Yipppeeee!!! I’m finally really really done with my Reed-Solomon encoding and decoding algorithm. Till today, this is the most challenging conceptual programming I have ever done and I believe that anything to do with Information Theory is indeed challenging. It took up a lot of my brain cells, but at the end I’m really proud of doing 99% of it all on my own and 1% credit to jazz for the debugging. So what does it exactly do??
I hope I explain it well for all of you, especially my non-engineering friends. Let’s put it in a little story about how NASA tries to send a beautiful Saturn Ring picture from the space ship to the earth. In a simple story… …
It first changes the picture pixel info into string of numbers:
message polynomial: 11 8 7 11 9 12 15
Before sending it out of the spaceship, the machine first encodes the message:
15 10 6 7 13 14 10 4 11 8 7 11 9 12 15
But well along the long journey from spaceship to the Earth, the encoded message has random errors in certain positions… obviously! 15 10 6 9 5 14 10 4 11 8 7 4 9 15 15
And upon reaching the earth, the machine applies Reed-Solomon Decoding algorithm to calculate the exact error and hence recover back the original message… brilliant isn’t it?!??! 15 10 6 7 13 14 10 4 11 8 7 11 9 12 15
I obviously couldn’t put up the entire Matlab codes and here’s the simple boring program which will randomly generate everything. It takes a bit of time to generate the numbers, so please wait for a while and stare at the blank screen :P I know it looks simple, but the intermediate steps are not! I hope one day when I have more time, I can put up a better interactive program where the user can key in the message and error polynomials and then you all can play with it!! Oh… if any of you want the m-file can please gimme a nudge?!?!?
But for now, I’m staring at it and still wondering how on earth i wrote all those code…
beta(ii+1,kk)=gfAdd(beta(ii+1,kk)+1,gfMul(gfDiv(tri(ii,1)+1,triP(ii,1)+1)+1,betaP(ii,kk)+1)+1);
What on earth is that?!?! Uh… let me take a break and look at more pictures and relish in the ultimate beauty - the mysteries of universe :D