The Performance of Polar Codes for Multilevel Flash

The Performance of Polar Codes for Multi-level Flash Memories Yue Li joint work with Hakim Alhussien, Erich F. Haratsch, and Anxiao (Andrew) Jiang March 10 th, 2014

NAND Flash Memory … … … The circuit board of a SSD … Blocks … 4 pages/WL 2

Multi-Level Cells 10 00 01 11 2 bits/cell • Four different kinds of pages: • Lower even • Lower odd • Upper even • Upper odd 3

Why Polar Codes? • Desire for optimal ECCs. • Excellent properties – Capacity-achieving – Theoretical guarantee of error floor performance – Efficient encoding and decoding algorithms 4

Encoding Input User Bits Frozen bits Polar Codeword Flash channels Frozen Channels G Noisy Codeword Information Bits Erdal Arıkan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels, " IEEE Transactions on Information Theory, 2009. confidential 5

Successive Cancellation Decoding Frozen Channels Estimated user bits Noisy Codeword Erdal Arıkan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels, " IEEE Transactions on Information Theory, 2009. confidential 6

Successive Cancellation Decoding Frozen Channels Estimated user bits Noisy Codeword Erdal Arıkan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels, " IEEE Transactions on Information Theory, 2009. confidential 7

Successive Cancellation Decoding Frozen Channels Estimated user bits Noisy Codeword Erdal Arıkan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels, " IEEE Transactions on Information Theory, 2009. confidential 8

Is polar code suitable for flash memories? 2 • Make polar code work in flash memory • Performance evaluations 3 • Adaptive decoding 1

Code Length Adaptation • Polar codes have length N = 2 m • The code lengths in flash memory need to be flexible. 10

Shortening M K – K’ C K’ N – K’ Noisy C Est. M N – K’ K’ 11

Evaluation with Random Data Pseudo-random Data (0, 1, 1, 0, …, 1) (1, 0, …, 1) … (1, 0, …, 1) Not generated by polar encoder Cycling / Retention (0, 0, 1, 1, …, 1) (1, 0, 0, 0, …, 1) 13

Treating Random Data as Codewords (u 1, u 2, …, u. N) = (x 1, x 2, …, x. N) -1 G Invertibl Input Output e Channel parameters Construct codes Frozen Bits 14

Hard and Soft Sensing Reference threshold voltages 11 01 00 10 Cell Voltage P( V | bit = 0 ) LLR = log P( V | bit = 1 ) __________ 15

2 • Performance Evaluation 16

Experimental Setup • Construct one polar code for each kind of page. • List successive cancellation decoding [Tal and Vardy 2011] – List size = 32 with CRC • Block length – 7943 bits shortened from 8192 bits • Code rates – 0. 93, 0. 94, 0. 95 • Flash data – obtained by characterizing 2 X-nm MLC flash chips – 6 -month retention 17

Hard and Soft Decoding Hard Decoding Soft Decoding 18

Different Block Lengths 19

Asymmetric and Symmetric Errors 20

3 • Adaptive Decoding 21

Code Rate Switching Is repetitive code construction needed at rate-switching PECs? BER Correction Capability 0 R 1 pec 1 R 2 pec 2 R 2 pec 3 PEC 22

Why Code Reconstruction is Not Needed? 23

With and Without Code Reconstruction Upper odd page Average 24

Summary • On the flash data – Polar codes are comparable to LDPC codes using hard and soft sensing – Larger block lengths do not improve decoding performance a lot – More symmetric, better decoding performance – Repetitive code construction is not necessary for adaptive decoding 25

Future Directions • Error floor performance • Comparing with LDPC decoder with the same hardware latency • Efficient hardware implementations Thank You 26