Concatenated Raptor Codes in NAND Flash Memory

Geunyeong Yu; Jaekyun Moon

Home/Archive/arXiv

arXiv · 1312.6101

Concatenated Raptor Codes in NAND Flash Memory

Geunyeong Yu·Jaekyun Moon

View original source ↗Read source document ↗Export metadata ↓

Abstract

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 allowing 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-Chaudhuri-Hocquenghem (BCH) codes.

Explore related subjects

cs.IT math.IT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Geunyeong Yu, Jaekyun Moon. 2013-12-20. Concatenated Raptor Codes in NAND Flash Memory. https://arxiv.org/abs/1312.6101

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bistatic Target Detection by Exploiting Both Deterministic Pilots and Unknown Random Data Payloads

Integrated sensing and communication (ISAC) plays a crucial role in 6G, to enable innovative applications such as drone surveillance, urban air mobility, and low-altitude logistics. However, the hybrid ISAC signal, which comprises deterministic pilot and random data payload components, poses challenges for target detection due to two reasons: 1) these two components cause coupled shifts in both the mean and variance of the received signal, and 2) the random data payloads are typically unknown to the sensing receiver in the bistatic setting. Unfortunately, these challenges could not be tackled by existing target detection algorithms. In this paper, a generalized likelihood ratio test (GLRT)-based detector is derived, by leveraging the known deterministic pilots and the statistical characteristics of the unknown random data payloads. Due to the analytical intractability of exact performance characterization, we perform an asymptotic analysis for the false alarm probability and detection probability of the proposed detector. The results highlight a critical trade-off: both deterministic and random components improve detection reliability, but the latter also brings statistical uncertainty that hinders detection performance. Simulations validate the theoretical findings and demonstrate the effectiveness of the proposed detector, which highlights the necessity of designing a dedicated detector to fully exploited the signaling resources assigned to random data payloads.

cs.IT↗

arXiv2026

On Unbiased Parameter Estimation and Signal Reconstruction

In this paper, we extend the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction for an arbitrary number of non-zero parameters. The topic touches on exact reconstructibility, most commonly studied in compressed sensing and multisource estimation across various imaging problems. The theoretical results derive upper bounds on the number of recoverable parameters in the noiseless case, and define a probability measure to assess the likelihood of recovering all non-zero parameters with correct magnitude order. The work provides a mathematical explanation of the open question regarding the noise robustness of standardized and unbiased methods. The paper also reveals a trade-off between the number of sensors and the signal-to-noise ratio. Numerical experiments demonstrate the theoretical findings.

cs.IT↗

arXiv2026

Minimum enclosing Bregman balls made easy

In this work, we revisit the problem of computing minimum enclosing Bregman balls (Bregman MEBs) of finite sets of parameters. First, we show that Bregman MEBs are equivalent to MEBs of corresponding weighted point sets with respect to the power distance. We then report an efficient Frank--Wolfe $(1+ε)$-approximation algorithm for computing power MEBs, for any $ε>0$. This power MEB approximation algorithm coincides with the Bregman MEB approximation algorithm of Nock and Nielsen (2005) when expressed in the dual gradient space. Finally, we show that the Bregman potential lifting transforms used to construct Bregman Voronoi diagrams can be reinterpreted as the classical paraboloid lifting transform applied to corresponding weighted point sets. In particular, Bregman MEB circumcenters lie on the farthest Bregman Voronoi diagrams or equivalently on the corresponding farthest power diagrams.

cs.IT↗