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ERROR CONTROL CODING

One Step Majority LogicDecoder

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What is One Step Majority Logic Decoding?

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General Type II one step ajority

logic decoder

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General Type II One Step MajorityLogic Decoder Steps

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General Type I one step ajority

logic decoder

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General Type I one step ajority

logic decoder steps

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MAJORITYLOGIC

DECODING

MULTIPLE

STEP

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!Majority"Logic decoding algorith #asde$ised in %&'( )y Reed *or a class o*+ltiple"error"correcting codes

disco$ered )y M+ller,

!Most ajority"logic decoda)le codes

*o+nd so *ar are cyclic codes,

INTRODUCTION

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•In error detection and correction- majoritylogic decodig is a ethod to decode

repetition codes- )ased on the ass+ptionthat the largest n+)er o* occ+rrences o* asy)ol #as the transitted sy)ol,

•MAJORITY!LOGIC decodig i" a "im#le#roced$re%partic+larly s+ited *or hard#areipleentations +singost eleentary circ+its,

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Why is M+ltiple step Majority logicDecoding +sed..,,?????

• The one"step ajority"logic decoding*or a cyclic code is )ased on thecondition that a set o* J parity-checks+s orthogonal on a single error digitcan )e *ored,

•

 This decoding ethod is e/ecti$e *orcodes that are copletelyorthogonali0a)le or *or codes #ith large

 J copared to their ini+n distance

dmin.

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COMPUTATIONDefnition   A set o J parity check sums A1,A2,…,AJis said to )e orthogonal on the set E if and only if 

•E$ery error digit eil in E is checked by everycheck s+ 1j *or % 2 j ≤ J

•no other error digit is chec3ed )y ore than one

chec3 s+,

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L!STEP ORT&OGONOLI'ATION(

•1 code is said to )e L-step orthogonalizable (or L-stepajority"logic decoda)le4 i* L-steps of orthogonali0ation are re5+ired to a3e a decodingdecision on an error digit, The decoding process is

called L-step majority-logic decoding.

•1 code is said to )e copletely L-steporthogonali0a)le i* J is one less than the minimun

distance o* the code 6 i,e,- J dmin-! ".

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 T78ES O9 M1:ORIT7 LOGICDECODER

 There are t#o types o* ipleenting

ajority logic decoder; T78E"IDeterines-

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 T78E"II L"STE8 M1:ORIT7 LOGIC

DECODER

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STE8S IN=OL=ED IN T>EDECODING 8ROCEDRE

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 T78E"I L"STE8 M1:ORIT7 LOGIC

DECODER

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STE8S IN=OL=ED IN DECODING

8ROCEDRE

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 E