Statistical Characterization of Noise and Interference in NAND Flash Memory

Jaekyun Moon,Jaehyeong No,Sangchul Lee,Sangsik Kim,Seokhwan Choi,Yunheub Song IEEE 2013 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS PART 1 R Vol.60 No.8

<P>Given the limited set of empirical input/output data from flash memory cells, we describe a technique to statistically analyze different sources that cause the mean-shifts and random fluctuations in the read values of the cells. In particular, for a given victim cell, we are able to quantify the amount of interference coming from any arbitrarily chosen set of potentially influencing cells. The effect of noise and interference on the victim cell after repeated program/erase cycles as well as baking is also investigated. The results presented here can be used to construct a channel model with data-dependent noise and interference characteristics, which in turn can be utilized in designing and evaluating advanced coding and signal processing methods for flash memory.</P>

제주도 지역 삼나무와 편백나무의 연륜생장과 기후인자와의 상관관계 연구

김문일(Kim, Moon-Il),이우균(Lee, Woo-Kyun),변재균(Byun, Jaekyun) 대한공간정보학회 2011 한국공간정보학회 학술대회 Vol.2011 No.5

본 연구는 제주 지역의 삼나무와 편백나무의 연륜생장과 주요 기상인자인 월별 온도와 강수량간의 상관관계를 분석하였다. 연륜생장량은 연령에 의해 영향을 받을 수 있으며 DBH, 밀도, 경쟁 및 기상, 강수, 습도와 같은 기상인자에 의한 영향을 받는다. 연륜생장량과 기상인자간의 관계를 규명하기 위해 개체목을 수간석해한 후, 흉고직경 높이의 단판을 분석하여 연도별 연륜생장량을 측정하였다. 측정된 연륜생장량은 음지수생장곡선을 이용하여 표준화한 뒤 기상인자들과 분석을 실시하였다.

Concatenated Raptor Codes in NAND Flash Memory

Geunyeong Yu,Jaekyun Moon IEEE 2014 IEEE journal on selected areas in communications Vol.32 No.5

<P>Two concatenated coding schemes based on fixed-rate Raptor codes are proposed for error control in NAND flash memory. One is geared for off-line recovery of uncorrectable pages and the other is designed for page error correction during the normal read mode. Both proposed coding strategies assume hard-decision decoding of the inner code with inner decoding failure generating erasure symbols for the outer Raptor code. Raptor codes allow low-complexity decoding of very long codewords while providing capacity-approaching performance for erasure channels. For the off-line page recovery scheme, one whole NAND block forms a Raptor codeword with each inner codeword typically made up of several Raptor symbols. An efficient look-up-table strategy is devised for Raptor encoding and decoding which avoids using large buffers in the controller despite the substantial size of the Raptor code employed. The potential performance benefit of the proposed scheme is evaluated in terms of the probability of block recovery conditioned on the presence of uncorrectable pages. In the suggested page-error-correction strategy, on the other hand, a hard-decision-iterating product code is used as the inner code. The specific product code employed in this work is based on row-column concatenation with multiple intersecting bits to allow the use of longer component codes. In this setting the collection of bits captured within each intersection of the row-column codes acts as the Raptor symbol(s), and the intersections of failed row codes and column codes are declared as erasures. The error rate analysis indicates that the proposed concatenation provides a considerable performance boost relative to the existing error correcting system based on long Bose-Chauduri-Hocquenghem (BCH) codes.</P>

Easily Computed Lower Bounds on the Information Rate of Intersymbol Interference Channels

Seongwook Jeong,Jaekyun Moon IEEE 2012 IEEE transactions on information theory Vol.58 No.2

<P>Provable lower bounds are presented for the information rate I(X; X+S+N) where X is the symbol drawn independently and uniformly from a finite-size alphabet, S is a discrete-valued random variable (RV) and N is a Gaussian RV. It is well known that with S representing the precursor intersymbol interference (ISI) at the decision feedback equalizer (DFE) output, I(X; X+S+N) serves as a tight lower bound for the symmetric information rate (SIR) as well as capacity of the ISI channel corrupted by Gaussian noise. When evaluated on a number of well-known finite-ISI channels, these new bounds provide a very similar level of tightness against the SIR to the conjectured lower bound by Shamai and Laroia at all signal-to-noise ratio (SNR) ranges, while being actually tighter when viewed closed up at high SNRs. The new lower bounds are obtained in two steps: First, a “mismatched” mutual information function is introduced which can be proved as a lower bound to I(X; X+S+N). Secondly, this function is further bounded from below by an expression that can be computed easily via a few single-dimensional integrations with a small computational load.</P>

Low-Complexity Iterative Channel Estimation for Turbo Receivers

Daejung Yoon,Jaekyun Moon IEEE 2012 IEEE TRANSACTIONS ON COMMUNICATIONS Vol.60 No.5

<P>This letter discusses a receiver-side channel estimation algorithm well-suited to turbo equalizers for multiple-input multiple-output (MIMO) systems. The proposed technique is a Kalman-based channel estimator that runs on parallel single-input single-output (SISO) channels. Soft-decision-feedback interference cancellation is utilized to reduce the MIMO channel estimation problem into multiple SISO channel estimation problems. Unlike existing methods, however, the inherent correlation that exists among the output samples of the successive interference canceller is suppressed via careful puncturing of observation samples. The quality of soft decisions and channel estimates are also continuously monitored and incorporated in the Kalman filter update process.</P>

Breaking the Trapping Sets in LDPC Codes: Check Node Removal and Collaborative Decoding

Soonyoung Kang,Jaekyun Moon,Jeongseok Ha,Jinwoo Shin IEEE 2016 IEEE TRANSACTIONS ON COMMUNICATIONS Vol.64 No.1

