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

2. 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

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. Results
5/9/2005
EE 241 Project

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

11. 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

12. 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