Kui Cai

Singapore University of Technology and Design · science and math cluster

In this work, we study two types of constraints on two-dimensional binary arrays. Given p ∈ [0, 1], ϵ ∈ [0, 1/2], we study • The p -bounded constraint: a binary vector of size n is said to be p -bounded if its weight is at most pn , • The ϵ-balanced constraint: a binary vector of size n is said to be ϵ-balanced if its weight is within [...

In this work, we propose efficient constrained coding schemes to significantly reduce the sneak path interference (SPI), a fundamental and challenging problem, in the crossbar resistive memory arrays. Particularly, we attempt to combat the sneak path effect locally as follows. For arrays of size (n \times n), we study coding methods that enforce...

In this work, we investigate a challenging problem, which has been considered to be an important criterion in designing codewords for DNA computing purposes, namely secondary structure avoidance in single-stranded DNA molecules. In short, secondary structure refers to the tendency of a single-stranded DNA sequence to fold back upon itself, thus b...

In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has undetectable errors, is performed before the outer fountain code decoding. We propose a novel and efficient de...

The maximum achievable rate is derived for resistive random-access memory (ReRAM) channel with sneak-path interference. Based on the mutual information spectrum analysis, the maximum achievable rate of ReRAM channel with independent and identically distributed (i.i.d.) binary inputs is derived as an explicit function of channel parameters such as t...

Due to the crossbar array architecture, the sneakpath problem severely degrades the data integrity in the resistive random access memory (ReRAM). In this letter, we investigate the channel quantizer design for ReRAM arrays with multiple reads, which is a typical technique to improve the data recovery performance of data storage systems. Starting wi...

In this work, we investigate a challenging problem, which has been considered to be an important criterion in designing codewords for DNA computing purposes, namely secondary structure avoidance in single-stranded DNA molecules. In short, secondary structure refers to the tendency of a single-stranded DNA sequence to fold back upon itself, thus bec...

Spin-torque transfer magnetic random access memory (STT-MRAM) is a promising emerging non-volatile memory (NVM) technology with wide applications. However, the data recovery of STT-MRAM is affected by the diversity of channel raw bit error rate (BER) across different dies caused by process variations, as well as the unknown resistance offset due to...

In this paper, we construct q -ary two-deletion correcting codes and burst-deletion correcting codes, where q ≥ 2 is an even integer. For two-deletion codes, our construction has redundancy 5 log n + O (log q log log n ) and has encoding complexity near-linear in n , where n is the length of the message sequences. For burst-deletion...

In this work, we present a new version of non-binary VT codes that are capable of correcting a single deletion or single insertion. Moreover, we provide the first known linear time algorithms that encode user messages into these codes of length n over the $q$-ary alphabet for $q\ge 2$ with at most $\ceil{\log_q n} + 1$ redundant symbols, while the...

Aiming to improve the error correction performance of polar codes, researchers have proposed employing the product coding structure involving RS codes of different rates in the horizontal direction and the short polar codewords along the vertical direction. However, there is no efficient algorithm optimizing the rate allocation of RS codes. In orde...

In this paper, we construct systematic $q$-ary two-deletion correcting codes and burst-deletion correcting codes, where $q\geq 2$ is an even integer. For two-deletion codes, our construction has redundancy $5\log n+O(\log q\log\log n)$ and has encoding complexity near-linear in $n$, where $n$ is the length of the message sequences. For burst-deleti...

In this paper, we propose a finite alphabet iterative decoder (FAID) named rate-compatible mutual-information-maximizing quantized shuffled min-sum (RC-MIM-QSMS) decoder, for decoding quasi-cyclic low-density parity-check (QC-LDPC) codes with various code rates. Our proposed decoder exchanges the coarsely quantized messages represented by symbols f...

We consider construction of deletion and substitution correcting codes with low redundancy and efficient encoding/ decoding. First, by simplifying the method of Sima et al . (ISIT 2020), we construct a family of binary single-deletion $s$ -substitution correcting codes with redundancy $(s+1) (2s+1)\log _{2} n+o(\log _{2} n)$ and encoding comp...

