We study error-correcting codes for an adversarial nanopore channel, where a $q$-ary string is first transformed by an inter-symbol interference channel with window size $\ell$ into a sequence of overlapping $\ell$-mers, and an adversary then corrupts this $\ell$-mer sequence by introducing at most $t$ edits. For the deletion-only nanopore channel, we show that the optimal redundancy of $t$-deletion-correcting codes of length $n$ lies between $t\log_q n+Ω(1)$ and $2t\log_q n-\log_q\log_2 n+O(1)$. We then give two explicit deletion-correcting constructions in the regime $t\leq \min\{(\ell-1)/2,(\ell+2)/3\}$. The first construction relies on generalized Reed-Solomon codes and has redundancy $2t\log_q n+Θ(\log\log n)$. The second is based on Sidon sets (or rather $B_t$ sequences) and has redundancy $t\log_q n+Θ(\log\log n)$, matching the lower bound to first order. We further extend the $B_t$-based approach to the edit channel, allowing insertions, deletions, and substitutions of $\ell$-mers. In the regime $t\leq \min\{(\ell-1)/4,(\ell+2)/6\}$, this gives explicit $t$-edit-correcting codes with redundancy $t\log_q n+Θ(\log\log n)$, which is first-order optimal.

We derive Singleton-type bounds on the free distance and column distances of trellis codes. Our results show that, at a given time instant, the maximum attainable column distance of trellis codes can exceed that of convolutional codes. Moreover, using expander graphs, we construct trellis codes over constant-size alphabets that achieve a rate-distance trade-off arbitrarily close to that of convolutional codes with a maximum distance profile. By comparison, all known constructions of convolutional codes with a maximum distance profile require working over alphabets whose size grows at least exponentially with the number of output symbols per time instant.

We derive a lower bound on the amount of information accessed to repair failed nodes within a single rack from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share the same rack. Furthermore, we construct a family of rack-aware minimum-storage regenerating (MSR) codes with the property that the number of symbols accessed for repairing a single failed node attains the bound with equality for all admissible parameters. In contrast, previous constructions of rack-aware optimal-access MSR codes were only known for limited parameters.

The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all possible lengths of the string. In this work, we present binary codes of length$n$in which every codeword can be efficiently reconstructed from its erroneous prefix-suffix compositions with at most$t$composition errors, which include any combination of insertions, deletions and substitutions. All our constructions have decoding complexity polynomial in$n$.

We study a deterministic nanopore channel model that consists of an inter-symbol interference (ISI) channel and a deletion channel. By leveraging the ISI effect, we observe that when the number of deletions is relatively small, correcting deletions in the nanopore channel amounts to pinpointing the locations of the deletions, without regard to the values of the deletions. Drawing upon this observation, we propose a construction of two-deletion correcting codes of length n over an alphabet of size q with redundancy at most 3 logqn + o(1).

Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and weight from the compositions of their prefixes and suffixes of every possible length. We provide necessary and sufficient conditions for the multiset of strings so that unique reconstruction up to reversal is possible.

Convolutional codes with a maximum distance profile attain the largest possible column distances for the maximum number of time instants and thus have outstanding error-correcting capability especially for streaming applications. Explicit constructions of such codes are scarce in the literature. In particular, known constructions of convolutional codes with ratek/nand a maximum distance profile require a field of size at least exponential innfor general code parameters. At the same time, the only known lower bound on the field size is the trivial bound that is linear inn. In this paper, we show that a finite field of size ΩL(nL-1) is necessary for constructing convolutional codes with ratek/nand a maximum distance profile of lengthL. As a direct consequence, this rules out the possibility of constructing convolutional codes with a maximum distance profile of lengthL≥ 3 over a finite field of sizeO(n). Additionally, we also present an explicit construction of convolutional code with ratek/nand a maximum profile of length L = 1 over a finite field of sizeO(nmin{k,n-k}), achieving a smaller field size than known constructions with the same profile length.

