Abstract In semantic segmentation, even state-of-the-art deep learning models fall short of the performance required in certain high-stakes applications such as medical image analysis. In these cases, performance can be improved by allowing a model to abstain from making predictions when confidence is low, an approach known as selective prediction. While well-known in the classification literature, selective prediction has been underexplored in the context of semantic segmentation. This paper tackles the problem by focusing on image-level abstention, which involves producing a single confidence estimate for the entire image, in contrast to previous approaches that focus on pixel-level uncertainty. Assuming the Dice coefficient as the evaluation metric for segmentation, two main contributions are provided in this paper: (i) In the case of known marginal posterior probabilities, we derive the optimal confidence estimator, which is observed to be intractable for typical image sizes. Then, an approximation computable in linear time, named Soft Dice Confidence (SDC), is proposed and proven to be tightly bounded to the optimal estimator. (ii) When only an estimate of the marginal posterior probabilities are known, we propose a plug-in version of the SDC and show it outperforms all previous methods, including those requiring additional tuning data. These findings are supported by experimental results on both synthetic data and real-world data from six medical imaging tasks, including out-of-distribution scenarios, positioning the SDC as a reliable and efficient tool for selective prediction in semantic segmentation.

This letter presents an incoherent change detection algorithm (CDA) for wavelength-resolution synthetic aperture radar (SAR) based on convolutional neural networks (CNNs). The proposed CDA includes a segmentation CNN, which localizes potential changes, and a classification CNN, which further analyzes these candidates to classify them as real changes or false alarms. Compared to state-of-the-art solutions on the CARABAS-II data set, the proposed CDA shows a significant improvement in performance, achieving, in a particular setting, a detection probability of 99% at a false alarm rate of 0.0833/km2.

This article presents two supervised change detection algorithms (CDA) based on convolutional neural networks (CNN) that use stacks of co-registered wavelength-resolution synthetic aperture radar (SAR) images to detect changes in an image under monitoring. The additional information of a scene of interest provided by SAR image stacks can be explored to enhance the performance of change detection algorithms. In particular, stacks of images with similar statistics can be obtained for ultra-wideband (UWB) very high frequency (VHF) SAR systems, as they produce images highly stable in time. The proposed CDAs can be summed up into four stages: difference image formation, semantic segmentation, clustering, and change classification. The CNN-GSP algorithm is based on a ground scene prediction (GSP) image, which is used as a reference to form a difference image (DI). A CNN-based model then analyzes the DI. The CNN-MDI algorithm feeds multiple DIs with identical monitored images to a CNN-based model, which will concurrently analyze their features. Tests with CARABAS-II data show that the proposed CDAs can outperform other state-of-the-art algorithms that also use stacks of WR-SAR images. Beyond that, the proposed algorithms outperformed a CNN-based CDA that does not use image stacks, which shows that CNN-based algorithms can use the additional information provided by stacks of SAR images to reduce false alarm occurrences while increasing the probability of detection of changes.

This article investigates the massive random access Gaussian channel with a focus on small payloads. For this problem, grant-based schemes have been regarded as inefficient due to the necessity of large feedbacks and the use of inefficient scheduling request methods. This articles attempts to answer whether grant-based schemes can be competitive against state-ot-art grantless schemes and worthy of further investigation. In order to compare these schemes fairly, a novel model is proposed, and, under this model, a novel grant-based scheme is proposed. The scheme uses Ordentlich and Polyanskiy's grantless method to transmit small coordination indices in order to perform the scheduling request, which allows both the request from the users to be efficient and the feedback to be small. We also present improvements to the Ordentlich and Polyanskiy's scheme, allowing it to transmit information through the choice of sub-block, as well as to handle collisions of the same message, significantly improving the method for very small messages. Simulation results show that, if a small feedback is allowed, the proposed scheme performs closely to the state-of-art while using simpler coding schemes, suggesting that novel grant-based schemes should not be dismissed as a potential solution to the massive random access problem.

Lattice codes are elegant and powerful structures that not only achieve the capacity of the additive white Gaussian noise (AWGN) channel but are also a key ingredient to many multiterminal schemes that exploit linearity properties. However, constructing lattice codes that can realize these benefits with low complexity is still a challenging problem. In this paper, efficient encoding and decoding algorithms are proposed for multilevel binary low-density parity-check (LDPC) lattices constructed via Construction D' whose complexity is linear in the total number of coded bits. Moreover, a generalization of Construction D' is proposed, which relaxes some of the nesting constraints on the parity-check matrices of the component codes, leading to a simpler and improved design. Based on this construction, low-complexity multilevel LDPC lattices are designed whose performance under multistage decoding is comparable to that of polar lattices and close to that of low-density lattice codes on the power-unconstrained AWGN channel.

We propose efficient encoding and decoding algorithms for Construction D` multilevel LDPC lattices whose complexity is linear in the total number of coded bits. Moreover, we propose a generalization of Construction D ` that relaxes some of the nesting constraints on the component codes, leading to a simpler and improved design. Based on this construction, low-complexity multilevel LDPC lattices are designed whose performance under multistage lattice decoding is comparable to that of polar lattices on the power-unconstrained AWGN channel.

Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach to communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.

Compute-and-forward (C&F) is a promising new approach to interference management, enjoying several advantages over other information-theoretic schemes. C&F usually requires channel state information (CSI) at the receivers so that an “optimal” scaling factor can be computed for the purposes of decoding. In this paper, a blind C&F scheme-i.e., one not requiring CSI-is developed. Rather than attempting to compute the optimal scaling factor, this new scheme seeks one or more “good” scalars, i.e., scalars that allow correct decoding despite possibly being suboptimal. The region of all such good scalars is characterized. To find a good scalar, a computationally efficient scheme is proposed which involves error-detection, a hierarchically organized list, as well as a use of the smoothing lemma from lattice theory. Simulation results show that our blind C&F scheme achieves-for a class of nested lattice codes-the same throughput as its CSI-enabled counterpart at the expense of, approximately, a two-fold increase in computational complexity in the high-throughput region. Moreover, our blind C&F scheme can be applied to multisource multirelay networks with a good performance/complexity tradeoff.

Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding schemes can be constructed. This paper considers the problem of communication over a finite-ring matrix channel Y = AX + BE, where X is the channel input, Y is the channel output, E is random error, and A and B are random transfer matrices. Tight capacity results are obtained and simple polynomial-complexity capacity-achieving coding schemes are provided under the assumption that A is uniform over all full-rank matrices and BE is uniform over all rank-t matrices, extending the work of Silva, Kschischang, and Kötter (2010), who handled the case of finite fields. This extension is based on several new results, which may be of independent interest, that generalize concepts and methods from matrices over finite fields to matrices over finite chain rings.

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai Our main contribution shows that as long as the sum of the number of links the adversary can jam (denoted by ZO) and the number of links he can eavesdrop on (denoted by ZI) is less than the network capacity (denoted by C) (i.e., ), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this scheme as a module to design codes that allow communication at the source rate of C- ZO when there are no security requirements, and codes that allow communication at the source rate of C- ZO- ZI while keeping the communicated message provably secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. We also prove that the rate-region obtained is information-theoretically optimal. In proving our results, we correct an error in prior work by a subset of the authors in this paper.

Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over finite rings, more efficient physical-layer network coding schemes can be constructed. This paper considers the problem of communication over a finite-chain-ring matrix channel Y = AX + BZ, where X is the channel input, Y is the channel output, Z is random noise, and A and B are random transfer matrices. Tight capacity results are obtained and simple polynomial-complexity capacity-achieving coding schemes are provided under certain distributions of A, B, and Z, extending the work of Silva, Kschischang and Kötter (2010), who handled the case of finite fields. This extension is based on several new results that generalize concepts and methods from matrices over finite fields to matrices over finite chain rings.

The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, an algebraic approach is taken to show its potential in practical, nonasymptotic, settings. A general framework is developed for studying nested-lattice-based PNC schemes-called lattice network coding (LNC) schemes for short-by making a direct connection between C&F and module theory. In particular, a generic LNC scheme is presented that makes no assumptions on the underlying nested lattice code. C&F is reinterpreted in this framework, and several generalized constructions of LNC schemes are given. The generic LNC scheme naturally leads to a linear network coding channel over modules, based on which noncoherent network coding can be achieved. Next, performance/complexity tradeoffs of LNC schemes are studied, with a particular focus on hypercube-shaped LNC schemes. The error probability of this class of LNC schemes is largely determined by the minimum intercoset distances of the underlying nested lattice code. Several illustrative hypercube-shaped LNC schemes are designed based on Constructions A and D, showing that nominal coding gains of 3 to 7.5 dB can be obtained with reasonable decoding complexity. Finally, the possibility of decoding multiple linear combinations is considered and related to the shortest independent vectors problem. A notion of dominant solutions is developed together with a suitable lattice-reduction-based algorithm.

This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes that all transfer matrices with the same rank are equiprobable, so that the channel is completely characterized by the rank distribution of the transfer matrix. This model is seen to be more flexible than previously proposed ones in describing random linear network coding systems subject to link erasures, while still being sufficiently simple to allow tractability. The model is also conservative in the sense that its capacity provides a lower bound on the capacity of any channel with the same rank distribution. A main contribution is to express the channel capacity as the solution of a convex optimization problem which can be easily solved by numerical computation. For the special case of constant-rank input, a closed-form expression for the capacity is obtained. The behavior of the channel for asymptotically large field size or packet length is studied, and it is shown that constant-rank input suffices in this case. Finally, it is proved that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general model.

Compute-and-forward (C&F) relaying usually requires channel state information (CSI) at the receivers so that an “optimal” scale factor can be computed for the purposes of decoding. In this paper, a blind C&F scheme - i.e., one not requiring CSI - is developed. Rather than attempting to compute the optimal scale factor, this new scheme seeks one (or more) “good” scalars, i.e., scalars which allow correct decoding despite possibly being sub-optimal. The region of all such good scalars is characterized. To find a good scalar, a computationally efficient scheme, involving error-detection and a hierarchically organized list, is proposed. Simulation results show that this blind C&F scheme achieves - for a class of lattices admitting an efficient trellis decoder - the same throughput as its CSI-enabled counterpart, at the expense of, approximately, a ten-fold increase in computational complexity in the high-throughput region.

