arXiv subjects

Anxiao Jiang

Publications and source records attributed to Anxiao Jiang.

9 recordsLinked to original sources

arXiv2026

A New Class of Geometric Analog Error Correction Codes for Crossbar Based In-Memory Computing

Analog error correction codes have been proposed for analog in-memory computing on resistive crossbars, which can accelerate vector-matrix multiplication for machine learning. Unlike traditional communication or storage channels, this setting involves a mixed noise model with small perturbations and outlier errors. A number of analog codes have been proposed for handling a single outlier, and several constructions have also been developed to address multiple outliers. However, the set of available code families remains limited, covering only a narrow range of code lengths and dimensions. In this paper, we study a recently proposed family of geometric codes capable of handling multiple outliers, and develop a geometric analysis that characterizes their m-height profiles.

cs.IT↗

arXiv2026

On the Height Profile of Analog Error-Correcting Codes

In recent work, it has been shown that maintaining reliability in analog vector--matrix multipliers can be modeled as the following coding problem. Vectors in $\mathbb{R}^k$ are encoded into codewords of a linear $[n,k,d]$ code $C$ over $\mathbb{R}$. For prescribed positive reals $δ< Δ$, additive errors of magnitude at most $δ$ are tolerable and need no handling, yet outlying errors of magnitude greater than $Δ$ are to be located or detected. The trade-off between the ratio $Δ/δ$ and the number of outlying errors that can be handled is determined by the height profile of $C$; as such, the height profile provides a finer description of the error handling capability of $C$, compared to the minimum distance $d$, which only determines the number of correctable errors. This work contains a further study of the notion of the height profile. Several characterizations of the height profile are presented, thereby yielding methods for computing it. The starting point is formulating this computation as an optimization problem that is solved by a set of linear programs. This, in turn, leads to a combinatorial characterization of the height profile as a maximum (or max--min) over a certain finite set of codewords of $C$. Moreover, this characterization is shown to have a simple geometric interpretation when the columns of the generator matrix of $C$ all have the same $L_2$ norm. Through examples of several code families, it is demonstrated how the results herein can be used to compute the height profile explicitly.

cs.IT↗

arXiv2023

CODA: Temporal Domain Generalization via Concept Drift Simulator

In real-world applications, machine learning models often become obsolete due to shifts in the joint distribution arising from underlying temporal trends, a phenomenon known as the "concept drift". Existing works propose model-specific strategies to achieve temporal generalization in the near-future domain. However, the diverse characteristics of real-world datasets necessitate customized prediction model architectures. To this end, there is an urgent demand for a model-agnostic temporal domain generalization approach that maintains generality across diverse data modalities and architectures. In this work, we aim to address the concept drift problem from a data-centric perspective to bypass considering the interaction between data and model. Developing such a framework presents non-trivial challenges: (i) existing generative models struggle to generate out-of-distribution future data, and (ii) precisely capturing the temporal trends of joint distribution along chronological source domains is computationally infeasible. To tackle the challenges, we propose the COncept Drift simulAtor (CODA) framework incorporating a predicted feature correlation matrix to simulate future data for model training. Specifically, CODA leverages feature correlations to represent data characteristics at specific time points, thereby circumventing the daunting computational costs. Experimental results demonstrate that using CODA-generated data as training input effectively achieves temporal domain generalization across different model architectures.

cs.LG↗

arXiv2020

CodNN -- Robust Neural Networks From Coded Classification

Deep Neural Networks (DNNs) are a revolutionary force in the ongoing information revolution, and yet their intrinsic properties remain a mystery. In particular, it is widely known that DNNs are highly sensitive to noise, whether adversarial or random. This poses a fundamental challenge for hardware implementations of DNNs, and for their deployment in critical applications such as autonomous driving. In this paper we construct robust DNNs via error correcting codes. By our approach, either the data or internal layers of the DNN are coded with error correcting codes, and successful computation under noise is guaranteed. Since DNNs can be seen as a layered concatenation of classification tasks, our research begins with the core task of classifying noisy coded inputs, and progresses towards robust DNNs. We focus on binary data and linear codes. Our main result is that the prevalent parity code can guarantee robustness for a large family of DNNs, which includes the recently popularized binarized neural networks. Further, we show that the coded classification problem has a deep connection to Fourier analysis of Boolean functions. In contrast to existing solutions in the literature, our results do not rely on altering the training process of the DNN, and provide mathematically rigorous guarantees rather than experimental evidence.

