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Kui Cai1, K.A.S Immink2, and Zhen Mei1

Advanced Coding and Signal Processing Lab 1Singapore University of Technology and Design (SUTD)

2Turing Machine Corporation, Netherlands

Cascaded Channel Model, Analysis, and Hybrid Decoding for Spin-Torque Transfer

Magnetic Random Access Memory (STT-MRAM)

9TH ANNUAL NON-VOLATILE MEMORIES WORKSHOP, UCSD, MARCH 2018

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Introduction of STT-MRAM

A promising emerging non-volatile memory (NVM) technology – Non-volatility

– High endurance

– Good scalability

– High write/read speed

– Low power consumption

‘1->0’ ‘0->1’

magnetic tunneling junction (MTJ)

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Major Technical Challenges

Process variation & thermal fluctuation result in the simultaneous existence of 3 types of errors

Write errors – Process variation induced variation of the MTJ geometry and

nMOS transistor size

=> widened distribution of the switching current

threshold & variation of the transistor driving current

– Thermal fluctuation => switching is probabilistic

– The write error rate for 0->1 switching (P1), is much higher than that for 1->0 switching (P0)

Read disturb errors – Accidental flipping of MTJ during read (Pr)

– Caused by a large read current due to process variation or thermal fluctuation

Read decision errors – Fail to differentiate the two resistance states due to widened

resistance distributions

– Caused by process variation induced variations of the tunneling oxide thickness and cross-section area, the tunneling oxide imperfection and the interfacial scattering effect

MTJ switching current

pro

ba

bility d

ensity f

unction

Block schematic of MTJ switching current distribution

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Modeling of STT-MRAM

Memory physics based modeling [1]

– Modeling of switching current distributions

• Analytical approach to compute Jc using macrospin model

• Statistical approach to compute MTJ switching current distributions

– Modeling of magnetization dynamical switching using LLG equations

• Switching current vs switching time

– Modeling of NMOS transistors

• Generates MTJ driving current distributions for given NMOS parameters at a specific technology node

– Modeling of static resistance distributions

• Statistical model to estimate distributions due to parametric variations

• Quantum tunneling model: interface imperfections; oxygen vacancy defects in MgO

Memory circuit level modeling – Compact models [2]

[1] B. Chen, K. Cai, G.C. Han, S.T. Lim, and M. Tran, “A portable dynamic switching model for perpendicular magnetic tunnel junctions considering both thermal and process variations”, IEEE Trans. Magnetic, vol. 51, no. 11, Article #:1300704, Nov. 2015. [2] W. Guo et al., “SPICE modelling of magnetic tunnel junctions written by spin-transfer torque,” J. Phys. D, Appl. Phys., vol. 43, no. 21, pp. 215001-1–215001-8, 2010.

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We propose a new class of binary-input, asymmetric, and memoryless channel model, the cascaded binary asymmetric channel (BAC) and Gaussian mixture channel (GMC) model [3]

– A communication type of channel model

The combined model of the write error and read disturb error

[3] K. Cai and K.A.S Immink, “Cascaded Channel Model, Analysis, and Hybrid Decoding for Spin-Torque Transfer Magnetic Random Access Memory (STT-MRAM),” IEEE Trans. Magnetics, vol. 53, no. 11, Article #:8204311, Nov. 2017.

The Cascaded BAC and GMC Channel Model

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The Cascaded BAC and GMC Channel Model

Cascaded Binary Asymmetric Channel (BAC) and Gaussian Mixture Channel (GMC) Model

Significantly improves the memory array error rate simulation speed

Facilitates the theoretical design and analysis of the memory sensing and error correction

coding schemes for STT-MRAM

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Channel raw bit error rate (BER) analysis

Channel Raw Bit Error Rate (BER)

Dominant error events distributions

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Soft-Output Channel Detection Algorithm

Soft-output detector for the cascaded BAC-GMC channel

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The Maximum Likelihood (ML) Decision Criterion

