7 research outputs found
Towards Endurable, Reliable and Secure Flash Memories-a Coding Theory Application
Storage systems are experiencing a historical paradigm shift from hard disk to nonvolatile memories due to its advantages such as higher density, smaller size and non-volatility. On the other hand, Solid Storage Disk (SSD) also poses critical challenges to application and system designers. The first challenge is called endurance. Endurance means flash memory can only experience a limited number of program/erase cycles, and after that the cell quality degradation can no longer be accommodated by the memory system fault tolerance capacity. The second challenge is called reliability, which means flash cells are sensitive to various noise and disturbs, i.e., data may change unintentionally after experiencing noise/disturbs. The third challenge is called security, which means it is impossible or costly to delete files from flash memory securely without leaking information to possible eavesdroppers.
In this dissertation, we first study noise modeling and capacity analysis for NAND flash memories (which is the most popular flash memory in market), which gains us some insight on how flash memories are working and their unique noise. Second, based on the characteristics of content-replication codewords in flash memories, we propose a joint decoder to enhance the flash memory reliability. Third, we explore data representation schemes in flash memories and optimal rewriting code constructions in order to solve the endurance problem. Fourth, in order to make our rewriting code more practical, we study noisy write-efficient memories and Write-Once Memory (WOM) codes against inter-cell interference in NAND memories. Finally, motivated by the secure deletion problem in flash memories, we study coding schemes to solve both the endurance and the security issues in flash memories. This work presents a series of information theory and coding theory research studies on the aforesaid three critical issues, and shows that how coding theory can be utilized to address these challenges
ΠΠ½Π°Π»ΠΈΠ· ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΊΠ°ΡΠΊΠ°Π΄Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ Π²ΡΠ½ΠΎΡΠ»ΠΈΠ²ΠΎΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠΎΠ²Π½Π΅Π²ΠΎΠΉ NAND ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ
ΠΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ Π·Π°ΠΏΠΈΡΠΈ Π² ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΠΈΠΏΠ°Ρ
NAND ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ, Π΄ΠΎΡΡΠΈΠ³Π°Π΅ΠΌΠΎΠ΅ ΠΊΠ°ΠΊ Π·Π° ΡΡΠ΅Ρ ΡΠΌΠ΅Π½ΡΡΠ°ΡΡΠ΅Π³ΠΎΡΡ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ°Π·ΠΌΠ΅ΡΠ° ΡΡΠ΅ΠΉΠΊΠΈ, ΡΠ°ΠΊ ΠΈ Π±Π»Π°Π³ΠΎΠ΄Π°ΡΡ Π²ΠΎΠ·ΡΠ°ΡΡΠ°ΡΡΠ΅ΠΌΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΡ
ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ ΡΡΠ΅ΠΉΠΊΠΈ, ΡΠΎΠΏΡΠΎΠ²ΠΎΠΆΠ΄Π°Π΅ΡΡΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΠ΅ΠΌ Π½Π°Π΄Π΅ΠΆΠ½ΠΎΡΡΠΈ Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ Π΄Π°Π½Π½ΡΡ
β Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠΈ ΠΎΡΠΈΠ±ΠΊΠΈ, Π²ΡΠ½ΠΎΡΠ»ΠΈΠ²ΠΎΡΡΠΈ (ΡΠΈΡΠ»Π° ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ) ΠΈ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ. Π‘ΡΠ°Π½Π΄Π°ΡΡΠ½ΡΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ΠΌ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠΌ ΠΏΠΎΠ²ΡΡΠΈΡΡ Π½Π°Π΄Π΅ΠΆΠ½ΠΎΡΡΡ Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ Π΄Π°Π½Π½ΡΡ
