын

Wonderful video. you deserve many cups of coffee.

@fgtdjkg 9 ай бұрын

Great job! Very good explained, you are awesome

@georgettebeulah4427 4 жыл бұрын

This video make so much sense and can relate a lot to it.

@ВиталийОвчаренко-и1н 6 ай бұрын

It seems like you're referring to the process of understanding and implementing Linear Codes, specifically Error Correcting Codes (ECC) using Generator Matrices. Let me break it down into stages for you. 1. Understanding Error Correcting Codes (ECC): ECCs are essential in data transmission and storage to protect information from errors that may occur during the process. They work by adding redundancy to the original data, allowing the receiver to detect and sometimes even correct errors. 2. Linear Codes: Linear codes are a subset of Error Correcting Codes, where the codewords generated are linear combinations of the original information symbols. These codes have several advantages, such as efficient encoding and decoding algorithms, and the ability to correct errors based on their structure. 3. Generator Matrix: A generator matrix is a square matrix used to represent a linear code. It is an essential tool for encoding data using the code. The generator matrix, denoted as G, is an m x n matrix, where m is the number of parity check bits added, and n is the number of information bits. 4. Decoding Problems: Decoding is the process of recovering the original information from the received codeword, which may contain errors. There are different decoding techniques for linear codes, such as: a. Hard Decision Decoding: In this method, the received signal is quantized into discrete levels, and the decoder makes a hard decision on the most likely transmitted symbol. b. Soft Decision Decoding: This technique uses the received signal's continuous amplitude information to make more accurate decisions about the transmitted symbols. c. Maximum Likelihood Decoding: This method aims to find the codeword that is most likely to have been transmitted, given the received signal. It is generally computationally expensive but provides the best performance. d. Minimum Distance Decoding: This approach focuses on decoding the codeword that is closest to the received signal in terms of Hamming distance. It is based on the fact that the minimum distance between codewords determines the code's error correction capability. 5. Stages in Deciding Problems: When dealing with decoding problems in linear codes, you would typically follow these stages: a. Encode the original information bits using the generator matrix G. b. Transmit the encoded message over a communication channel. c. Receive the encoded message, which may contain errors. d. Decode the received message using one of the decoding techniques mentioned above. e. Determine the most likely original information bits based on the decoded message. Remember, the choice of decoding technique and the specific stages involved may vary depending on the type of linear

@adeemmmm 9 ай бұрын

Very well explained, Thank you

@mazayong99 Жыл бұрын

Very good lecture! Thanks

@ivanm71 5 жыл бұрын

I've told to police that I didn't wrote "weed", just 3 errors occurred in "food" due message transfer. They didn't believe me((

@woodenstick3517 Жыл бұрын

If I pass my exam I will donate you.

@qin6409 2 жыл бұрын

thank you, you really saved my life

@m1_r.0o0 4 жыл бұрын

Thank you! Keep up the good content/quality! New sub here :)

@zhiyidong3367 10 ай бұрын

Thank you !!! 🤩Very good videos

@PROJECTJoza100 Ай бұрын

Ajmo FEROVCI!

@phumlanimbabela-thesocialc3285 3 жыл бұрын

Great lecture

@darthmoomoo 5 жыл бұрын

2:06 . That's what she said.

@abenedict85 3 жыл бұрын

so in your cube example, one test you could perform to decode the message is to look at the vertex in question and decide if it falls on one side or the other of a hyperplane that partitions the space. I noticed that the generator matrix [1 1 1] is also the coordinates for the vector of the normal of the hyperplane for the cube. is there an analog for the 4,7 example? is the generator matrix the normal of the hyperplane?

@eigenchris 3 жыл бұрын

I'm not sure I know how to answer that question. The codewords always form a line/plane/cube/hyperplane subspace of the larger space, since the sum of any two codewords gives another codeword. The rows of the generator matrix are the "basis vectors" for this subspace, meaning you can get to all codewords in the space by scaling the rows of the G matrix by different amounts. In that cube example, the 2 codewords form a 1D line, with a single basis vector of [1 1 1], and the plane orthogonal to that line happens to cut the 3D space in 2. I'm not sure if there's a way to generalized that to higher dimensions. As I said, I just think of the rows of G as being basis vectors for the valid codeword subspace.

@abenedict85 3 жыл бұрын

@@eigenchris I think it has to do with the null space of the H matrix. I love your videos btw

@eigenchris 3 жыл бұрын

@@abenedict85 The "image" of the generator matrix is the same as the nullspace of the H matrix. This is why G*H = 0.

@whatever-ko8qx 4 жыл бұрын

Everything is connected, isn’t it? Quite fascinating.

@AswanthCR7 5 жыл бұрын

your videos are the best. why is the first video private?

@moneerkutt1228 4 жыл бұрын

you're amazing, god bless you

@blazingsniper1239 4 жыл бұрын

what uml diagram software you using ?

@eigenchris 4 жыл бұрын

Almost all of the diagrams I make by hand in Powerpoint. That crazy 7D one I drew with the help of a short Javascript program I wrote with an HTML5 canvas. It listed all the vertices and edges for a 7D cube and projected it down to 2D space.