<P>Trapping sets strongly degrade performance of low-density parity check (LDPC) codes in the low-error-rate region. This creates significant difficulties for the deployment of LDPC codes to low-error-rate applications such as storage and wireless systems with no or limited retransmission options. We propose a novel technique for breaking trapping sets based on collaborative decoding that utilizes two different decoding modes. While the main decoding mode executes message passing based on the original parity check matrix of the corresponding LDPC code, the sub-decoding mode operates on a modified parity check matrix formed by removing a portion of check nodes in the factor graph representation of the given code. The modified parity check matrix is designed to promote a passing of correct information into erroneous variable nodes in the trapping set. Theoretical properties of the proposed trapping-set-breaking technique have been established based on the notion of the improved separation for the trapped variable nodes. Simulation results show that the proposed collaborative LDPC decoding scheme switching between the two decoding modes back and forth effectively breaks dominant trapping sets of various known types of regular and irregular LDPC codes.</P>

Communication Turbo Equalization of 2-D Intersymbol Interference Using Multiple 1-D Constituent Equalizers

Jaehyeong No,Jaekyun Moon IEEE 2015 IEEE transactions on magnetics Vol.51 No.9

<P>A 2-D soft-in, soft-out equalizer consisting of multiple low-complexity constituent equalizers is proposed for the turbo equalization of 2-D intersymbol interference. The constituent equalizers are simple 1-D linear equalizers running in different directions over a 2-D array of storage cells. Simulation results as well as an extrinsic information transfer chart analysis indicate that the proposed concatenation provides performance comparable with finite-window trellis-based equalizers while requiring a much lower complexity level.</P>

The Error-Pattern-Correcting Turbo Equalizer: Spectrum Thinning at High SNRs

Alhussien, Hakim,Jaekyun Moon IEEE 2011 IEEE transactions on information theory Vol.57 No.2

<P>The error-pattern correcting code (EPCC) is a code designed to correct frequently observed error cluster patterns of the intersymbol interference (ISI) channel. This paper focuses on developing theoretical understanding of the performance of serial concatenation of the EPCC with an outer recursive systematic convolutional code (RSCC) in ISI channel environments. To analyze the performance of this EPCC-RSCC concatenation, an upper union bound on the maximum-likelihood (ML) bit-error rate (BER), averaged over all possible interleavers, is derived which offers crucial insights into the error floor behavior of the matching turbo decoder. The ML bound is also used to compare the performance of EPCC-RSCC to that of a stand-alone RSCC in serial concatenation to precoded and nonprecoded ISI channels. This comparison shows that by targeting the low Hamming-weight interleaved errors of the RSCC, which result in low Euclidean distance error events in the channel detector, EPCC-RSCC exhibits a much lower BER floor compared to conventional schemes, especially for high rate applications and short interleaver lengths. The error rate performance of an iterative suboptimal turbo equalizer (TE), called TE-EPCC, is also demonstrated to converge close to the ML bound at high SNR.</P>

Soft-In Soft-Out DFE and Bi-Directional DFE

Seongwook Jeong,Jaekyun Moon IEEE 2011 IEEE TRANSACTIONS ON COMMUNICATIONS Vol.59 No.10

<P>We design a soft-in soft-out (SISO) decision feedback equalizer (DFE) that performs better than its linear counterpart in turbo equalizer (TE) setting. Unlike previously developed SISO-DFEs, the present DFE scheme relies on extrinsic information formulation that directly takes into account the error propagation effect. With this new approach, both error rate simulation and the extrinsic information transfer (EXIT) chart analysis indicate that the proposed SISO-DFE is superior to the well-known SISO linear equalizer (LE). This result is in contrast with the general understanding today that the error propagation effect of the DFE degrades the overall TE performance below that of the TE based on a LE. We also describe a new extrinsic information combining strategy involving the outputs of two DFEs running in opposite directions, that explores error correlation between the two sets of DFE outputs. When this method is combined with the new DFE extrinsic information formulation, the resulting 'bidirectional' turbo-DFE achieves excellent performance-complexity tradeoffs compared to the TE based on the BCJR algorithm or on the LE. Unlike turbo LE or turbo DFE, the turbo BiDFE's performance does not degrade significantly as the feedforward and feedback filter taps are constrained to be time-invariant.</P>

Soft-Decision-Driven Channel Estimation for Pipelined Turbo Receivers

Daejung Yoon,Jaekyun Moon IEEE 2011 IEEE TRANSACTIONS ON COMMUNICATIONS Vol.59 No.8

<P>We consider channel estimation specific to turbo equalization for multiple-input multiple-output (MIMO) wireless communication. We develop a soft-decision-driven sequential algorithm geared to the pipelined turbo equalizer architecture operating on orthogonal frequency division multiplexing (OFDM) symbols. One interesting feature of the pipelined turbo equalizer is that multiple soft-decisions become available at various processing stages. A tricky issue is that these multiple decisions from different pipeline stages have varying levels of reliability. This paper establishes an effective strategy for the channel estimator to track the target channel, while dealing with observation sets with different qualities. The resulting algorithm is basically a linear sequential estimation algorithm and, as such, is Kalman-based in nature. The main difference here, however, is that the proposed algorithm employs puncturing on observation samples to effectively deal with the inherent correlation among the multiple demapper/decoder module outputs that cannot easily be removed by the traditional innovations approach. The proposed algorithm continuously monitors the quality of the feedback decisions and incorporates it in the channel estimation process. The proposed channel estimation scheme shows clear performance advantages relative to existing channel estimation techniques.</P>