1. CAFO: Cost Aware Flip Optimization for Asymmetric Memories RAKAN MADDAH *, SEYED MOHAMMAD SEYEDZADEH AND RAMI MELHEM COMPUTER SCIENCE DEPARTMENT UNIVERSITY OF PITTSBURGH HPCA 2015

2. Introduction  DRAM and NAND Flash are facing physical limitations putting their scalability into question DRAM: Decrease in cell reliability and Increase in power consumption NAND Flash: Endurance degradation and Increase in number of transient and hard errors  Phase-Change Memory (PCM) and Spin-Transfer Torque Random Access Memory (STT-RAM)are a promising alternative Scalability, low access latency and close to zero leakage power Initial assessments and evaluations are encouraging

3. Challenges  PCM and STT-RAM have a number of challenges that needs to be dealt with before deployment in functional systems PCM suffers from limited endurance STT-RAM suffers from high write bit error rate  Solution: Bit flip minimization Service write requests while flipping as few bits as possible Preserves PCM’s endurance and improves STT-RAM’s write reliability

4. Previous Work Differential Write: compares old data against new data and then only flips differing cells. Flip-N-Write: encodes write data into either its regular or inverted form and then picks the encoding that yields in less flips in comparison against old data Flip-Min: encodes write data into a set of data vectors and then picks the vector that yields in less flips in comparison against old data 00111 01001 Old New Saves 2 bit flips 00111 01001 Old New 10110 Saves 3 bit flips 00111 01001 Old New 1 10110 New 2 Saves 4 bit flips 10111 New 3

5. Write Asymmetries  PCM The RESET state is more detrimental to endurance than the set state  STT-RAM Anti-parallel magnetization is more prone to write errors than parallel magnetization SET (“1”) RESET (“0”) Time Power Free Layer Oxide Layer Reference Layer Free Layer Oxide Layer Reference Layer Parallel magnetization (“0”) Anti-parallel magnetization (“1”)

6. Contribution  Observation: existing schemes fail to exploit the write asymmetry 0001 1111 0000 Saves 1 bit flip Old New Saves 3 bit flips Writing a “0” is 4 times more detrimental to endurance than writing a“1” Number of bit flips is oblivious to the write asymmetry!

7. Contribution  Observation: existing schemes fail to exploit the write asymmetry Focusing solely on the number of bit flips is oblivious to the write asymmetry  Proposal: move from the concept of “bit flip reduction” to “cost reduction”  Cost Aware Flip Optimization (CAFO) Cost model: captures the write asymmetry and assigns a cost for a given write operation Coding engine: encodes the write data into a form that result in overall cost reduction

8. Cost Model  Compare write data to currently stored data and associate a cost to each cell  The costs “a”, “b”, “c” and “d” depend on the technology being modeled and the optimization objective (endurance, energy, error rate) 00110111 10101010 acdbabdb Currently Stored Data New Data Cost of Writing a: 0  1, b: 1  0, c: 0  0, d:1  1 With a write cost we can define a gain among different encodings

9. Gain Calculation C= 2a + 3b + 1c + 2d = 8 C encoded = 1a + 2b + 2c + 3d = 5 Gain G = C- C encoded = 8 – 5 = 3 00110111 10101010 Currently Stored Data New Data acdbabdb Cost of Writing cbadcdad Encoded Data a: 0  1, b: 1  0, c: 0  0, d:1  1 Costs: a = 1, b = 2, c = 0, d = 0 01010101 A positive gain implies that it is less costly to write the data encoded How to encode Data?