Resistive random-access memory (ReRAM) is an emerging non-volatile memory technology for high-density and high-speed data storage. However, the sneak path interference (SPI) occurred in the ReRAM crossbar array seriously affects its data recovery performance. In this letter, we first propose a quantized channel model of ReRAM, based on which we des...

In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,\epsilon>0$, we study (i) The $p$-bounded constraint: a binary vector of size $m$ is said to be $p$-bounded if its weight is at most $pm$, and (ii) The $\epsilon$-balanced constraint: a binary vector of size $m$ is said to be $\epsilon$-balance...

In this paper, we propose a framework of the mutual information-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes by using simple mappings and fixed-point additions. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and can be implemented based on either...

In this work, given n,ϵ > 0, two efficient encoding (decoding) methods are presented for mapping arbitrary data to (from) n×n binary arrays in which the weight of every row and every column is within [(1/2–ϵ)n, (1/2+ϵ)n], which is referred to as the ϵ-balanced constraint. The first method combines the divide and conquer algorithm and a modification...

Advances in synthesis and sequencing technologies have made DNA macromolecules an attractive medium for digital information storage. Compared with the ex vivo method that stores data in a non-biological environment, there have been considerations and attempts to store data in living organisms, also known as the in vivo method or live DNA due to sev...

In this letter, we propose a two-stage design method to construct memory efficient mutual information-maximizing quantized min-sum (MIM-QMS) decoder for rate-compatible low-density parity-check (LDPC) codes. We first develop a modified density evolution to design a unique set of lookup tables (LUTs) that can be used for rate-compatible LDPC codes....

Resistive random access memory (ReRAM) is a promising emerging non-volatile memory (NVM) technology that shows high potential for both data storage and computing. However, its crossbar array architecture leads to the sneak path (SP) problem, which may severely degrade the data storage reliability of ReRAM. Due to the complicated nature of the SP-in...

Despite the great promises that the resistive random access memory (ReRAM) has shown as the next generation of non-volatile memory technology, its crossbar array structure leads to a severe sneak path interference to the signal read back from the memory cell. In this paper, we first propose a novel belief propagation (BP) based detector for the sne...

In this letter, we propose a two-stage design method to construct memory efficient mutual information-maximizing quantized min-sum (MIM-QMS) decoder for rate-compatible low-density parity-check (LDPC) codes. We first develop a modified density evolution to design a unique set of lookup tables (LUTs) that can be used for rate-compatible LDPC codes....

In this paper, we present an explicit construction of list-decodable codes for single-deletion and single-substitution with list size two and redundancy 3log n+4, where n is the block length of the code. Our construction has lower redundancy than the best known explicit construction by Gabrys et al. (arXiv 2021), whose redundancy is 4log n+O(1).

Resistive random-access memory is one of the most promising candidates for the next generation of non-volatile memory technology. However, its crossbar array structure causes severe “sneak-path" interference, which also leads to strong inter-cell correlation. Recent works have mainly focused on sub-optimal data detection schemes by ignoring inter-c...

The error‐correcting performance of multi‐level‐cell (MLC) NAND flash memory is closely related to the block length of error‐correcting codes (ECCs) and log‐likelihood‐ratios of the read‐voltage thresholds. Driven by this issue, this paper optimizes the read‐voltage thresholds for MLC flash memory to improve the decoding performance of ECCs with fi...

The subblock energy-constrained codes (SECCs) and sliding window-constrained codes (SWCCs) have recently attracted attention due to various applications in communication systems such as simultaneous energy and information transfer. In a SECC, each codeword is divided into smaller non-overlapping windows, called subblocks, and every subblock is cons...

Despite the great promises that the resistive random access memory (ReRAM) has shown as the next generation of non-volatile memory technology, its crossbar array structure leads to a severe sneak path interference to the signal read back from the memory cell. In this paper, we first propose a novel belief propagation (BP) based detector for the sne...