cs.LG↗

arXiv2019

Machine Learning for Error Correction with Natural Redundancy

The persistent storage of big data requires advanced error correction schemes. The classical approach is to use error correcting codes (ECCs). This work studies an alternative approach, which uses the redundancy inherent in data itself for error correction. This type of redundancy, called Natural Redundancy (NR), is abundant in many types of uncompressed or even compressed files. The complex structures of Natural Redundancy, however, require machine learning techniques. In this paper, we study two fundamental approaches to use Natural Redundancy for error correction. The first approach, called Representation-Oblivious, requires no prior knowledge on how data are represented or compressed in files. It uses deep learning to detect file types accurately, and then mine Natural Redundancy for soft decoding. The second approach, called Representation-Aware, assumes that such knowledge is known and uses it for error correction. Furthermore, both approaches combine the decoding based on NR and ECCs. Both experimental results and analysis show that such an integrated scheme can substantially improve the error correction performance.

cs.IT↗

arXiv2016

Joint Source-Channel Decoding of Polar Codes for Language-Based Source

We exploit the redundancy of the language-based source to help polar decoding. By judging the validity of decoded words in the decoded sequence with the help of a dictionary, the polar list decoder constantly detects erroneous paths after every few bits are decoded. This path-pruning technique based on joint decoding has advantages over stand-alone polar list decoding in that most decoding errors in early stages are corrected. In order to facilitate the joint decoding, we first propose a construction of dynamic dictionary using a trie and show an efficient way to trace the dictionary during decoding. Then we propose a joint decoding scheme of polar codes taking into account both information from the channel and the source. The proposed scheme has the same decoding complexity as the list decoding of polar codes. A list-size adaptive joint decoding is further implemented to largely reduce the decoding complexity. We conclude by simulation that the joint decoding schemes outperform stand-alone polar codes with CRC-aided successive cancellation list decoding by over 0.6 dB.

cs.IT↗

arXiv2015

Asymmetric Error Correction and Flash-Memory Rewriting using Polar Codes

We propose efficient coding schemes for two communication settings: 1. asymmetric channels, and 2. channels with an informed encoder. These settings are important in non-volatile memories, as well as optical and broadcast communication. The schemes are based on non-linear polar codes, and they build on and improve recent work on these settings. In asymmetric channels, we tackle the exponential storage requirement of previously known schemes, that resulted from the use of large Boolean functions. We propose an improved scheme, that achieves the capacity of asymmetric channels with polynomial computational complexity and storage requirement. The proposed non-linear scheme is then generalized to the setting of channel coding with an informed encoder, using a multicoding technique. We consider specific instances of the scheme for flash memories, that incorporate error-correction capabilities together with rewriting. Since the considered codes are non-linear, they eliminate the requirement of previously known schemes (called polar write-once-memory codes) for shared randomness between the encoder and the decoder. Finally, we mention that the multicoding scheme is also useful for broadcast communication in Marton's region, improving upon previous schemes for this setting.

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arXiv2013

Systematic Error-Correcting Codes for Rank Modulation

The rank-modulation scheme has been recently proposed for efficiently storing data in nonvolatile memories. Error-correcting codes are essential for rank modulation, however, existing results have been limited. In this work we explore a new approach, \emph{systematic error-correcting codes for rank modulation}. Systematic codes have the benefits of enabling efficient information retrieval and potentially supporting more efficient encoding and decoding procedures. We study systematic codes for rank modulation under Kendall's $τ$-metric as well as under the $\ell_\infty$-metric. In Kendall's $τ$-metric we present $[k+2,k,3]$-systematic codes for correcting one error, which have optimal rates, unless systematic perfect codes exist. We also study the design of multi-error-correcting codes, and provide two explicit constructions, one resulting in $[n+1,k+1,2t+2]$ systematic codes with redundancy at most $2t+1$. We use non-constructive arguments to show the existence of $[n,k,n-k]$-systematic codes for general parameters. Furthermore, we prove that for rank modulation, systematic codes achieve the same capacity as general error-correcting codes. Finally, in the $\ell_\infty$-metric we construct two $[n,k,d]$ systematic multi-error-correcting codes, the first for the case of $d=O(1)$, and the second for $d=Θ(n)$. In the latter case, the codes have the same asymptotic rate as the best codes currently known in this metric.

cs.IT↗

arXiv2009

Position Modulation Code for Rewriting Write-Once Memories

A write-once memory (wom) is a storage medium formed by a number of ``write-once'' bit positions (wits), where each wit initially is in a `0' state and can be changed to a `1' state irreversibly. Examples of write-once memories include SLC flash memories and optical disks. This paper presents a low complexity coding scheme for rewriting such write-once memories, which is applicable to general problem configurations. The proposed scheme is called the \emph{position modulation code}, as it uses the positions of the zero symbols to encode some information. The proposed technique can achieve code rates higher than state-of-the-art practical solutions for some configurations. For instance, there is a position modulation code that can write 56 bits 10 times on 278 wits, achieving rate 2.01. In addition, the position modulation code is shown to achieve a rate at least half of the optimal rate.

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