Reliability is a Fungible ResourceFungible ResourcesReliability and Area (I)Pfail $ Area FungibilityReliability and Area (II)Distributed VotingDouble EncodingRecursive EncodingPfail $ Area FungibilityExample: erfc(A1/4)Only for some functionsConclusionsReliability is a Fungible ResourceFrancois Francois ImpensImpens, Isaac , Isaac ChuangChuangMIT Media Laboratory& Department of PhysicsFungible Resources• $$ ⇔ Gold• Euros ⇔ $$• Mass ⇔ Energy• Space ⇔ Time ⇔ Energy• Claim:Reliability⇔ Space / Time / EnergyReliability and Area (I)• But also Pfail(A)• Example: MOSFETVoltageProbability0 1VthσPfail↔ Area Fungibility• What tradeoffs are possible?Pfail(A)εAε• Larger area, more reliable• Generic behavior!• Molecular, Quantum, …Is this the best possible?AreaReliability and Area (II)• Consider a circuit which fails with probability εCircuit: εCircuit 1: εCircuit 3: εCircuit 2: εVoteArea: ~3APfail: ~3ε2Area: APfail: εDistributed VotingP1P2P3MAJMAJMAJ• Immune to any single gate failure• Failure probability:Double Encoding P1P2P3P1P2P3P1P2P3Dist. MAJDist. MAJ Dist. MAJDist. MAJArea:Failure probability:Recursive Encoding• Recursion:• Area:• Failure probability: • Threshold:Pfail↔ Area Fungibility• What tradeoffs are possible?Pfail(A)P1P2P3MAJMAJMAJεε’• Area • PfailAεA’εAreaExample: erfc(A1/4)300 Area100 2000246810~10-1210-9Normal PfailFault Tolerant-log(Pfail)Reliability ↔ AreaFungible RegionOnly for some functionsFunction Effective RegionConclusionsReliability ↔ Space, Time, EnergyFault Tolerance can save resrouces• CMOS?•
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