An official website of the United States government
This paper uses a mutual-information maximization paradigm to optimize the voltage levels written to cells in a Flash memory. To enable low-latency, each page of Flash memory stores only one coded bit in each Flash memory cell. For example, three-level cell (TL) Flash has three bit channels, one for each of three pages, that together determine which of eight voltage levels are written to each cell. Each Flash page is required to store the same number of data bits, but the various bits stored in the cell typically do not have to provide the same mutual information. A modified version of dynamic-assignment Blahut-Arimoto (DAB) moves the constellation points and adjusts the probability mass function for each bit channel to increase the mutual information of a worst bit channel with the goal of each bit channel providing the same mutual information. The resulting constellation provides essentially the same mutual information to each page while negligibly reducing the mutual information of the overall constellation. The optimized constellations feature points that are neither equally spaced nor equally likely. However, modern shaping techniques such as probabilistic amplitude shaping can provide coded modulations that support such constellations.
more »
« less
Write Voltage Optimization to Increase Flash Lifetime in a Two-Variance Gaussian Channel
For a two-variance model of the Flash read channel that degrades as a function of the number of program/erase cycles, this paper demonstrates that selecting write voltages to maximize the minimum page mutual information (MI) can increase device lifetime. In multi-level cell (MLC) Flash memory, one of four voltage levels is written to each cell, according to the values of the most-significant bit (MSB) page and the least-significant bit (LSB) page. In our model, each voltage level is then distorted by signal-dependent additive Gaussian noise that approximates the Flash read channel. When performing an initial read of a page in MLC flash, one (for LSB) or two (for MSB) bits of information are read for each cell of the page. If LDPC decoding fails after the initial read, then an enhanced-precision read is performed. This paper shows that jointly designing write voltage levels and read thresholds to maximize the minimum MI between a page and its associated initial or enhanced-precision read bits can improve LDPC decoding performance.
more »
« less
- Award ID(s):
- 1955660
- PAR ID:
- 10540373
- Publisher / Repository:
- IEEE
- Date Published:
- ISSN:
- 2157-8117
- ISBN:
- 979-8-3503-8284-6
- Page Range / eLocation ID:
- 1143 to 1148
- Subject(s) / Keyword(s):
- Flash Memory Write Voltage Signal Constellation Optimization
- Format(s):
- Medium: X
- Location:
- Athens, Greece
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper introduces a mutual information (MI) maximization paradigm that adapts the locations and probabilities of write levels to iteratively increase the mutual information of the weakest bit channel and hence improve the reliability of its corresponding page. In this way, we seek a constellation of write levels that delivers the same amount of mutual information to the bit channel for each page, so that all pages are equally reliable. For simplicity, we consider the example of TLC Flash with an additive white Gaussian noise (AWGN) channel model, but the principle may be applied to denser cells and more realistic channel models.more » « less
-
Phase Change Memory (PCM) is an attractive candidate for main memory, as it offers non-volatility and zero leakage power while providing higher cell densities, longer data retention time, and higher capacity scaling compared to DRAM. In PCM, data is stored in the crystalline or amorphous state of the phase change material. The typical electrically controlled PCM (EPCM), however, suffers from longer write latency and higher write energy compared to DRAM and limited multi-level cell (MLC) capacities. These challenges limit the performance of data-intensive applications running on computing systems with EPCMs. Recently, researchers demonstrated optically controlled PCM (OPCM) cells with support for 5bits/cellin contrast to 2bits/cellin EPCM. These OPCM cells can be accessed directly with optical signals that are multiplexed in high-bandwidth-density silicon-photonic links. The higher MLC capacity in OPCM and the direct cell access using optical signals enable an increased read/write throughput and lower energy per access than EPCM. However, due to the direct cell access using optical signals, OPCM systems cannot be designed using conventional memory architecture. We need a complete redesign of the memory architecture that is tailored to the properties of OPCM technology. This article presents the design of a unified network and main memory system called COSMOS that combines OPCM and silicon-photonic links to achieve high memory throughput. COSMOS is composed of a hierarchical multi-banked OPCM array with novel read and write access protocols. COSMOS uses an Electrical-Optical-Electrical (E-O-E) control unit to map standard DRAM read/write commands (sent in electrical domain) from the memory controller on to optical signals that access the OPCM cells. Our evaluation of a 2.5D-integrated system containing a processor and COSMOS demonstrates2.14 ×average speedup across graph and HPC workloads compared to an EPCM system. COSMOS consumes3.8×lower read energy-per-bit and5.97×lower write energy-per-bit compared to EPCM. COSMOS is the first non-volatile memory that provides comparable performance and energy consumption as DDR5 in addition to increased bit density, higher area efficiency, and improved scalability.more » « less
-
Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more attention recently due to advances in erasure conversion for various types of qubits including neutral atoms, trapped ions, and superconducting qubits. Belief propagation with guided decimation (BPGD) decoding of quantum LDPC codes has demonstrated good performance in bit-flip and depolarizing noise. In this work, we apply BPGD decoding to quantum erasure channels. Using a natural modification, we show that BPGD offers competitive performance on quantum erasure channels for multiple families of quantum LDPC codes. Furthermore, we show that the performance of BPGD decoding on erasure channels can sometimes be improved significantly by either adding damping or adjusting the initial channel log-likelihood ratio for bits that are not erased. More generally, our results demonstrate BPGD is an effective general-purpose solution for erasure decoding across the quantum LDPC landscape.more » « less
-
MLC NAND flash memory uses the voltages of the memory cells to represent bits. High voltages cause much more damage on the cells than low voltages. The free space that need not store bits is leveraged to reduce the usage of those high voltages and thus extend the lifetime of the MLC memory. However, limited by the conventional data representation rule that represents bits by the voltage of one single cell, the high voltages are still used in a high probability. To fully explore the potential of the free space on reducing the usage of high voltages, we propose a novel data representation aware of damage, named DREAM. DREAM uses the voltage combinations of multiple cells instead of the voltage of one single cell to represent bits. It enables to represent the same bits through flexibly replacing the high voltages in some cells with the low voltages in other cells when free space is available. Hence, high voltages which cause more damage are less used and the lifetime of the MLC memory is extended. Theoretical analysis results demonstrate the effectiveness and efficiency of DREAM.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ISIT57864.2024.10619406