We present coding methods for generating ℓ-symbol constrained codewords taken from a set, S, of allowed codewords. In standard practice, the size of the set S, denoted by M=|S|, is truncated to an integer power of two, which may lead to a serious waste of capacity. We present an efficient and low-complexity coding method for avoiding the truncation...

Consider the computations at a node in a message passing algorithm. Assume that the node has incoming and outgoing messages x = (x1, x2, xn) and y = (y1, y2, yn), respectively. In this paper, we investigate a class of structures that can be adopted by the node for computing y from x, where each yj, j = 1, 2, ..., n is computed via a binary tree wit...

Resistive random-access memory (ReRAM) is a promising non-volatile memory technology for achieving high-density and high-speed data storage. However, its crossbar array structure leads to a severe problem known as the sneak path interference (SPI), which is data dependent and correlated within a memory array. Meanwhile, variations of the memory fab...

We investigate a basic decentralized caching network with coded prefetching under nonuniform requests and arbitrary file popularities, where a server containing $N$ files is connected to $K$ users, each with limited cache memory of $M$ files through a shared link. In the decentralized placement phase, the server encodes all files by the maxim...

We propose coding techniques that simultaneously limit the length of homopolymers runs, ensure the GC-content constraint, and are capable of correcting a single edit error in strands of nucleotides in DNA-based data storage systems. In particular, for given l , ∈ > 0, we propose simple and efficient encoders/decoders that transform binary sequenc...

In this work, given n, p>0 , efficient encoding/decoding algorithms are presented for mapping arbitrary data to and from n×n binary arrays in which the weight of every row and every column is at most pn. Such constraint, referred as p-bounded-weight-constraint, is crucial for reducing the parasitic currents in the crossbar resistive memory arrays,...

In this article, under a general cost function $C$ , we present a dynamic programming (DP) method to obtain an optimal sequential deterministic quantizer (SDQ) for $q$ -ary input discrete memoryless channel (DMC). The DP method has complexity $O(q (N-M)^{2}\,\,M)$ , where $N$ and $M$ are the alphabet sizes of the DMC output and quantizer...

As an emerging non-volatile memory (NVM) technology, spin-torque transfer magnetic random access memory (STT-MRAM) has received great attention in recent years since it combines the features of low switching energy, fast write/read speed, and high scalability. However, process variation and thermal fluctuation severely affect the data integrity of...

We investigate a new approach for designing spectral shaping block codes with a target spectrum, H_t(f), that has been specified at a plurality of frequencies. We analyze the probability density function of the spectral power density function of uncoded n-symbol bipolar code words. We present estimates of the redundancy and the spectrum of spectral...

Resistive random-access memory is one of the most promising candidates for the next generation of non-volatile memory technology. However, its crossbar structure causes severe "sneak-path" interference, which also leads to strong inter-cell correlation. Recent works have mainly focused on sub-optimal data detection schemes by ignoring inter-cell co...

Resistive random-access memory (ReRAM) is a promising candidate for the next generation non-volatile memory technology due to its simple read/write operations and high storage density. However, its crossbar array structure causes a severe interference effect known as the “sneak path.” In this paper, we propose channel coding techniques that can mit...

This paper proposes novel methods for designing two-dimensional (2-D) weight-constrained codes for reducing the parasitic currents in the crossbar resistive memory array. In particular, we present efficient encoding/decoding algorithms for capacity-approaching 2-D weight-constrained codes of size m×n, where each row has a weight pn with p < 1/2; an...

An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this article, we investigate codes that correct either a single indel or a single edit and provide linear-time algorithms that encode binary messages into these codes of length n. Over the quaternary alphabet, we provide two l...

The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. The common setup assumes the codebook to be the entire space and the problem is to determine the minimum number of distinct...

In this paper, we propose a general framework of the mutual infomration-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes, which can outperform the state-of-the-art lookup table (LUT) decoder by using simple mappings and fixed-point additions for the node updates. Our decoding method is generic in the sense that it can b...

This paper investigates a cache-aided cloud radio access network (C-RAN), comprising a central unit, K base stations (BSs) each with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> antennas, and M users each with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3...

