what happens if the error correcting code word is corrupted in RS code

1
votes

A message which has been encoded with Reed Solomon code and now I have the entire data which is message+code word. Now during transfer if there is a change in the message part then it is possible to decode but what if the code word itself got corrupted/changed? Is it possible to correct the code word as well? If it can be corrected how to do it? Or the Reed Solomon error correcting code itself will take care of correcting the corrupted Code word?

I'm bit confused. I hope I'll get a relevant answer. Thanks in advance.

1
error-correctionreed-solomon
What have you done to investigate this yourself? – Marichyasana
@Marichyasana I have played with a library reedsolo 0.3 in python and have changed tried changing the code word. So when I change it I wasn't able to retrieve the message. – Praveenupadrasta

1 Answers

2
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There an issue with the terminology in the question. A code word consists of the message data plus the parity (redundancy) data (what the question was calling the code word). In addition, the term code word usually means one with no errors (in either the message part or the parity part), one that is an exact multiple (polynomial with finite field coefficients multiplication) of the generator polynomial.

During correction, it doesn't matter if the errors are located in the message data or the parity data. As long as the total number of symbols in error is less than or equal to 1/2 times the number of parity symbols, then the errors are correctable. There are two types of Reed Solomon codes, the "original view", and the "BCH view", with most implementations being "BCH view.

The wiki article may help you understand.

https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction

In this "BCH view" section of the wiki article:

https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction#Systematic_encoding_procedure

the message is treated as a polynomial p(x) multiplied by x^t to make space for t parity symbols, and the remainder sr(x) = p(x)x^t mod g(x), where g(x) is the generator polymial. The code word is s(x) = p(x)x^t mod g(x) - sr(x). If using a binary based field for Reed Solomon, then addition and subtraction are both exclusive or.

Note that in other articles about Reed Solomon, usually t represents the number of symbols that can be corrected, and the number of parity symbols would be 2t (or for odd number of parity symbols 2t+1). The wiki article uses lambda: Λ for the coefficients of the locator polynomial, while other articles use sigma: σ for the same thing.