arXiv subjects

Kui Cai

Publications and source records attributed to Kui Cai.

At least 37 records · Page 2Linked to original sources

arXiv2024

Deep-Learning-Based Adaptive Error-Correction Decoding for Spin-Torque Transfer Magnetic Random Access Memory (STT-MRAM)

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 temperature change. Therefore, it is critical to develop effective decoding algorithms of error correction codes (ECCs) for STT-MRAM. In this article, we first propose a neural bit-flipping (BF) decoding algorithm, which can share the same trellis representation as the state-of-the-art neural decoding algorithms, such as the neural belief propagation (NBP) and neural offset min-sum (NOMS) algorithm. Hence, a neural network (NN) decoder with a uniform architecture but different NN parameters can realize all these neural decoding algorithms. Based on such a unified NN decoder architecture, we further propose a novel deep-learning (DL)-based adaptive decoding algorithm whose decoding complexity can be adjusted according to the change of the channel conditions of STT-MRAM. Extensive experimental evaluation results demonstrate that the proposed neural decoders can greatly improve the performance over the standard decoders, with similar decoding latency and energy consumption. Moreover, the DL-based adaptive decoder can work well over different channel conditions of STT-MRAM irrespective of the unknown resistance offset, with a 50% reduction of the decoding latency and energy consumption compared to the fixed decoder.

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arXiv2024

New Construction of $q$-ary Codes Correcting a Burst of at most $t$ Deletions

In this paper, for any fixed positive integers $t$ and $q>2$, we construct $q$-ary codes correcting a burst of at most $t$ deletions with redundancy $\log n+8\log\log n+o(\log\log n)+γ_{q,t}$ bits and near-linear encoding/decoding complexity, where $n$ is the message length and $γ_{q,t}$ is a constant that only depends on $q$ and $t$. In previous works there are constructions of such codes with redundancy $\log n+O(\log q\log\log n)$ bits or $\log n+O(t^2\log\log n)+O(t\log q)$. The redundancy of our new construction is independent of $q$ and $t$ in the second term.

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arXiv2023

A New Version of q-ary Varshamov-Tenengolts Codes with More Efficient Encoders: The Differential VT Codes and The Differential Shifted VT Codes

The problem of correcting deletions and insertions has recently received significantly increased attention due to the DNA-based data storage technology, which suffers from deletions and insertions with extremely high probability. In this work, we study the problem of constructing non-binary burst-deletion/insertion correcting codes. Particularly, for the quaternary alphabet, our designed codes are suited for correcting a burst of deletions/insertions in DNA storage. Non-binary codes correcting a single deletion or insertion were introduced by Tenengolts [1984], and the results were extended to correct a fixed-length burst of deletions or insertions by Schoeny et al. [2017]. Recently, Wang et al. [2021] proposed constructions of non-binary codes of length n, correcting a burst of length at most two for q-ary alphabets with redundancy log n+O(log q log log n) bits, for arbitrary even q. The common idea in those constructions is to convert non-binary sequences into binary sequences, and the error decoding algorithms for the q-ary sequences are mainly based on the success of recovering the corresponding binary sequences, respectively. In this work, we look at a natural solution in which the error detection and correction algorithms are performed directly over q-ary sequences, and for certain cases, our codes provide a more efficient encoder with lower redundancy than the best-known encoder in the literature.

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arXiv2023

On the Design of Codes for DNA Computing: Secondary Structure Avoidance Codes

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 becoming inactive in the computation process. While some design criteria that reduces the possibility of secondary structure formation has been proposed by Milenkovic and Kashyap (2006), the main contribution of this work is to provide an explicit construction of DNA codes that completely avoid secondary structure of arbitrary stem length. Formally, given codeword length n and arbitrary integer m>=2, we provide efficient methods to construct DNA codes of length n that avoid secondary structure of any stem length more than or equal to m. Particularly, when m = 3, our constructions yield a family of DNA codes of rate 1.3031 bits/nt, while the highest rate found in the prior art was 1.1609 bits/nt. In addition, for m>=3log n + 4, we provide an efficient encoder that incurs only one redundant symbol.

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arXiv2023

Basis-Finding Algorithm for Decoding Fountain Codes for DNA-Based Data Storage

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 decoding algorithm, namely basis-finding algorithm (BFA), followed by three implementations. The key idea of the BFA is to find a basis of the received symbols, and then use the most reliable basis elements to recover the source symbols with the inactivation decoding. Gaussian elimination is used to find the basis and to identify the most reliable basis elements. As a result, the BFA has polynomial time complexity. For random fountain codes, we are able to derive some theoretical bounds for the frame error rate (FER) of the BFA. Extensive simulations with Luby transform (LT) codes show that, the BFA has significantly lower FER than the belief propagation (BP) algorithm except for an extremely large amount of received symbols, and the FER of the BFA generally decreases as the average weight of basis elements increases.

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arXiv2022

Every Bit Counts: A New Version of Non-binary VT Codes with More Efficient Encoder

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 optimal redundancy required is at least $\log_q n + \log_q (q - 1)$ symbols. Our designed encoder reduces the redundancy of the best-known encoder of Tenengolts (1984) by at least $2+\log_q(3)$ redundant symbols, or equivalently $2\log_2 q+3$ redundant bits.

