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EFFICIENT LOGIC SHARING INPARALLEL CHIEN SEARCH USINGPARALLEL CHIEN SEARCH USINGALGORITHMIC APPROACH
Umair Ishaq, Jungsub Oh, Woojin Yang, Sungju ParkMultimedia Systems Lab,Dept. of Computer Science & Engineeringp p g gHanyang University, South Korea
BCH Codes
CONTENTS
BCH Decoder Chien searchConventional/parallel Chien SearchProposed AlgorithmSimulation ResultsImplementationConclusionConclusion
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Widely used in communication systems and digital
BCH CODES
y y gtechnology
Long Haul Optical CommunicationDi it l Vid B d tiDigital Video BroadcastingNAND Flash
N bit N bit K bitK bit N-bit N-bit K-bitK-bit
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A (n,k) binary BCH code decodes a n-bit codeword
BCH DECODER
( , ) yblock into a k-bit codeword.g(x) is the degree n-k generator polynomial.Block Diagram of Decoder
ELP Rootscodeword
ELP Error Location Polynomial
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CHIEN SEARCH
The Chien search block exhaustively examines whether i i t f Λ( ) f i 0 1 1αi is a root of Λ(x) for i = 0,1,…,n-1
=Error Locator Polynomial
Conventional generation gNeeds n cycles 5
CHIEN SEARCH (CONT…)
p-parallel Chien Searchp p
Cycles searching for error locations is reduced from n to n/pCycles searching for error locations is reduced from n to n/p 6
LOGIC SHARING IN CHIEN SEARCH
BCH (63, 30, 6) code, which can correct 6 errors. Its generator l i l ipolynomial is
g(x) = x6 + x + 1
Consider a constant FFM where the fixed multiplicands is α42 =α6*7Consider a constant FFM where the fixed multiplicands is α42 =α6 7.
Logic Repetition
b1 ^ b2 3 times
b1 ^ b5 4 times
b2 ^ b5 3 times
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Step 1:
PROPOSED ALGORITHM
Transform the output equations in matrix, named equation matrix
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Step 2: Compute similarity matrix
PROPOSED ALGORITHM(CONTD.)
Compute similarity matrix, take each row and check degree of similarity between other rows
Example:First row is taken and i il it b t fi tsimilarity between first row
and second row is b[1] ^ b[5] similarly check
i il it b t fi tsimilarity between first and other rows
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Step 3:
PROPOSED ALGORITHM(CONTD.)
Delete similar rows and rows containing less than 2 number of 1’sSort the similarity matrix in ascending order based upon number of in each prow.
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Step 4:
PROPOSED ALGORITHM(CONTD.)
Check for covered rows and covering rows and write covering rows in gterms of covered rows.
p5 = p0 ^ b[2]p7 = p6 ^ b[5]
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Step 5:
PROPOSED ALGORITHM(CONTD.)
Repeat step 4 for output equations.
O[0] = b[3] ^ p5O[1] = p7O[2] = p5O[3] = b[2]^p3O[4] = b[3]^b[5]^p7O[5] = b[2]^p7
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Step 6: PROPOSED ALGORITHM(CONTD.)
b[0] b[1] b[2] b[3] b[4] b[5]
Check for shortest path in output equations.
O[4] = b[3] ^ b[5] ^ p7 Now compute sum for each path.
Path 1,
sum 4 5 3 3 2 3
O[4] = b[3] ^ p6
Criteria:
Path 1,
O[4] = b[3]^b[5]^p7 = b[3]^b[5]^b[0]^b[1]^b[4]^b[5]
First compute column wise sum of similarity matrix.
Now select that path which has
Sum = 3+3+4+5+2+3=20Similarly
Now select that path which has minimum sum. Path 2,
Sum = 1413
The BCH (2047, 1926, 11)used for testing of algorithm
IMPLEMENTATION
used for testing of algorithm
Algorithm is implemented in MATLAB.
Coded in Verilog
ModelSim is used for Simulation
Xilinx ISE is used for Synthesis
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RESULTSCHIEN SEARCH complexity of BCH (2047, 1926, 11) code
with 2 FFMs Resource Sharingwith 2 FFMs Resource Sharing
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An algorithmic approach for logic sharing between
CONCLUSION
g pp g gthe multipliers of Chien Search is presented.Optimizations in terms of both area and frequency
hi dare achieved.
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THANKS
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