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WHAT'S YOUR ENGINEERING QUOTIENT?

Problem 5—You are given the task of designing a foward-error-correcting (FEC) scheme that will tolerate a bit error rate (BER) of 10^-3 with no significant degradation. Furthermore, you must use a minimum of additional bandwidth to accomplish this, preferably less than 4%.

"Fine," you say. "I'll use Reed-Solomon coding with a relatively large block size, say 200 bytes. A BER of 10^-3 is about one bad bit in 1000. In a block of 200 bytes (1600 bits), I'll typically see one or two errors. R-S coding requires two check bytes per byte corrected, so I only need 4 out of the 200 bytes to be check bytes, for an overhead of just 2%."

What is the flaw in this reasoning?

The flaw is in assuming that the bit errors are approximately periodic.

Although the average error rate is one per 1000 bits, the errors are randomly distributed. There is a quite significant probability of finding 3 or more errors in a block, and the R-S decoder will not be able to correct these.

Contributor: Dave Tweed

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