Energy-harvesting sliding-window constrained block codes guarantee that within any prescribed window of ℓ consecutive bits the constrained sequence has at least t, t≥1, 1’s. Prior art code design methods build upon the finite-state machine description of the (ℓ,t) constraint, but as the number of states equals ℓ choose t, a code design becomes proh...

Structured Gaussian elimination (SGE) is a class of methods for efficiently solving sparse linear systems. The key idea is to first triangulate the original linear systems. The maximum component (MC)-based strategies are widely used to implement the triangulation process. The most straightforward way to find the MC is through exhaustive search. Ins...

The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes for DNA storage channel, a new metric, termed the sequence-subset distance , is introduced, which generalize...

The subblock energy-constrained codes (SECCs) and sliding window-constrained codes (SWCCs) have recently attracted attention due to various applications in communcation systems such as simultaneous energy and information transfer. In a SECC, each codewod is divided into smaller non-overlapping windows, called subblocks, and every subblock is constr...

Consider the computations at a node in the message passing algorithms. Assume that the node has incoming and outgoing messages $\mathbf{x} = (x_1, x_2, \ldots, x_n)$ and $\mathbf{y} = (y_1, y_2, \ldots, y_n)$, respectively. In this paper, we investigate a class of structures that can be adopted by the node for computing $\mathbf{y}$ from $\mathbf{x...

Thanks to its superior features of fast read/write speed and low power consumption, spin-torque transfer magnetic random access memory (STT-MRAM) has become a promising non-volatile memory (NVM) technology that is suitable for many applications. However, the reliability of STT-MRAM is seriously affected by the variation of the memory fabrication pr...

We study properties and constructions of constrained binary codes that enable simultaneous energy and information transfer. We specifically study sliding-window constrained codes that guarantee that within any prescribed window of ℓ consecutive bits the constrained sequence has at least t, t > 1, 1’s. We present a K-state source, K = ℓ choose t, th...

Decoders minimizing the Euclidean distance between the received word and the candidate codewords are known to be optimal for channels suffering from Gaussian noise. However, when the stored or transmitted signals are also corrupted by an unknown offset, other decoders may perform better. In particular, applying the Euclidean distance on normalized...

Although studying in multiple-deletion correcting codes has made great progress in recent years, studying in codes correcting multiple deletions and substitutions simultaneously still in its beginning. Recent work by Smagloy et al. [12] gives a construction of single-deletion and single-substitution codes with redundancy 6log n + 8, where n is the...

Motivated by the application of fountain codes in the DNA-based data storage systems, in this paper, we consider the decoding of fountain codes when the received symbols have a chance to be incorrect. Unlike the conventional scenario where the received symbols are all error-free, the maximum likelihood (ML) decoding and maximum a posterior probabil...

The subblock energy-constrained codes (SECCs) have recently attracted attention due to various applications in communication systems such as simultaneous energy and information transfer. In a SECC, each codeword is divided into smaller subblocks, and every subblock is constrained to carry sufficient energy. In this work, we study SECCs under more g...

In this paper, we first propose coding techniques for DNA-based data storage which account the maximum homopolymer runlength and the GC-content. In particular, for arbitrary $\ell,\epsilon > 0$, we propose simple and efficient $(\epsilon, \ell)$-constrained encoders that transform binary sequences into DNA base sequences (codewords), that satisfy t...

Resistive random-access memory (ReRAM) is a promising candidate for the next generation non-volatile memory technology due to its simple read-write operation and high storage density. However, its crossbar array structure causes a server interference effect known as the "sneak path." In this paper, we address the sneak-path problem based on communi...

The error correcting performance of multi-level-cell (MLC) NAND flash memory is closely related to the block length of error correcting codes (ECCs) and log-likelihood-ratios (LLRs) of the read-voltage thresholds. Driven by this issue, this paper optimizes the read-voltage thresholds for MLC flash memory to improve the decoding performance of ECCs...

