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Unformatted text preview: CS70: Satish Rao: Lecture 13. Outline. 1. Error Correction. 2. Brute Force 3. BerlekampWelsh!!! Erasure Codes. Satellite GPS device Erasure Codes. Satellite GPS device 3 packet message. Erasure Codes. Satellite GPS device 3 packet message. Lose 3 out 6 packets. Erasure Codes. Satellite GPS device 3 packet message. So send 6! Lose 3 out 6 packets. 1 2 3 1 2 3 Erasure Codes. Satellite GPS device 3 packet message. So send 6! Lose 3 out 6 packets. 1 2 3 1 2 3 1 2 3 1 2 3 Erasure Codes. Satellite GPS device 3 packet message. So send 6! Lose 3 out 6 packets. 1 2 3 1 2 3 1 2 3 1 2 3 Erasure Codes. Satellite GPS device 3 packet message. So send 6! Lose 3 out 6 packets. 1 2 3 1 2 3 1 2 3 1 2 3 Gets packets 1,1,and 3. Problem: Want to send a message with n packets. Problem: Want to send a message with n packets. Channel: Lossy channel: loses k packets. Problem: Want to send a message with n packets. Channel: Lossy channel: loses k packets. Question: Can you send n + k packets and recover message? Problem: Want to send a message with n packets. Channel: Lossy channel: loses k packets. Question: Can you send n + k packets and recover message? A degree n 1 polynomial determined by any n points! Problem: Want to send a message with n packets. Channel: Lossy channel: loses k packets. Question: Can you send n + k packets and recover message? A degree n 1 polynomial determined by any n points! Erasure Coding Scheme: message = m , m 2 ,..., m n 1 . 1. Choose prime p ≈ 2 b for packet size b . 2. P ( x ) = m n 1 x n 1 + ··· m ( mod p ) . 3. Send P ( 1 ) ,..., P ( n + k ) . Problem: Want to send a message with n packets. Channel: Lossy channel: loses k packets. Question: Can you send n + k packets and recover message? A degree n 1 polynomial determined by any n points! Erasure Coding Scheme: message = m , m 2 ,..., m n 1 . 1. Choose prime p ≈ 2 b for packet size b . 2. P ( x ) = m n 1 x n 1 + ··· m ( mod p ) . 3. Send P ( 1 ) ,..., P ( n + k ) . Any n of the n + k packets gives polynomial ... Problem: Want to send a message with n packets. Channel: Lossy channel: loses k packets. Question: Can you send n + k packets and recover message? A degree n 1 polynomial determined by any n points! Erasure Coding Scheme: message = m , m 2 ,..., m n 1 . 1. Choose prime p ≈ 2 b for packet size b . 2. P ( x ) = m n 1 x n 1 + ··· m ( mod p ) . 3. Send P ( 1 ) ,..., P ( n + k ) . Any n of the n + k packets gives polynomial ...and message! Erasure Codes. Satellite GPS device Erasure Codes. Satellite GPS device n packet message. Erasure Codes. Satellite GPS device n packet message. Lose k packets. Erasure Codes. Satellite GPS device n packet message. So send n + k !...
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 Fall '11
 Rau
 Elementary algebra, Forward error correction

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