Cross-training has become a promising strategy to handle data heterogeneity problem in federated learning, which re-train a local model across different clients to improve its generalization capability in a privacy-preserving manner. Its main idea is to make the local models to fit the data of all clients. However, the heterogeneity between data sources may lead the local models to quickly forget the knowledge learned in several rounds of cross-training. To address the problem, this paper presents a novel prototype guided cross training mechanism, termed PGCT, to regularize the change of class-level data representations across clients. It includes two main modules, where the prototype guided representation learning module employs client-aware prototypes of data patterns learned by clustering to guide the learning of consistency representation across feature spaces. This maintains the similar decision boundary across different clients. The prototype-based feature augmentation module uses prototypes as soft attention regularizers to further aggregate rich information to enhance the discrimination of historical features. Experiments were conducted on four datasets in terms of performance comparison, ablation study and case study, and the results verified that PGCT can learn discriminative features with different classes under the guidance of prototypes, which leads to better performance than the state-of-the-art methods.

We study the problem of repairing Reed-Solomon codes with low-access complexity in the rack-aware storage model that allows collective information processing in the nodes that share the same rack. Building on recent work of the access complexity for the rack-aware storage model, we derive a lower bound on the amount of information accessed for repairing multiple failed nodes within a single rack from any number of helper racks. Further, we construct a family of Reed-Solomon codes that only require accessing a relatively small number of symbols to repair failed nodes in a single rack. In particular, for certain code parameters, our construction attains the bound on the access complexity with equality and thus has optimal access.

Representation learning for images has been advanced by recent progress in more complex neural models such as the Vision Transformers and new learning theories such as the structural causal models. However, these models mainly rely on the classification loss to implicitly regularize the class-level data distributions, and they may face difficulties when handling classes with diverse visual patterns. We argue that the incorporation of the structural information between data samples may improve this situation. To achieve this goal, this paper presents a framework termed Class-level Structural Relation Modeling and Smoothing for Visual Representation Learning (CSRMS), which includes the Class-level Relation Modelling, Class-aware Graph Sampling, and Relational Graph-Guided Representation Learning modules to model a relational graph of the entire dataset and perform class-aware smoothing and regularization operations to alleviate the issue of intra-class visual diversity and inter-class similarity. Specifically, the Class-level Relation Modelling module uses a clustering algorithm to learn the data distributions in the feature space and identify three types of class-level sample relations for the training set; Class-aware Graph Sampling module extends typical training batch construction process with three strategies to sample dataset-level sub-graphs; and Relational Graph-Guided Representation Learning module employs a graph convolution network with knowledge-guided smoothing operations to ease the projection from different visual patterns to the same class. Experiments demonstrate the effectiveness of structured knowledge modelling for enhanced representation learning and show that CSRMS can be incorporated with any state-of-the-art visual representation learning models for performance gains. The source codes and demos have been released at https://github.com/czt117/CSRMS.

Federated Learning aims to learn a global model on the server side that generalizes to all clients in a privacy-preserving manner, by leveraging the local models from different clients. Existing solutions focus on either regularizing the objective functions among clients or improving the aggregation mechanism for the improved model generalization capability. However, their performance is typically limited by the dataset biases, such as the heterogeneous data distributions and the missing classes. To address this issue, this paper presents a cross-silo prototypical calibration method (FedCSPC), which takes additional prototype information from the clients to learn a unified feature space on the server side. Specifically, FedCSPC first employs the Data Prototypical Modeling (DPM) module to learn data patterns via clustering to aid calibration. Subsequently, the cross-silo prototypical calibration (CSPC) module develops an augmented contrastive learning method to improve the robustness of the calibration, which can effectively project cross-source features into a consistent space while maintaining clear decision boundaries. Moreover, the CSPC module's ease of implementation and plug-and-play characteristics make it even more remarkable. Experiments were conducted on four datasets in terms of performance comparison, ablation study, in-depth analysis and case study, and the results verified that FedCSPC is capable of learning the consistent features across different data sources of the same class under the guidance of calibrated model, which leads to better performance than the state-of-the-art methods. The source codes have been released at https://github.com/qizhuang-qz/FedCSPC.

