Citation
Abstract
In this article we derive upper bounds on the decoder error probability for Reed-Solomon codes. By definition, “decoder error” occurs when the decoder finds a codeword other than the transmitted codeword, this is in contrast to “decoder failure,” which occurs when the decoder fails to find any codeword at all. Our results imply, for example, that for at error-correcting Reed-Solomon code of length q - 1 over GF(q), if more than t errors occur, the probability of decoder error is less than 1/t!, In particular, for the Voyager Reed-Solomon code, the probability of decoder error given a word error is smaller than 3 X 10-14. Thus, in a typical operating region with probabiliy 10-5 of word error, the probability of undetected word error is about 10719.
Details
- Volume
- 42-84
- Published
- February 15, 1986
- Pages
- 66–72
- File Size
- 416.1 KB