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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