相关论文: The E8 Lattice and Error Correction in Multi-Level…

A rewriting code construction for flash memories based upon lattices is described. The values stored in flash cells correspond to lattice points. This construction encodes information to lattice points in such a way that data can be written…

For communication systems with heavy burst noise, an optimal Forward Error Correction (FEC) scheme is expected to have a large burst error correction capacity while simultaneously owning moderate random error correction capability. This…

Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either naive modulation or its concatenation with error correction codes (ECC). This paper shows that lattice coding, as a joint ECC and modulation…

We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked…

With the ever-growing storage density, high-speed, and low-cost data access, flash memory has inevitably become popular. Multi-level cell (MLC) NAND flash memory, which can well balance the data density and memory stability, has occupied…

We consider FrodoKEM, a lattice-based cryptosystem based on LWE, and propose a new error correction mechanism to improve its performance. Our encoder maps the secret key block-wise into the Gosset lattice $E_8$. We propose two sets of…

Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…

We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables to store the constellation points and constellation bit labeling. To…

Reducing the threshold voltage of electronic devices increases their sensitivity to electromagnetic radiation dramatically, increasing the probability of changing the memory cells' content. Designers mitigate failures using techniques such…

Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…

In the information explosion era, the demand for high-density stable storage technologies is soaring. Multi-dimensional optical storage with femtosecond laser writing offers a potential solution for massive data storage. However, equipment…

In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…

A genie-aided decoder for finite dimensional lattice codes is considered. The decoder may exhaustively search through all possible scaling factors $\alpha \in \mathbb{R}$. We show that this decoder can achieve lower word error rate (WER)…

Block codes, which correct asymmetric errors with limited-magnitude, are studied. These codes have been applied recently for error correction in flash memories. The codes will be represented by lattices and the constructions will be based…

We propose a lattice-theoretic framework for modulo sampling of multidimensional bandlimited signals. Standard modulo analog-to-digital converters (ADCs) fold the signal component-wise into a square domain, reducing the recovery problem to…

Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…

Multiple reads of the same Flash memory cell with distinct word-line voltages provide enhanced precision for LDPC decoding. In this paper, the word-line voltages are optimized by maximizing the mutual information (MI) of the quantized…

Lattice codes with optimal decoding coefficient are capacity-achieving when dimension $N \rightarrow \infty$. In communications systems, finite dimensional lattice codes are considered, where the optimal decoding coefficients may still fail…

We study error-correcting codes for permutations under the infinity norm, motivated by a novel storage scheme for flash memories call rank modulation. In this scheme, a set of $n$ flash cells are combined to create a single virtual…