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arXiv2022

Mutual Information-Maximizing Quantized Belief Propagation Decoding of Regular LDPC Codes

In this paper, we propose a class of finite alphabet iterative decoder (FAID), called mutual information-maximizing quantized belief propagation (MIM-QBP) decoder, for decoding regular low-density parity-check (LDPC) codes. Our decoder follows the reconstruction-calculation-quantization (RCQ) decoding architecture that is widely used in FAIDs. We present the first complete and systematic design framework for the RCQ parameters, and prove that our design with sufficient precision at node update is able to maximize the mutual information between coded bits and exchanged messages. Simulation results show that the MIM-QBP decoder can always considerably outperform the state-of-the-art mutual information-maximizing FAIDs that adopt two-input single-output lookup tables for decoding. Furthermore, with only 3 bits being used for each exchanged message, the MIM-QBP decoder can outperform the floating-point belief propagation decoder at the high signal-to-noise ratio regions when testing on high-rate LDPC codes with a maximum of 10 and 30 iterations.

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arXiv2022

Non-binary Two-Deletion Correcting Codes and Burst-Deletion Correcting Codes

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-deletion codes, we first present a construction of binary codes with redundancy $\log n+9\log\log n+γ_t+o(\log\log n)$ bits $(γ_t$ is a constant that depends only on $t)$ and capable of correcting a burst of at most $t$ deletions, which improves the Lenz-Polyanskii Construction (ISIT 2020). Then we give a construction of $q$-ary codes with redundancy $\log n+(8\log q+9)\log\log n+o(\log q\log\log n)+γ_t$ bits and capable of correcting a burst of at most $t$ deletions.

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arXiv2022

Two dimensional RC/Subarray Constrained Codes: Bounded Weight and Almost Balanced Weight

In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,ε>0$, 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 $ε$-balanced constraint: a binary vector of size $m$ is said to be $ε$-balanced if its weight is within $[(0.5-ε)*m,(0.5+ε)*m]$. Such constraints are crucial in several data storage systems, those regard the information data as two-dimensional (2D) instead of one-dimensional (1D), such as the crossbar resistive memory arrays and the holographic data storage. In this work, efficient encoding/decoding algorithms are presented for binary arrays so that the weight constraint (either $p$-bounded constraint or $ε$-balanced constraint) is enforced over every row and every column, regarded as 2D row-column (RC) constrained codes; or over every subarray, regarded as 2D subarray constrained codes. While low-complexity designs have been proposed in the literature, mostly focusing on 2D RC constrained codes where $p = 1/2$ and $ε= 0$, this work provides efficient coding methods that work for both 2D RC constrained codes and 2D subarray constrained codes, and more importantly, the methods are applicable for arbitrary values of $p$ and $ε$. Furthermore, for certain values of $p$ and $ε$, we show that, for sufficiently large array size, there exists linear-time encoding/decoding algorithm that incurs at most one redundant bit.

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arXiv2022

Generalized Mutual Information-Maximizing Quantized Decoding of LDPC Codes with Layered Scheduling

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 the belief propagation (BP) algorithm or the min-sum (MS) algorithm. In particular, we propose the MIM density evolution (MIM-DE) to construct the lookup tables (LUTs) for the node updates. The computational complexity and memory requirements are discussed and compared to the LUT decoder variants. For applications with low-latency requirement, we consider the layered schedule to accelerate the convergence speed of decoding quasi-cyclic LDPC codes. In particular, we develop the layered MIM-DE to design the LUTs based on the MS algorithm, leading to the MIM layered quantized MS (MIM-LQMS) decoder. An optimization method is further introduced to reduce the memory requirement for storing the LUTs. Simulation results show that the MIM quantized decoders outperform the state-of-the-art LUT decoders in the waterfall region with both 3-bit and 4-bit precision over the additive white Gaussian noise channels. For small decoding iterations, the MIM quantized decoders also achieve a faster convergence speed compared to the benchmarks. Moreover, the 4-bit MIM-LQMS decoder can approach the error performance of the floating-point layered BP decoder within 0.3 dB in the moderate-to-high SNR regions, over both the AWGN channels and the fast fading channels.

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arXiv2022

List-decodable Codes for Single-deletion Single-substitution with List-size Two

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).

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arXiv2022

Memory Efficient Mutual Information-Maximizing Quantized Min-Sum Decoding for Rate-Compatible LDPC Codes

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. The constructed LUTs are optimized based on their discrepancy values and a merge function to reduce the memory requirement. Numerical results show that the proposed rate-compatible MIM-QMS decoder can reduce the memory requirement for decoding by up to 94.92% compared to the benchmark rate-compatible LUT-based decoder with generally faster convergence speed. In addition, the proposed decoder can approach the performance of the floating-pointing belief propagation decoder within 0.15 dB.

