More on the decoder error probability for Reed-Solomon codes

A combinatorial technique similar to the principle of inclusion and exclusion is used to obtain an exact formula for P/sub E/(u), the decoder error probability for Reed-Solomon codes. The P/sub E/(u) 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 are observed to approach the Qs of the codes rapidly as u gets large. An upper bound for the expression mod P/sub E/(u)/Q-1 mod is derived and shown to decrease nearly exponentially as u increases.<
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