CHANNEL CAPACITY FORMULATIONS FOR NON-VOLATILE MEMORIES WITH UNREACHABLE LEVELS

Dr. Haider Al Kim

doi:10.30572/2018/KJE/160334

Authors

Dr. Haider Al Kim Electronic and Communications Engineering, University of Kufa (UoK), Iraq https://orcid.org/0000-0002-2429-1565

DOI:

https://doi.org/10.30572/2018/KJE/160334

Keywords:

Non-volatile Memories, Defective Memory, Unreliable Cells, Error Correcting Codes, Shannon Capacity, Capacity-achieving Codes, Entropy

Abstract

This paper investigates the channel capacity of unreachable memory cells (UMCs), where a cell is deemed -unreachable if it cannot store values beyond a specific state, . Memories with these impairments are modeled as discrete memoryless channels (DMCs), similar to those used in information theory and communications. We derive Shannon-type capacity equations for memories with unreachable levels and substitution errors. These novel equations generalize classical Shannon capacity to systems with UMCs. We also compare ideal memories (without imperfections or errors) with normal memories aﬀected by random errors only, as well as defective and erroneous memories. Our ﬁndings corroborate previous studies, particularly regarding random distributions of defective cells. Our results highlight the impact of increasing faulty cells and substitution errors, demonstrating the necessity of greater redundancy to maintain system performance.

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References

Al Kim, H., S. Puchinger, et al. (Aug. 2023). “Coding and bounds for partially defective memory cells”. In: Designs, Codes and Cryptography. DOI:10.1007/s10623-023-01270-0.

Al Kim, H. and V. Sidorenko (Oct. 2023). “Codes for Memory Cells with Unreachable Levels”. In: International Symposium on Problems of Redundancy in Information and Control Systems 2023. Moscow, Russia.

Ben-Hur, Yuval and Yuval Cassuto (2021). “Coding on Dual-Parameter Barrier Channels beyond Worst-Case Correction”. In: 2021 IEEE Global Communications Conference (GLOBECOM), pp. 01–06. DOI: 10.1109/GLOBECOM46510.2021.9685188.

Brémaud, P. (2017). Discrete Probability Models and Methods. 78th. Switzerland: Springer International.

Compagnoni, C. Monzio et al. (2009). “Random Telegraph Noise Eﬀect on the Programmed Threshold-Voltage Distribution of Flash Memories”. In: IEEE Electron Device Letters 30.9, pp. 984–986. DOI: 10.1109/LED.2009.2026658.

Dolecek, L. and F. Sala (2016). Channel Coding Methods for Non-Volatile Memories.

Gabrys, R., F. Sala, and L. Dolecek (Sept. 2014). “Coding for unreliable ﬂash memory cells”. In: IEEE Commun. Lett. 18.9, pp. 1491–1494.

Gleixner, B., F. Pellizzer, and R. Bez (2009). “Reliability Characterization of Phase Change Memory”. In: 2009 10th Annual NVMTS. IEEE, pp. 7–11.

Heegard, C. (1983). “Partitioned Linear Block Codes for Computer Memory with ’Stuck-at’ De- fects”. In: IEEE Trans. Inf. Theory 29.6, pp. 831–842.

Heegard, C. and A. A. El Gamal (Sept. 1983). “On the Capacity of Computer Memory with De- fects”. In: IEEE Trans. Information Theory 29.5, pp. 731–739.

Hameed, Ashwaq (2021). “RAYLEIGH FADING - SHADOWING OF OUTDOOR CHANNELS ANALYSIS BASED ON SNR-PDF MODEL”. Kufa Journal of Engineering, vol. 10, no. 2, pp. 114-25, doi:10.30572/2018/KJE/100209.

Ali, Ameer H. and Saad S. Hreshee (2023). “GFDM TRANSCEIVER BASED ON ANN CHANNEL ESTIMATION”. Kufa Journal of Engineering, vol. 14, no. 1, pp. 33-49, doi:10.30572/2018/KJE/140103.

Al-Ja’afari, Mohannad, et al. (2021). “COMPARISON BETWEEN MLD AND ZF ALGORITHMS FOR MIMO WIRELESS SYSTEM AT RAYLEIGH CHANNEL”. Kufa Journal of Engineering, vol. 9, no. 4, pp. 13-22, doi:10.30572/2018/KJE/090402.

Kuznetsov, A. and B. Tsybakov (1974). “Coding for memories with defective cells”. In: Problems Inf. Transmiss. 10.2, pp. 52–60.

Mahdavifar, H. and A. Vardy (2015). “Explicit capacity achieving codes for defective memories”. In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 641–645. DOI: 10.1109/ISIT.2015.7282533.

Olivo, P., B. Ricco, and E. Sangiorgi (1986). “High-ﬁeld-induced voltage-dependent oxide charge”. In: Applied Physics Letters. ISSN: 0003-6951.

Pirovano, A. et al. (2004). “Reliability Study of Phase-Change Nonvolatile Memories”. In: IEEE Trans Device Mater Reliab 4.3, pp. 422–427.

Shannon, C. E. (Oct. 1948). “A Mathematical Theory of Communication”. In: Bell System Technical Journal 27, pp. 623–656.

Solomon, A. and Y. Cassuto (Sept. 2019). “Error-correcting WOM codes: Concatenation and joint design”. In: IEEE Trans. Inf. Theory 65.9, pp. 5529–5546.

Wachter-Zeh, A. and E. Yaakobi (2016). “Codes for Partially Stuck-at Memory Cells”. In: IEEE Trans. Inf. Theory 62.2, pp. 639–654.

Y. -D. Chih et al., “Design Challenges and Solutions of Emerging Nonvolatile Memory for Embedded Applications, ” 2021 IEEE International Electron Devices Meeting (IEDM), San Francisco, CA, USA, 2021, pp. 2.4.1-2.4.4, doi: 10.1109/IEDM19574.2021.9720557.