Π² ΠΌΠ½ΠΎΠ³ΠΎΡΡΠΎΠ²Π½Π΅Π²ΠΎΠΉ ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ, ΡΠ²Π»ΡΠ΅ΡΡΡ Π²Π²Π΅Π΄Π΅Π½ΠΈΠ΅ ΠΏΠΎΠΌΠ΅Ρ
ΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΠ³ΠΎ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ Π²Π²Π΅Π΄Π΅Π½ΠΈΡ ΠΏΠΎΠΌΠ΅Ρ
ΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΠ³ΠΎ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π² ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΡΡΡ Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎΡΡΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈ, ΡΠΎΡΠΌΠ°Π»ΠΈΠ·ΡΡΡΠ΅ΠΉ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΡ, ΡΠ²ΡΠ·Π°Π½Π½ΡΠ΅ Ρ Π·Π°ΠΏΠΈΡΡΡ ΠΈ ΡΡΠ΅Π½ΠΈΠ΅ΠΌ Π΄Π°Π½Π½ΡΡ
. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΈΡΠΊΠ°ΠΆΠ΅Π½ΠΈΠΉ, ΡΠΎΠΏΡΠΎΠ²ΠΎΠΆΠ΄Π°ΡΡΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡ Π·Π°ΠΏΠΈΡΠΈ/ΡΡΠΈΡΡΠ²Π°Π½ΠΈΡ Π² NAND ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ, ΠΈ ΡΠ²Π½ΡΠΉ Π²ΠΈΠ΄ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠ΅ΠΉ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ ΡΡΠΌΠ°. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π°ΠΏΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠ΅ΠΉ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ ΡΡΠΌΠ° ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΈΠΈ Π³Π°ΡΡΡΠΎΠ²Π° ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΈ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΠ°ΠΏΠ»Π°ΡΠ°, Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎ Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎ ΠΎΡΡΠ°ΠΆΠ°ΡΡΠ°Ρ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ ΡΡΠΌΠ° ΠΏΡΠΈ Π±ΠΎΠ»ΡΡΠΎΠΌ ΡΠΈΡΠ»Π΅ ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ. ΠΠ»Ρ ΡΡΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ Π°Π½Π°Π»ΠΈΠ· ΠΏΠΎΠΌΠ΅Ρ
ΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΠΊΠ°ΡΠΊΠ°Π΄Π½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ Ρ Π²Π½Π΅ΡΠ½ΠΈΠΌ ΠΊΠΎΠ΄ΠΎΠΌ Π ΠΈΠ΄Π°-Π‘ΠΎΠ»ΠΎΠΌΠΎΠ½Π° ΠΈ Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΠΌ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠΎΠ²Π½Π΅Π²ΡΠΌ ΠΊΠΎΠ΄ΠΎΠΌ, ΡΠΎΡΡΠΎΡΡΠΈΠΌ ΠΈΠ· Π΄Π²ΠΎΠΈΡΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ². ΠΡΠΏΠΎΠ»Π½Π΅Π½Π½ΡΠΉ Π°Π½Π°Π»ΠΈΠ· ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΏΠΎΠ»ΡΡΠΈΡΡ ΠΎΠ±ΠΌΠ΅Π½Π½ΡΠ΅ ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΡΡ ΠΎΡΠΈΠ±ΠΊΠΈ, ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΡΡ Π·Π°ΠΏΠΈΡΠΈ ΠΈ ΡΠΈΡΠ»ΠΎΠΌ ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΠΎΠ±ΠΌΠ΅Π½Π½ΡΠ΅ ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°ΡΡ, ΡΡΠΎ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΡΠ΅ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ Π·Π° ΡΡΠ΅Ρ ΠΎΡΠ΅Π½Ρ Π½Π΅Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ Π·Π°ΠΏΠΈΡΠΈ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ Π³ΡΠ°Π½ΠΈΡΠ½ΠΎΠ³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΡΠΈΡΠ»Π° ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ (ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΠ΅Π»Π΅ΠΌ) Π² 2β2.5 ΡΠ°Π·Π° ΠΏΡΠΈ ΡΠΎΡ
ΡΠ°Π½Π΅Π½ΠΈΠΈ ΡΡΠ΅Π±ΡΠ΅ΠΌΠΎΠ³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠΈ ΠΎΡΠΈΠ±ΠΊΠΈ Π½Π° Π±ΠΈΡ
ΠΠ½Π°Π»ΠΈΠ· ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΊΠ°ΡΠΊΠ°Π΄Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ Π²ΡΠ½ΠΎΡΠ»ΠΈΠ²ΠΎΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠΎΠ²Π½Π΅Π²ΠΎΠΉ NAND ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ