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arXiv2021

Belief Propagation based Joint Detection and Decoding for Resistive Random Access Memories

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 sneak path interference in ReRAM. Based on the conditions for a sneak path to occur and the dependence of the states of the memory cells that are involved in the sneak path, a Tanner graph for the ReRAM channel is constructed, inside which specific messages are updated iteratively to get a better estimation of the sneak path affected cells. We further combine the graph of the designed BP detector with that of the BP decoder of the polar codes to form a joint detector and decoder. Tailored for the joint detector and decoder over the ReRAM channel, effective polar codes are constructed using the genetic algorithm. Simulation results show that the BP detector can effectively detect the cells affected by the sneak path, and the proposed polar codes and the joint detector and decoder can significantly improve the error rate performance of ReRAM.

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arXiv2021

A Class of Optimal Structures for Node Computations in Message Passing Algorithms

Consider the computations at a node in a message passing algorithm. 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 $\mathbf{x}$, where each $y_j, j = 1, 2, \ldots, n$ is computed via a binary tree with leaves $\mathbf{x}$ excluding $x_j$. We make three main contributions regarding this class of structures. First, we prove that the minimum complexity of such a structure is $3n - 6$, and if a structure has such complexity, its minimum latency is $δ+ \lceil \log(n-2^δ) \rceil$ with $δ= \lfloor \log(n/2) \rfloor$, where the logarithm always takes base two. Second, we prove that the minimum latency of such a structure is $\lceil \log(n-1) \rceil$, and if a structure has such latency, its minimum complexity is $n \log(n-1)$ when $n-1$ is a power of two. Third, given $(n, τ)$ with $τ\geq \lceil \log(n-1) \rceil$, we propose a construction for a structure which we conjecture to have the minimum complexity among structures with latencies at most $τ$. Our construction method runs in $O(n^3 \log^2(n))$ time, and the obtained structure has complexity at most (generally much smaller than) $n \lceil \log(n) \rceil - 2$.

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arXiv2021

Dynamic Programming for Sequential Deterministic Quantization of Discrete Memoryless Channels

In this paper, 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 output, respectively. Then, starting from the quadrangle inequality, two techniques are applied to reduce the DP method's complexity. One technique makes use of the Shor-Moran-Aggarwal-Wilber-Klawe (SMAWK) algorithm and achieves complexity $O(q (N-M) M)$. The other technique is much easier to be implemented and achieves complexity $O(q (N^2 - M^2))$. We further derive a sufficient condition under which the optimal SDQ is optimal among all quantizers and the two techniques are applicable. This generalizes the results in the literature for binary-input DMC. Next, we show that the cost function of $α$-mutual information ($α$-MI)-maximizing quantizer belongs to the category of $C$. We further prove that under a weaker condition than the sufficient condition we derived, the aforementioned two techniques are applicable to the design of $α$-MI-maximizing quantizer. Finally, we illustrate the particular application of our design method to practical pulse-amplitude modulation systems.

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arXiv2021

Near-Optimal Detection for Both Data and Sneak-Path Interference in Resistive Memories with Random Cell Selector Failures

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 correlation and treating sneak-path interference as independent noise. We propose a near-optimal data detection scheme that can approach the performance bound of the optimal detection scheme. Our detection scheme leverages a joint data and sneak-path interference recovery and can use all inter-cell correlations. The scheme is appropriate for data detection of large memory arrays with only linear operation complexity.

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arXiv2020

Systematic Single-Deletion Multiple-Substitution Correcting Codes

Recent work by Smagloy et al. (ISIT 2020) shows that the redundancy of a single-deletion $s$-substitution correcting code is asymptotically at least $(s+1)\log n+o(\log n)$, where $n$ is the length of the codes. They also provide a construction of single-deletion and single-substitution codes with redundancy $6\log n+8$. In this paper, we propose a family of systematic single-deletion $s$-substitution correcting codes of length $n$ with asymptotical redundancy at most $(3s+4)\log n+o(\log n)$ and polynomial encoding/decoding complexity, where $s\geq 2$ is a constant. Specifically, the encoding and decoding complexity of the proposed codes are $O(n^{s+3})$ and $O(n^{s+2})$, respectively.

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arXiv2020

Performance Limit and Coding Schemes for Resistive Random-Access Memory Channels

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 mitigate both the sneak-path interference and the channel noise. The main challenge is that the sneak-path interference is data-dependent, and also correlated within a memory array, and hence the conventional error correction coding scheme will be inadequate. In this work, we propose an across-array coding strategy that assigns a codeword to multiple independent memory arrays, and exploit a real-time channel estimation scheme to estimate the instantaneous status of the ReRAM channel. Since the coded bits from different arrays experience independent channels, a "diversity" gain can be obtained during decoding, and when the codeword is adequately distributed over different memory arrays, the code actually performs as that over an uncorrelated channel. By performing decoding based on the scheme of treating-interference-as-noise (TIN), the ReRAM channel over different memory arrays is equivalent to a block varying channel we defined, for which we propose both the capacity bounds and a coding scheme. The proposed coding scheme consists of a serial concatenation of an optimized error correction code with a data shaper, which enables the ReRAM system to achieve a near capacity limit storage efficiency.

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