Peer reviewed Publikation in Master Journal List
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Non-volatile NAND flash memories store information as an electrical charge. Different read reference voltages are applied to read the data. However, the threshold voltage distributions vary due to aging effects like program erase cycling and data retention time. It is necessary to adapt the read reference voltages for different life-cycle conditions to minimize the error probability during readout. In the past, methods based on pilot data or high-resolution threshold voltage histograms were proposed to estimate the changes in voltage distributions. In this work, we propose a machine learning approach with neural networks to estimate the read reference voltages. The proposed method utilizes sparse histogram data for the threshold voltage distributions. For reading the information from triple-level cell (TLC) memories, several read reference voltages are applied in sequence. We consider two histogram resolutions. The simplest histogram consists of the zero-and-one ratios for the hard decision read operation, whereas a higher resolution is obtained by considering the quantization levels for soft-input decoding. This approach does not require pilot data for the voltage adaptation. Furthermore, only a few measurements of extreme points of the threshold voltage distributions are required as training data. Measurements with different conditions verify the proposed approach. The resulting neural networks perform well under other life-cycle conditions.
Reed-Muller (RM) codes have recently regained some interest in the context of low latency communications and due to their relation to polar codes. RM codes can be constructed based on the Plotkin construction. In this work, we consider concatenated codes based on the Plotkin construction, where extended Bose-Chaudhuri-Hocquenghem (BCH) codes are used as component codes. This leads to improved code parameters compared to RM codes. Moreover, this construction is more flexible concerning the attainable code rates. Additionally, new soft-input decoding algorithms are proposed that exploit the recursive structure of the concatenation and the cyclic structure of the component codes. First, we consider the decoding of the cyclic component codes and propose a low complexity hybrid ordered statistics decoding algorithm. Next, this algorithm is applied to list decoding of the Plotkin construction. The proposed list decoding approach achieves near-maximum-likelihood performance for codes with medium lengths. The performance is comparable to state-of-the-art decoders, whereas the complexity is reduced.
Mutual Information Analysis for Generalized Spatial Modulation Systems With Multilevel Coding
(2022)
Generalized Spatial Modulation (GSM) enables a trade-off between very high spectral efficiencies and low hardware costs for massive MIMO systems. This is achieved by transmitting information via the selection of active antennas from a set of available antennas besides the transmission of conventional data symbols. GSM systems have been investigated concerning various aspects like suitable signal constellations, efficient detection algorithms, hardware implementations, spatial precoding, and error control coding. On the other hand, determining the capacity of GSM is challenging because no closed-form expressions have been found so far. This paper investigates the mutual information for different GSM variants. We consider a multilevel coding approach, where the antenna selection and IQ modulation are encoded independently. Combined with multistage decoding, such an approach enables low-complexity capacity-achieving coded modulation. The influence of the data symbols on the mutual information is illuminated. We analyze the portions of mutual information related to antenna selection and the IQ modulation processes which depend on the GSM variant and the signal constellation. Moreover, the potential of spatial modulation for massive MIMO systems with many transmit antennas is investigated. Especially in systems with many transmit antennas much information can be conveyed by antenna selection.
The growing error rates of triple-level cell (TLC) and quadruple-level cell (QLC) NAND flash memories have led to the application of error correction coding with soft-input decoding techniques in flash-based storage systems. Typically, flash memory is organized in pages where the individual bits per cell are assigned to different pages and different codewords of the error-correcting code. This page-wise encoding minimizes the read latency with hard-input decoding. To increase the decoding capability, soft-input decoding is used eventually due to the aging of the cells. This soft-decoding requires multiple read operations. Hence, the soft-read operations reduce the achievable throughput, and increase the read latency and power consumption. In this work, we investigate a different encoding and decoding approach that improves the error correction performance without increasing the number of reference voltages. We consider TLC and QLC flashes where all bits are jointly encoded using a Gray labeling. This cell-wise encoding improves the achievable channel capacity compared with independent page-wise encoding. Errors with cell-wise read operations typically result in a single erroneous bit per cell. We present a coding approach based on generalized concatenated codes that utilizes this property.
Error correction coding for optical communication and storage requires high rate codes that enable high data throughput and low residual errors. Recently, different concatenated coding schemes were proposed that are based on binary BCH codes with low error correcting capabilities. In this work, low-complexity hard- and soft-input decoding methods for such codes are investigated. We propose three concepts to reduce the complexity of the decoder. For the algebraic decoding we demonstrate that Peterson's algorithm can be more efficient than the Berlekamp-Massey algorithm for single, double, and triple error correcting BCH codes. We propose an inversion-less version of Peterson's algorithm and a corresponding decoding architecture. Furthermore, we propose a decoding approach that combines algebraic hard-input decoding with soft-input bit-flipping decoding. An acceptance criterion is utilized to determine the reliability of the estimated codewords. For many received codewords the stopping criterion indicates that the hard-decoding result is sufficiently reliable, and the costly soft-input decoding can be omitted. To reduce the memory size for the soft-values, we propose a bit-flipping decoder that stores only the positions and soft-values of a small number of code symbols. This method significantly reduces the memory requirements and has little adverse effect on the decoding performance.
The performance and reliability of non-volatile NAND flash memories deteriorate as the number of program/erase cycles grows. The reliability also suffers from cell to cell interference, long data retention time, and read disturb. These processes effect the read threshold voltages. The aging of the cells causes voltage shifts which lead to high bit error rates (BER) with fixed pre-defined read thresholds. This work proposes two methods that aim on minimizing the BER by adjusting the read thresholds. Both methods utilize the number of errors detected in the codeword of an error correction code. It is demonstrated that the observed number of errors is a good measure for the voltage shifts and is utilized for the initial calibration of the read thresholds. The second approach is a gradual channel estimation method that utilizes the asymmetrical error probabilities for the one-to-zero and zero-to-one errors that are caused by threshold calibration errors. Both methods are investigated utilizing the mutual information between the optimal read voltage and the measured error values.
Numerical results obtained from flash measurements show that these methods reduce the BER of NAND flash memories significantly.