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March 2002doc.: IEEE /221r0 Slide 1Submission Chris Heegard, TI Texas Instruments 141 Stony Circle, Suite 130 Santa Rosa California (707) , A Precoder for Limiting Scrambler Error Propagation Chris Heegard, Ph.D. & Richard Williams, Ph.D. Home and Wireless Networking

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March 2002doc.: IEEE /221r0 Slide 2Submission Chris Heegard, TI Scrambler Error Propagation Scrambler –Changing the initial state changes the scramble sequence Helpful in retransmissions –The initial state is determined at the transmitter and sent to the receiver –An error in transmitting the state can lead to infinite error propagation

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March 2002doc.: IEEE /221r0 Slide 3Submission Chris Heegard, TI The Space of Scramble Sequences The set of scramble sequences satisfy –The output of an FIR filter with transfer function g(D) –(c 0, c 1, …, c n-1 ) determine (c n, c n+1, …) –There is a one-to-one correspondence between the initial 2 n initial states and the 2 n scramble sequences –The sequences form a vector space of dimension n The difference between two sequences is a sequence –If g(D) is primitive then the non-zero sequences are maximal length with period 2 n -1 E.g., g(D)=1 +D 4 +D 7 (IEEE ) In this case, the set consists of the zero sequence plus the 2 n -1 phases of a periodic sequence with period 2 n -1

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March 2002doc.: IEEE /221r0 Slide 4Submission Chris Heegard, TI Error Propagation If –The difference is 0 If –The difference is a scramble sequence! This limits the performance of RS FEC –Becomes the dominate error mechanism –An error in initial state corrupts every RS symbol

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March 2002doc.: IEEE /221r0 Slide 5Submission Chris Heegard, TI Solution: precode Transmitter –After RS encoder, precode with 1/g(D) filter Receiver –Before RS decoder, postcode with g(D) filter –An error in initial state corrupts only 1 RS symbol (8 bits) Solution is transparent to the PHY, can be done in the MAC only

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March 2002doc.: IEEE /221r0 Slide 6Submission Chris Heegard, TI Conclusion Initial state infinite error propagation limits RS FEC A simple precoder/postcoder fixes the problem –Limits error to one RS symbol

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