Deep learning has been proven to be effective in image classification tasks. However, existing methods may face difficulties in distinguishing complex images due to the distraction caused by diverse image content. To overcome this challenge, we propose a class-aware convolution and attentive aggregation (CA-Net) framework that improves the effectiveness of representation learning and reduces the influence of irrelevant background. CA-Net includes three main modules: the discrete representation learning (DRL) module that uses a group learning method to learn discriminative representations, the class-aware score of discrete representation (CSDR) module that infers class-aware scores to generate weights for representation learners, and the class-aware representation fusion module(CRF) that aggregates class-aware representations using the class-aware scores as a guide. Our experimental results on three benchmarking datasets show that CA-Net improves the performance of state-of-the-art backbones and enhances feature extraction robustness.

We derive a lower bound on the amount of information accessed to repair a single failed node from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share the same rack. Furthermore, we construct a family of rack-aware MSR codes with the number of symbols accessed for repair attaining the bound with equality for all admissible parameters. Constructions of rack-aware optimal-access MSR codes were only known for limited parameters.

We construct a family of$(n,k)$convolutional codes with degree$\delta \in \{k,n-k\}$that have a maximum distance profile. The field size required for our construction is$\Theta (n^{2\delta })$, which improves upon the known constructions of convolutional codes with a maximum distance profile. Our construction is based on the theory of skew polynomials.

The prediction of peptide secondary structures is fundamentally important to reveal the functional mechanisms of peptides with potential applications as therapeutic molecules. In this study, we propose a multi-view deep learning method named Peptide Secondary Structure Prediction based on Multi-View Information, Restriction and Transfer learning (PSSP-MVIRT) for peptide secondary structure prediction. To sufficiently exploit discriminative information, we introduce a multi-view fusion strategy to integrate different information from multiple perspectives, including sequential information, evolutionary information and hidden state information, respectively, and generate a unified feature space. Moreover, we construct a hybrid network architecture of Convolutional Neural Network and Bi-directional Gated Recurrent Unit to extract global and local features of peptides. Furthermore, we utilize transfer learning to effectively alleviate the lack of training samples (peptides with experimentally validated structures). Comparative results on independent tests demonstrate that our proposed method significantly outperforms state-of-the-art methods. In particular, our method exhibits better performance at the segment level, suggesting the strong ability of our model in capturing local discriminative information. The case study also shows that our PSSP-MVIRT achieves promising and robust performance in the prediction of new peptide secondary structures. Importantly, we establish a webserver to implement the proposed method, which is currently accessible via http://server.malab.cn/PSSP-MVIRT. We expect it can be a useful tool for the researchers of interest, facilitating the wide use of our method.

Locally recoverable (LRC) codes and their variants have been extensively studied in recent years. In this paper we focus on cyclic constructions of LRC codes and derive conditions on the zeros of the code that support the property of hierarchical locality. As a result, we obtain a general family of hierarchical LRC codes for a new range of code parameters. We also observe that our approach enables one to represent an LRC code in quasicyclic form, and use this representation to construct tail-biting convolutional LRC codes with locality. Among other results, we extend the general approach to cyclic codes with locality to multidimensional cyclic codes, yielding new families of LRC codes with availability, and construct a family of$q$-ary cyclic hierarchical LRC codes of unbounded length.

We address two aspects of the repair problem of Reed-Solomon codes. First, we propose a new repair scheme for the RS codes constructed in [Tamo-Ye-Barg, IEEE Trans. Inf. Theory, May 2019] which in addition to optimal repair bandwidth is also robust to erroneous information provided by the helper nodes. Next, we construct a new family of RS codes with optimal access for the repair of any single failed node. We also prove that any scalar MDS code with optimal repair bandwidth can be furnished with a repair scheme with the optimal access property.

Locally recoverable (LRC) codes and their variants have been extensively studied in recent years. In this paper we focus on cyclic LRC codes, presenting two results regarding codes with hierarchical locality and codes with availability. Regarding hierarchical LRC codes, we observe that the cyclic codes of Tamo et al. (2016) can be generalized to yield optimal families with multiple levels of locality for a broader range of parameters than known previously. We also observe that the general approach to cyclic codes with locality can be extended to multidimensional cyclic codes, yielding new families of LRC codes with availability.