Power line communication (PLC) advances smart grid technology by offering a convenient and efficient data transmission service. However, due to the severe PLC channel condition and ever-growing traffic load in the PLC backhaul, reliable communications among widely distributed in-home PLC users is highly energy-consuming. In this paper, we put forth...

We describe properties and constructions of constraint-based codes for DNA-based data storage which account for the maximum repetition length and AT/GC balance. Generating functions and approximations are presented for computing the number of sequences with maximum repetition length and AT/GC balance constraint. We describe routines for translating...

The practical NAND flash memory suffers from various non-stationary noises that are difficult to be predicted. For example, the data retention noise induced channel offset is unknown during the readback process, and hence severely affects the reliability of data recovery from the memory cell. In this paper, we first propose a novel recurrent neural...

The subblock energy-constrained codes (SECCs) have recently attracted attention due to various applications in communication systems such as simultaneous energy and information transfer. In a SECC, each codeword is divided into smaller subblocks, and every subblock is constrained to carry sufficient energy. In this work, we study SECCs under more g...

We report on the feasibility of k-means clustering techniques for the dynamic threshold detection of encoded q-ary symbols transmitted over a noisy channel with partially unknown channel parameters. We first assess the performance of k-means clustering technique without dedicated constrained coding. We apply constrained codes which allows a wider r...

Consider a centralized caching network with a single server and $K$ users. The server has a database of $N$ files with each file being divided into $F$ packets ($F$ is known as subpacketization), and each user owns a local cache that can store $\frac{M}{N}$ fraction of the $N$ files. We construct a family of centralized coded caching schemes with p...

An efficient concatenation of error correction codes with constrained codes is proposed in this paper. Generally, constrained codes are designed to match specified channels, whereas error correction coding schemes are designed to correct the channel errors. They both play important roles to ensure the integrity of data in data storage systems. In t...

A very low-complexity on-off division multiple access (ODMA) scheme is proposed for K-user non-orthogonal multiple access (NOMA) systems. At the transmission side, each user employs the same length-m channel code whose coded bits, after modulation, are sent in a random time-hopping manner. Specifically, m coded bits are randomly scheduled and sent...

We propose coding techniques that limit the length of homopolymers runs, ensure the GC-content constraint, and are capable of correcting a single edit error in strands of nucleotides in DNA-based data storage systems. In particular, for given $\ell, {\epsilon} > 0$, we propose simple and efficient encoders/decoders that transform binary sequences i...

The protograph low‐density parity‐check (LDPC) codes possess many attractive properties, such as the low encoding/decoding complexity and better error floor performance, and hence have been successfully applied to different types of communication and data storage channels. In this study, the authors design protograph LDPC codes for communication sy...

Thanks to its superior features of non-volatility, fast read/write speed, high endurance, and low power consumption, spin-torque transfer magnetic random access memory (STT-MRAM) has become a promising candidate for the next generation non-volatile memories (NVMs) and storage class memories (SCMs). However, it has been found that the write errors a...

As emerging memories such as spin-torque transfer magnetic random access memory (STT-MRAM) suffer from reliability issues caused by process variations and thermal fluctuations, the design of channel quantizer with the minimum number of quantization bits is critical to support effective error correction coding for ensuring high-density and high-spee...

We analyze codes for DNA-based data storage which accounts for the maximum homopolymer repetition length and GC-AT balance. We present a new precoding method for translating words with a maximum run of k zeros into words with a maximum homopolymer run m = k + 1, which is atractive for securing GC-AT balance. Generating functions are presented for e...

Mobile edge computing (MEC) provides computational services at the edge of networks by offloading tasks from user equipments (UEs). This letter employs an unmanned aerial vehicle (UAV) as the edge computing server to execute offloaded tasks from the ground UEs. We jointly optimize user association, UAV trajectory, and uploading power of each UE to...

This letter studies a basic wireless caching network where a source server is connected to a cache-enabled base station (BS) that serves multiple requesting users. A critical problem is how to improve cache hit rate under dynamic content popularity. To solve this problem, the primary contribution of this work is to develop a novel dynamic content u...