Correlation between Iterative Methods and Convolution Codes

[Th3HoopMan]

Hey guys so I have this Calc 3 project and the end is throwing me for a loop. I've done the encoding part, and I've coded the standard iterative methods, but I don't see how the two correlate so I can use the iterative methods to decode a "y stream" with the inputs specified.
http://i.imgur.com/7wIEoHJ.png http://i.imgur.com/FINnNZZ.png

So these iterative methods take in an A|b , an initial guess, and a tolerance. I understand decoding the stream is solving the reverse equation Aix = yi and the Jacobi and Gauss-Seidel methods do that, but. Where would the y stream fit into this equation? I'm mainly asking because I don't understand how to format the y stream to fit with the method equations. According to the assignment the y stream is a combination of y0 and y1 (11, 0, 11) which doesn't seem like it would fit anywhere. Do I convert that y stream into a vector somehow? and does it replace b?

 

[jvicens]

Hey there,

It seems like you have a good understanding of the iterative methods and their purpose in solving equations. The y stream in this case is actually a vector, and it does replace the b vector in the equation Aix = b. This is because the y stream is the result of encoding a message using a specific encoding matrix A.

To use the iterative methods to decode the y stream, you would first need to convert the y stream into a vector form. This can be done by simply listing out the values in the y stream as coordinates, so in this case, the y vector would be (11, 0, 11). This vector would then replace the b vector in the equation Aix = b.

Once you have the y vector, you can use it in the iterative methods just like you would use any other vector. The initial guess can be any vector, and the tolerance is used to determine the accuracy of the solution. The iterative methods will then use the y vector and the encoding matrix A to solve for the x vector, which will be the decoded message.

I hope this helps clarify how the y stream fits into the equation and how you can use the iterative methods to decode it. Good luck with your project!