Optimum decoding for the cascaded BAC-GMC channel

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Extended Hamming Codes with Hybrid Decoding

The state of the art ECCs for STT-MRAM – Everspin’s 16Mb MRAM: (71, 64) Hamming code [4]

– TDK-Headway’s 8Mb STT-MRAM test chip (2017): 2-bit ECC [5]

As an example, we adopt an extended Hamming code

– (72, 64) extended Hamming code

We first propose a modified Chase decoder with ML metric for STT-MRAM

We further present a two-stage hybrid decoder

Successful error

correction? Yes

No

Hard decision-decoding

Modified Chase decoding

Exit

[4] https://www.everspin.com/file/162/download

[5] http://hobbydocbox.com/Radio/66149727-Basic-principles-challenges-and-opportunities-of-stt-mram-for-embedded-memory-applications.html

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• Chase decoder with ML metric

performs significantly better than

both the hard-decision decoder

(HDD) and Chase decoder with the

conventional metric

• The two-stage hybrid decoder

achieves similar performance with

the full Chase decoder

• The (72, 64) code with hybrid

decoding performs significantly

better than (71, 64) code with

hybrid decoding

• The hybrid decoder can greatly

improve the system’s tolerance to

the process variation (2% more), in

the presence of write errors 8 9 10 11 12 13 14 15 16

10-5

10-4

10-3

10-2

10-1

100

0/

0 (%)

FE

R

P1=110-4

1 w/o ECC

2 (71,64) code, HDD

3 (71, 64) code, Chase, Cascaded ML metric

4 (71, 64) code, Hybrid

5 (72, 64) code, HDD

6 (72, 64) code, Chase, SED metric

7 (72, 64) code, Chase, GMC ML metric

8 (72, 64) code, Chase, Cascaded ML metric

9 (72, 64) code, Hybrid

Simulation Results

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10-6

10-5

10-4

10-3

10-2

10-5

10-4

10-3

10-2

10-1

100

P1

FE

R

1 w/o ECC

2 (71,64) code, HDD

3 (71, 64) code, Chase, BAC-GMC ML metric

4 (71, 64) code, Hybrid

5 (72, 64) code, HDD

6 (72, 64) code, Chase, SED metric

7 (72, 64) code, Chase, GMC ML metric

8 (72, 64) code, Chase, BAC-GMC ML metric

9 (72, 64) code, Hybrid

Simulation Results (contd.)

• There is a high error floor at

FER = 4×10-4, for the HDDs of both

the (71,64) code and (72, 64) code.

This means the system will never

work with the HDD, no matter how

small the write error rate P1 is

• The hybrid decoder of the (71, 64)

code only slightly lower the error

floor.

• The (72, 64) code with hybrid

decoding overcomes the high error

floor with the HDD, and improves

the maximum affordable write error

rate

• The hybrid decoder can greatly

improve the system tolerance to the

write errors, irrespective of the

resistance spread.

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Decoding Latency Analysis

• The decoding latency of the hybrid decoder is just 0.11% higher than the hard-decision decoder

Computational complexity analysis of the full-Chase decoder

Latency of the hybrid decoder

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Conclusions

We have proposed the cascaded BAC-GMC model, a new communication type of channel model for STT-MRAM – To significantly improve the memory array error rate simulation speed

– To facilitate the theoretical design and analysis of the memory sensing and error correction coding schemes for STT-MRAM

We have derived for the cascaded BAC-GMC channel – The channel raw BERs

– The bit LLR

– The ML decision criterion

As an example, we present a hybrid decoding algorithm for extended Hamming codes for the cascaded channel – The hybrid decoding algorithm can significantly improve the system’s tolerance to

both the write errors and the read errors, with little increase of the decoding latency over the HDD

– It can also be directly applied to other extended BCH codes, for the applications of NVMs with relaxed requirement on the decoding latency

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Subsequent Work

“Polar coding for STT-MRAM”

– Accepted by Intermag 2018

“Dynamic threshold detection based on pearson

distance detection”

– Accepted by IEEE Trans. Commun.