10. Encoding Auxiliary bits  Auxiliary bits serve as inversion flags  Coding steps: 1.Compute rows gain 2.Flip all rows with positive gain

11. Encoding  Auxiliary bits serve as inversion flags  Coding steps: 1.Compute rows gain 2.Flip all rows with positive gain 3.Compute columns gain 4.Flip all columns with positive gain 5.Repeat process until all rows and columns show a zero or negative gain  Alteration between row and column flips yields in additional cost reduction

12. Encoding example  Costs: a = 1, b = 1, c = 0, d = 0—”1” represents a cell that is to be flipped, “0” otherwise 10010110 11100100 01100011 01101100 10111001 11010100 01001001 11100101 0 0 0 0 0 0 0 0 00000000 0 0 0 0 +2 0 -2 +2 Gain

13. Encoding example  Costs: a = 1, b = 1, c = 0, d = 0—”1” represents a cell that is to be flipped, “0” otherwise 10010110 11100100 01100011 01101100 10111001 11010100 01001001 11100101 0 0 0 0 0 0 0 0 00000000 0 0 0 0 +2 0 -2 +2 0 0 0 0 1 0 0 1 00000000 0 0 0 0 -2 0 -2 +4 -2 -2 -2 +2 0 -4 10010110 11100100 01100011 01101100 01000110 11010100 01001001 00011010 Flip rows with + gain

14. Encoding example  Costs: a = 1, b = 1, c = 0, d = 0—”1” represents a cell that is to be flipped, “0” otherwise 0 0 0 0 1 0 0 1 01000100 11010010 10100000 00100111 00101000 00000010 10010000 00001101 01011110 0 -4 0 -6 -4 -2 +2 -2 -4 -2 -2 -2 -2 0 -4 Flip columns with + gain 10010110 11100100 01100011 01101100 10111001 11010100 01001001 11100101 0 0 0 0 0 0 0 0 00000000 0 0 0 0 +2 0 -2 +2 0 0 0 0 1 0 0 1 00000000 0 0 0 0 -2 0 -2 +4 -2 -2 -2 +2 0 -4 10010110 11100100 01100011 01101100 01000110 11010100 01001001 00011010 Flip rows with + gain

15. Encoding example  Costs: a = 1, b = 1, c = 0, d = 0—”1” represents a cell that is to be flipped, “0” otherwise 0 0 0 0 1 0 0 0 01000100 -6 0 -2 0 -4 -2 0 -6 -0 -6 -4 -4 -2 -2 11010010 10100000 00100111 00101000 00000010 10010000 00001101 10100001 21 flips 33 flips 0 0 0 0 1 0 0 1 01000100 11010010 10100000 00100111 00101000 00000010 10010000 00001101 01011110 0 -4 0 -6 -4 -2 +2 -2 -4 -2 -2 -2 -2 0 -4 10010110 11100100 01100011 01101100 10111001 11010100 01001001 11100101 0 0 0 0 0 0 0 0 00000000 0 0 0 0 +2 0 -2 +2 0 0 0 0 1 0 0 1 00000000 0 0 0 0 -2 0 -2 +4 -2 -2 -2 +2 0 -4 10010110 11100100 01100011 01101100 01000110 11010100 01001001 00011010 Encoding terminates as no row or column shows a positive gain Flip columns with + gain Flip rows with + gain

16. Row only Inversion 1001 0110 1110 0100 0110 0011 0110 1100 1011 1001 1101 0100 0100 1001 1110 0101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 FN W 1001 0110 0001 0100 0110 0011 0110 1100 0100 1001 0010 0100 0100 1001 0001 0101 33 flips 25 flips

17. Encoding example  Costs: a = 1, b = 1, c = 0, d = 0—”1” represents a cell that is to be flipped, “0” otherwise 0 0 0 0 1 0 0 0 01000100 -6 0 -2 0 -4 -2 0 -6 -0 -6 -4 -4 -2 -2 11010010 10100000 00100111 00101000 00000010 10010000 00001101 10100001 21 flips 33 flips 0 0 0 0 1 0 0 1 01000100 11010010 10100000 00100111 00101000 00000010 10010000 00001101 01011110 0 -4 0 -6 -4 -2 +2 -2 -4 -2 -2 -2 -2 0 -4 10010110 11100100 01100011 01101100 10111001 11010100 01001001 11100101 0 0 0 0 0 0 0 0 00000000 0 0 0 0 +2 0 -2 +2 0 0 0 0 1 0 0 1 00000000 0 0 0 0 -2 0 -2 +4 -2 -2 -2 +2 0 -4 10010110 11100100 01100011 01101100 01000110 11010100 01001001 00011010 Flip columns with + gain Flip rows with + gain Can We do better?

