Transcript Efficient Soft-Decision Decoding of Reed

Efficient Soft-Decision
Decoding of ReedSolomon Codes
Clemson University
Center for Wireless Communications
SURE 2006
Presented By:
Sierra Williams
Claflin University
Outline
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Background
Methods
Results
Future Work
Introduction
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Applications of Reed-Solomon codes
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Storage Devices
Wireless or Mobile Communications
Digital Television
High Speed Modems
Reason for Research
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Minimize the number of errors
Introduction
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Block Error Control Codes
Uncoded Data Stream
k- symbol block
Block Encoder
n- symbol block
Coded Data Stream
Introduction
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An (n,k,d)q Reed-Solomon code
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n is # of symbols in block
k is the message symbols
d is the minimum distance
q is # of elements in Galois field
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Corrects t = (n-k)/2 errors or s= n-k erasures
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Introduction
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Example An (8,4,5)8 Reed-Solomon code
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GF(8)= {0, 1, α, α2, α3, α4 ,α5 ,α6}
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t = 2 (Correct double errors)
s =4 (Correct 4 erasures)
Introduction
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Coherent Multiple Frequency Shift Keying (MFSK)
Transmission
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Map elements of GF(8) to 8 different frequencies
s0(t)=
2E
cos (ω0t) ,
T
2E
si+1(t)=
cos (ω0t) ,
T
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0t T
0  t  T,
i = 0,1,…,6
Therefore, r(t) = s(t) +n(t) , where n(t) is AWGN
(Additive White Gaussian noise)
Introduction
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Correlation receiver for coherent MFSK
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Yields 8 soft-decision outputs for each transmitted
frequency
e.g.
If s0t transmitted the correlation outputs would be
r0 = E + n0 and ri = ni , i = 1,2,…,7 where ni is
a Gaussian random number
Methods
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The C++ Program
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Generates 8 sets of 8 random numbers
Value of signal added to first element as noise
Sort each array
Hard-decision error
Finding beta and receiver array elements
Determine codeword
Methods
Results
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Using the list decoding approaches maximum
likelihood with fewer operations
Future Work
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Using not only the least likely to list decode
but 2nd least likely and so on.
Acknowledgments
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Rahul Amin
Dr. John Komo
Clemson University SURE Program
Questions?