On-Chip ECC for Low-Power SRAM Design

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Presentation transcript:

On-Chip ECC for Low-Power SRAM Design Hsin-I Liu EE 241 Project 5/9/2005

Outline Introduction to low-power SRAM Introduction on error correction code Analysis of data retention voltage in SRAM Simulations and results 5/9/2005 EE 241 Project

Low-Power SRAM Concept: Reduce the standby Vdd to data retention voltage (DRV) V2 (V) 5/9/2005 EE 241 Project

Modeling DRV DRV is modeled as i.i.d. gamma random variable 5/9/2005 SRAM Chip DRV DRV is modeled as i.i.d. gamma random variable 5/9/2005 EE 241 Project

Error Correction Code Adding parity check into information Non-trivial binary code Easy to encode Parameters fixed Hamming code, Golay code Linear block code Parameters flexible Reed-Solomon code Least parity overhead k information symbols n-k parity symbols n symbols 5/9/2005 EE 241 Project

Applying ECC to SRAM Latency In proportional to block size In this project: Hamming (15,11), Golay(23,12), and RS(15,11) Implementation characteristics are well-known 5/9/2005 EE 241 Project

Model Setup r redundant rows Memory size: M× N ECC block size: n info length: i N columns M rows Row redundancy: r rows Standby cycles: T n symbols ECC i info Metrics: 5/9/2005 EE 241 Project

N columns M rows r redundant rows n symbols ECC i info Model Analysis For certain standby voltage, retention ability can be modeled as Bernoulli r.v. For certain pe of a row, pe of a block can be derived Inside a block, pe of each cell can be found by solving binomial distribution Row redundancy can also be modeled as binomial r.v. 5/9/2005 EE 241 Project

Results 5/9/2005 EE 241 Project

Results (cont.) 5/9/2005 EE 241 Project

Results (cont.) 5/9/2005 EE 241 Project Number of columns Standby Voltage (mV) Hamming RS Golay 256 201.36 194.78 176.36 512 206.53 198.59 179.26 1024 210.04 201.76 182.12 Hardware overhead (gates/bit) 9.091 22.727 58.333 5/9/2005 EE 241 Project

Conclusion Hamming code introduces the least overhead For short waiting time, Hamming code can reduce Eb from 50% to 2x As waiting time goes to infinity, Reed-Solomon saves the power by 3x 5/9/2005 EE 241 Project