18. Encoding Optimization  Write cost can be further reduced even if no row or column shows a positive gain 0100 0011 1000 1000 0 0 0 0 0000 -2 0 0 1 0 0 1000 0 0 -4 -20-4 1100 0100 0000 0000 5 flips 3 flips Flip row and column together Gain

19. Encoding Optimization  Write cost can be further reduced even if no row or column shows a positive gain Flipping both a row and a column, leaves their intersecting cell un- inverted The local gain of the intersecting cell has to subtracted from the total gain of the corresponding row and columns Gain is achieved if G r + G c – 2g r+c > 0 GcGc GrGr g r+c 0100 0011 1000 1000 0 0 0 0 0000 -2 0 0 1 0 0 1000 0 0 -4 -20-4 1100 0100 0000 0000 Flip row and column together Gain

20. Encoding Optimization (cont.)  Generalize to Flipping 1 column with multiple rows (Vice Versa) 0000 0011 1001 1100 0 0 0 0 0000 -4 0 0 0 0100 1000 0010 1000 0 1 1 0 0100 Gain -2 0-2 0 0 0 6 flips4 flips Flip 2 rows and 2column together

21. Aux. Bits Cost  The cost of updating the auxiliary bits can be easily incorporated in the gain calculation 001101101 10101010 a: 0  1, b: 1  0, c: 0  0, d:1  1 acdbabdc b cabdcdbad C = 2a + 3b + 2c +d = 8 C inverted = 2a + 2b + 2c +2d = 6 G= C – C inverted = 8 - 6 = 2 Cost of Writing Gain Currently Stored Data New Data Cost of Writing Inverted Data Costs: a = 1, b = 2, c = 0, d = 0 Old aux bit has to be flipped to “0” Old aux bit stays the same 01010101

22. Decoding  Simple: XOR the corresponding vertical and horizontal aux bits Output of “1”: read cell value inverted Output of “0”: read cell valued un-inverted 0000 0011 1001 1100 0 0 0 0 0000 0100 1000 0010 1000 0 1 1 0 0100 0000 0011 1001 1100 Encode Decode

23. Decoding  Simple: XOR the corresponding vertical and horizontal aux bits Output of “1”: read cell value inverted Output of “0”: read cell valued un-inverted 0000 0011 1001 1100 0 0 0 0 0000 0100 1000 0010 1000 0 1 1 0 0100 0000 0011 1001 1100 Encode Decode

24. Evaluation  Compare Against Flip-Min and Flip-N-Write (FNW)  Experiment with various block sizes of matching space overhead  Compute average cost reduction achieved by every scheme relative to differential write  Experiment with random input stream and memory traces collected from various SPEC benchmark programs  Model both PCM and STT-RAM through setting the cost labels to match the underlying technology

25. Cost Reduction vs. Cost oblivious FNW and Flip-Min Overhead: 3.125% Overhead: 12.5%Overhead: 6.25%

26. Cost Reduction vs. Cost oblivious FNW and Flip-Min Overhead: 3.125% Overhead: 12.5%Overhead: 6.25%

27. Cost Reduction vs. Cost aware FNW and Flip-Min Overhead: 12.5%Overhead: 6.25% Overhead: 3.125% Cost Model Improves FNW and Flip Min

28. Cost Model Improvement

29. Optimization Isolation At least 15% of cost reduction without encoding optimization

30. STT-RAM Cost Reduction Costs: a = 1, b = 0, c = 0, d = 0 Overhead: 12.5%Overhead: 6.25% Overhead: 3.125%

31. Benchmark Data Costs: a = 1, b = 2, c = 0, d = 0 Block Size: 128B (6.25% overhead)

32. Conclusion  Bit flip Minimization techniques are oblivious to write asymmetries  Move from the concept of bit flip minimization to cost Reduction  CAFO ◦Cost model that captures the asymmetry in the write cost ◦2D Encoder that minimizes the overall cost of write operations

33. Questions?