Citation
Abstract
This article is an extension of a recent paper by McEliece and Swanson dealing with the decoder error probability for Reed-Solomon codes (more generally, linear MDS codes). McEliece and Swanson offered an upper bound on PE(u), the decoder error probability given that u symbol errors occur. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. In this article, by using a combinatoric technique—the principle of inclusion and exclusion an exact formula for PE(u) is derived. The PE(u)’s for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the PE(u)’s are observed to approach the Q's of the codes rapidly as u gets large. An upper bound for the expression |/PE(u)/Q/ - 1| is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that PE(u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.
Details
- Volume
- 42-91
- Published
- November 15, 1987
- Pages
- 213–223
- File Size
- 405.1 KB