The increasing storage density of modern NAND flash memory chips, achieved both due to scaling down the cell size, and due to the increasing number of used cell states, leads to a decrease in data storage reliability, namely, error probability, endurance (number of P/E cycling) and retention time. Error correction codes are often used to improve the reliability of data storage in multilevel flash memory. The effectiveness of using error correction codes is largely determined by the model accuracy that exhibits the basic processes associated with writing and reading data. The paper describes the main sources of disturbances for a flash cell that affect the threshold voltage of the cell in NAND flash memory, and represents an explicit form of the threshold voltage distribution. As an approximation of the obtained threshold voltage distribution, a Normal-Laplace mixture model was shown to be a good fit in multilevel flash memories for a large number of rewriting cycles. For this model, a performance analysis of the concatenated coding scheme with an outer Reed-Solomon code and an inner multilevel code consisting of binary component codes is carried out. The performed analysis makes it possible to obtain tradeoffs between the error probability, storage density, and the number of P/E cycling. The resulting tradeoffs show that the considered concatenated coding schemes allow, due to a very slight decrease in the storage density, to increase the number of P/E cycling up to 2β2.5 times than their nominal endurance specification while maintaining the required value of the bit error probability.ΠΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ Π·Π°ΠΏΠΈΡΠΈ Π² ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΠΈΠΏΠ°Ρ
NAND ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ, Π΄ΠΎΡΡΠΈΠ³Π°Π΅ΠΌΠΎΠ΅ ΠΊΠ°ΠΊ Π·Π° ΡΡΠ΅Ρ ΡΠΌΠ΅Π½ΡΡΠ°ΡΡΠ΅Π³ΠΎΡΡ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ°Π·ΠΌΠ΅ΡΠ° ΡΡΠ΅ΠΉΠΊΠΈ, ΡΠ°ΠΊ ΠΈ Π±Π»Π°Π³ΠΎΠ΄Π°ΡΡ Π²ΠΎΠ·ΡΠ°ΡΡΠ°ΡΡΠ΅ΠΌΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΡ
ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ ΡΡΠ΅ΠΉΠΊΠΈ, ΡΠΎΠΏΡΠΎΠ²ΠΎΠΆΠ΄Π°Π΅ΡΡΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΠ΅ΠΌ Π½Π°Π΄Π΅ΠΆΠ½ΠΎΡΡΠΈ Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ Π΄Π°Π½Π½ΡΡ
β Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠΈ ΠΎΡΠΈΠ±ΠΊΠΈ, Π²ΡΠ½ΠΎΡΠ»ΠΈΠ²ΠΎΡΡΠΈ (ΡΠΈΡΠ»Π° ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ) ΠΈ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ. Π‘ΡΠ°Π½Π΄Π°ΡΡΠ½ΡΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ΠΌ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠΌ ΠΏΠΎΠ²ΡΡΠΈΡΡ Π½Π°Π΄Π΅ΠΆΠ½ΠΎΡΡΡ Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ Π΄Π°Π½Π½ΡΡ
Π² ΠΌΠ½ΠΎΠ³ΠΎΡΡΠΎΠ²Π½Π΅Π²ΠΎΠΉ ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ, ΡΠ²Π»ΡΠ΅ΡΡΡ Π²Π²Π΅Π΄Π΅Π½ΠΈΠ΅ ΠΏΠΎΠΌΠ΅Ρ
ΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΠ³ΠΎ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ Π²Π²Π΅Π΄Π΅Π½ΠΈΡ ΠΏΠΎΠΌΠ΅Ρ
ΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΠ³ΠΎ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π² ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΡΡΡ Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎΡΡΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈ, ΡΠΎΡΠΌΠ°Π»ΠΈΠ·ΡΡΡΠ΅ΠΉ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΡ, ΡΠ²ΡΠ·Π°Π½Π½ΡΠ΅ Ρ Π·Π°ΠΏΠΈΡΡΡ ΠΈ ΡΡΠ΅Π½ΠΈΠ΅ΠΌ Π΄Π°Π½Π½ΡΡ
. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΈΡΠΊΠ°ΠΆΠ΅Π½ΠΈΠΉ, ΡΠΎΠΏΡΠΎΠ²ΠΎΠΆΠ΄Π°ΡΡΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡ Π·Π°ΠΏΠΈΡΠΈ/ΡΡΠΈΡΡΠ²Π°Π½ΠΈΡ Π² NAND ΡΠ»Π΅Ρ-ΠΏΠ°ΠΌΡΡΠΈ, ΠΈ ΡΠ²Π½ΡΠΉ Π²ΠΈΠ΄ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠ΅ΠΉ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ ΡΡΠΌΠ°. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π°ΠΏΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠ΅ΠΉ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ ΡΡΠΌΠ° ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΈΠΈ Π³Π°ΡΡΡΠΎΠ²Π° ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΈ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΠ°ΠΏΠ»Π°ΡΠ°, Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎ Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎ ΠΎΡΡΠ°ΠΆΠ°ΡΡΠ°Ρ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ ΡΡΠΌΠ° ΠΏΡΠΈ Π±ΠΎΠ»ΡΡΠΎΠΌ ΡΠΈΡΠ»Π΅ ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ. ΠΠ»Ρ ΡΡΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ Π°Π½Π°Π»ΠΈΠ· ΠΏΠΎΠΌΠ΅Ρ
ΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΠΊΠ°ΡΠΊΠ°Π΄Π½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ Ρ Π²Π½Π΅ΡΠ½ΠΈΠΌ ΠΊΠΎΠ΄ΠΎΠΌ Π ΠΈΠ΄Π°-Π‘ΠΎΠ»ΠΎΠΌΠΎΠ½Π° ΠΈ Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΠΌ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠΎΠ²Π½Π΅Π²ΡΠΌ ΠΊΠΎΠ΄ΠΎΠΌ, ΡΠΎΡΡΠΎΡΡΠΈΠΌ ΠΈΠ· Π΄Π²ΠΎΠΈΡΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ². ΠΡΠΏΠΎΠ»Π½Π΅Π½Π½ΡΠΉ Π°Π½Π°Π»ΠΈΠ· ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΏΠΎΠ»ΡΡΠΈΡΡ ΠΎΠ±ΠΌΠ΅Π½Π½ΡΠ΅ ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΡΡ ΠΎΡΠΈΠ±ΠΊΠΈ, ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΡΡ Π·Π°ΠΏΠΈΡΠΈ ΠΈ ΡΠΈΡΠ»ΠΎΠΌ ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΠΎΠ±ΠΌΠ΅Π½Π½ΡΠ΅ ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°ΡΡ, ΡΡΠΎ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΡΠ΅ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ Π·Π° ΡΡΠ΅Ρ ΠΎΡΠ΅Π½Ρ Π½Π΅Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ Π·Π°ΠΏΠΈΡΠΈ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ Π³ΡΠ°Π½ΠΈΡΠ½ΠΎΠ³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΡΠΈΡΠ»Π° ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΠ΅ΡΠ΅Π·Π°ΠΏΠΈΡΠΈ (ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΠ΅Π»Π΅ΠΌ) Π² 2β2.5 ΡΠ°Π·Π° ΠΏΡΠΈ ΡΠΎΡ
ΡΠ°Π½Π΅Π½ΠΈΠΈ ΡΡΠ΅Π±ΡΠ΅ΠΌΠΎΠ³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠΈ ΠΎΡΠΈΠ±ΠΊΠΈ Π½Π° Π±ΠΈΡ
On the Capacity of Multilevel NAND Flash Memory Channels
In this paper, we initiate a first information-theoretic study on multilevel
NAND flash memory channels with intercell interference. More specifically, for
a multilevel NAND flash memory channel under mild assumptions, we first prove
that such a channel is indecomposable and it features asymptotic equipartition
property; we then further prove that stationary processes achieve its
information capacity, and consequently, as its order tends to infinity, its
Markov capacity converges to its information capacity; eventually, we establish
that its operational capacity is equal to its information capacity. Our results
suggest that it is highly plausible to apply the ideas and techniques in the
computation of the capacity of finite-state channels, which are relatively
better explored, to that of the capacity of multilevel NAND flash memory
channels.Comment: Submitted to IEEE Transactions on Information Theor