The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate freely without taxing the system bandwidth, and that the only information transmission that counts is the one between the racks. This assumption implies that the nodes within each of the racks can collaborate before providing information to the failed node. The main emphasis of the paper is on code construction for this storage model. We present an explicit family of maximum distance separable (MDS) array codes that support recovery of a single failed node from any number of helper racks using the minimum possible amount of inter-rack communication(such codes are said to provide optimal repair). The codes are constructed over finite fields of size comparable to the code length. We also derive a bound on the number of symbols accessed at helper nodes for the purposes of repair, and construct a code family that approaches this bound, while still maintaining the optimal repair property. Finally, we present a construction of scalar Reed-Solomon codes that support optimal repair for the rack-oriented storage model.

Recently Reed-Solomon (RS) codes were shown to possess a repair scheme that supports repair of failed nodes with optimal repair bandwidth. In this paper, we extend this result in two directions. First, we propose a new repair scheme for the RS codes constructed in [Tamo-Ye-Barg, IEEE Transactions on Information Theory, vol. 65, May 2019] and show that repair is robust to erroneous information provided by the helper nodes while maintaining the optimal repair bandwidth. Second, we construct a new family of RS codes with optimal access for the repair of any single failed node. We also show that the constructed codes can accommodate both features, supporting optimal-access repair with optimal error-correction capability. Going beyond RS codes, we also prove that any scalar MDS code with repair bandwidth attaining the cutset bound affords a repair scheme with optimal access property.

We consider erasure coding for a model of storage that assumes that nodes are organized into equally sized groups, called racks, such that repairing failed nodes is limited only by inter-rack communication, while transmission of data within a rack does not contribute to the repair bandwidth. We present explicit families of MDS array codes that support recovery of a single failed node from any number of helper racks using the minimum possible amount of inter-rack communication. One of our constructions also has the additional property of low access. Finally, we present a construction of scalar Reed-Solomon codes that support optimal repair for the rack-oriented storage model.

In the q-ary online (or “causal”) channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword x = (x1,..., xn) ∈ {0, 1,..., q-1}nsymbol-by-symbol via a channel limited to at most pn errors and p*n erasures. The channel is “online” in the sense that at the ith step of communication the channel decides whether to corrupt the ith symbol or not based on its view so far, i.e., its decision depends only on the transmitted symbols (x1, . . ., xi). This is in contrast to the classical adversarial channel in which the corruption is chosen by a channel that has full knowledge of the sent codeword x. In this paper, we study the capacity of q-ary online channels for a combined corruption model, in which the channel may impose at most pn errors and at most p*n erasures on the transmitted codeword. The online channel (in both the error and erasure case) has seen a number of recent studies, which present both upper and lower bounds on its capacity. In this paper, we give a full characterization of the capacity as a function of q, p, and p*.

In the q-ary online (causal) channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword x = (x1, . . . , xn) ∈ {0, 1, . . . , q - 1}nsymbol-by-symbol via a channel limited to at most p*n errors (symbol changes) and p*n erasures. The channel is "online" (i.e., "causal") in the sense that at the ith step of communication the channel decides whether to corrupt the ith symbol or not only based on its view of the symbols (x1,. . . , xi). This is in contrast to the classical adversarial channel in which the corruption is chosen with full knowledge of the sent codeword x. In this work we extend the results obtained in [1]-[4] (in which the capacities of binary online bit-flip-only channels, and separately binary online erasure-only channels were characterized). We here extend those prior results in two important ways. First, we obtain the capacity of q-ary online channels for general q (rather than just q = 2). Second, we analyze combined error-erasure corruption models (rather than studying them separately). Characterization of this much broader class of symmetric online channels gives a fuller understanding of the effects of causality on jamming adversaries. The extensions in this paper require novel approaches for both optimal code designs, and matching information-theoretic converse arguments.

In the binary online (or "causal") channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword x = (x1,...,xn) ∈ {0,1}n bit by bit via a channel limited to at most pn corruptions. The channel is "online" in the sense that at the ith step of communication the channel decides whether to corrupt the ith bit or not based on its view so far, i.e., its decision depends only on the transmitted bits (x1,...,xi). This is in contrast to the classical adversarial channel in which the error is chosen by a channel that has full knowledge of the transmitted codeword x.