reed solomon - Berlekamp-Massey Algorithm not working for Syndrome's Least significant Symbol being 0

I am trying to implement this algorithm in above picture. The Berlekamp-Massey algorithm solves the following problem in a RS(n,k) system : Given a syndrome polynomial S(z) = {S(n-k-1),........S(2),S(1),S(0)}, finds the Smallest degree Error polynomial. This algorithm works fine for all Syndromes but when S(0) becomes 0, the error polynomial is incorrect. Is there anything missing from the algorithm mentioned ??...Read more

reed solomon - Error detection capability using Berlekamp-Massey algorithm

I have implemented RS( n=1023,k=995 ) with 10 bits in each symbol. To find the error polynomial we are using Berlekamp-Massey(B-M) algorithm. The error detection capability of our code should be n-k = 1023-995 = 28. The error correction capability is (n-k)/2 = 14. The B-M algorithm works perfectly fine for errors less than or equal to 14. How to determine the number of errors if more than 14 errors occur??( As the correction will fail if the errors are greater than 14). I wanted to know if there is any limitation in this algorithm to find the ...Read more

reed solomon - Error correction code capability

Is it possible to achieve 25%+ error correction capability when output cannot be bigger than 175% of input?I was looking for Reed-Solomon code. With 255 output symbols, I can have 145 input symbols. (145 * 1.75 < 255)That means (110/2)/255 * 100% = 21.5%Is there any method or other error correction code to achieve 25%+?Thanks...Read more

forwarderrorcorrection - what is the maximum error correction capability REED-SOLOMON code?

I found that (255,223,32) RS code where 255 = output symbols of RS encoder 223 = input symbols to the RS encoderand each symbol is of 8 bit width is the most widely used one and it can correct upto 16 (255-223/2) symbols errors; where a symbol error occurs if at-least one bit among 8 bits of a symbol is corrupted, even all 8 bits can be corrupted in the worst case. I have the following doubts1) Does the above mentioned RS code has the capability to correct all 16 error symbols, where in each error symbol all 8 bits are corrupted ?2) The (25...Read more

How to find possible errors in Reed-Solomon with only the syndrome?

I am working on an assignment for a class I am taking. I need to give the location and magnitude of a codeword's error, if possible, for a couple given syndromes. If I can figure out the methodology on how to do it for one I could do the rest, but I am lost on the first one. Here is the syndrome: [2, 2, 0, 1]I am to use a Reed-Solomon code with q = 11 and the primitive element as 2.I created the following H matrix trying to solve this:1 1 1 1 1 1 1 1 1 11 2 4 8 5 10 9 7 3 61 4 5 9 3 2 8 10 7 61 8 9 6 4 10 3 ...Read more

reed-solomon error correction extended Euclid algorithm

i don't understand R & D White Paper WHP 031(page 26) constant factor r=9.My calcuation is factor r=7two polynomial are belows7*(x^2)+ 7*(x^1)+9 , 3*(x^1)+14 Would you explain how 9 is extracted ?I try to resolve using GF multiplication table and extened Euclid algorithm....Read more