Forward Error Correction. Steven Marx CSC457 12/04/2001. Outline. What is FEC? Why do we need it? How does it work? Where is it used?. What is FEC?. Send k packets Reconstruct n packets Such that we can tolerate k-n losses Called an (n, k) FEC code. What is FEC? (2). Why FEC?.
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An easy example:
(n, k) = (2, 3) FEC code
transmitting two numbers: a and b
Send three packets:
3. a + b
Could be represented as matrix multiplication
To decode, use subset of rows.
y = Gx, where G is a “generator matrix”
G is constructed in such a way that any subset of rows is linearly independent.
A “systematic” generator matrix includes the identity matrix.
An example: GF(5) -> α = 2
3 = 23 mod 5
4 = 22 mod 5
3 * 4 = 23+2 mod 5
= 32 mod 5
= 2 mod 5
3 * 4 = 12 mod 5
= 2 mod 5