The construction of lattice network coding schemes through signal codes is revisited. First, it is shown that the nominal coding gain of signal codes can be carried over from AWGN channels to lattice network coding. This demonstrates the potential of using signal codes in lattice network coding. However, in order to achieve the promised performance gain, all the side information related to shaping should be transmitted to the receiver. Second, the problem of delivering the side information to the receiver is considered. In particular, a generic scheme is proposed which can be optimized by solving a lattice design problem. Finally, two solutions to the lattice design problem are presented and the simulation results suggest that-with a reasonable overhead-the promised performance gain can be achieved by using our proposed scheme.

This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. Our model allows this transfer matrix to have any rank, while assuming that all transfer matrices with the same rank are equiprobable. While in general the capacity cannot be obtained in closed form, we provide a simplification of the problem (from qnmto O(n) variables) which allows for easy numerical computation. A tight upper bound on the capacity is also derived, and for the special case of constant-rank input, we obtain an exact formula. Several existing results can be obtained as special cases of our approach. In addition, we prove that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general case.

This work presents an error control scheme for noncoherent linear network coding under an adversarial error model. The scheme relies on the assumption that the transmitter and the receiver share a random key that is secret from the adversary. The scheme is shown to achieve, asymptotically in the packet length, the highest possible rate under this model-which is significantly higher than what can be achieved without a shared key. Previous approaches to key-based error control required either an asymptotically large field or an impractically long key. The proposed scheme removes both restrictions, and is therefore suitable for practical applications of network coding. The scheme is based on MRD codes and makes crucial use of extension field ideas.

In this work, network coding is employed to obtain maximum diversity order in a network where the users have independent information to transmit to a common base station. We elaborate on the recently proposed generalized dynamic network codes (GDNC), which can only achieve part of the maximum diversity order when the inter-user channels are subject to outages. In particular, by allowing the users to perform network decoding, in this paper we show that maximum diversity order can be achieved. Results are restricted to the 2-user case, although some discussion regarding the general case is provided.

The problem of securing a network coding communication system against an eavesdropper is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop on μ arbitrarily chosen links. The objective is to provide reliable communication to all receivers, while guaranteeing that the source information remains information-theoretically secure from the adversary. A coding scheme is proposed that can achieve the maximum possible rate of n - μ packets. The scheme, which is based on rank-metric codes, has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying linear network code. The only requirement of the scheme is that the packet length be at least n, which is shown to be strictly necessary for universal communication at the maximum rate. A further scenario is considered where the adversary is allowed not only to eavesdrop but also to inject up to t erroneous packets into the network, and the network may suffer from a rank deficiency of at most ρ. In this case, the proposed scheme can be extended to achieve the rate of n - ρ - 2t - μ packets. This rate is shown to be optimal under the assumption of zero-error communication.

The problem of designing new physical-layer network coding (PNC) schemes via lattice partitions is considered. Building on a recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, we take an algebraic approach to show its potential in non-asymptotic settings. We first relate Nazer-Gastpar's approach to the fundamental theorem of finitely generated modules over a principle ideal domain. Based on this connection, we generalize their code construction and simplify their encoding and decoding methods. This not only provides a transparent understanding of their approach, but more importantly, it opens up the opportunity to design efficient and practical PNC schemes. Finally, we apply our framework for PNC to a Gaussian relay network and demonstrate its advantage over conventional PNC schemes.

We study a non-multicast secure network coding problem with two receivers. First we study a linear-deterministic channel model with two receivers and a collection of eavesdroppers, which generalizes the Ozarow-Wyner wiretap channel II. The secrecy capacity region for independent and common messages is characterized and is achieved by concatenating a coset-coding scheme based on maximum rank distance codes with a repetition code. By applying our coding scheme at the source node of a network that uses an underlying generic network code we also establish the secrecy capacity region of a network coding problem with two sinks and one sender node.

This paper considers the problem of securing a linear network coding system against an adversary that is both an eavesdropper and a jammer. The network is assumed to transport n packets from source to each receiver, and the adversary is allowed to eavesdrop on μ arbitrarily chosen links and also to inject up to t erroneous packets into the network. The goal of the system is to achieve zero-error communication that is information-theoretically secure from the adversary. Moreover, this goal must be attained in a universal fashion, i.e., regardless of the network topology or the underlying network code. An upper bound on the achievable rate under these requirements is shown to be n - μ - 2t packets per transmission. A scheme is proposed that can achieve this maximum rate, for any n and any field size q, provided the packet length m is at least n symbols. The scheme is based on rank-metric codes and admits low-complexity encoding and decoding. In addition, the scheme is shown to be optimal in the sense that the required packet length is the smallest possible among all universal schemes that achieve the maximum rate.

This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random network coding. The model assumes thatnpackets of lengthmare transmitted over the network, and up toterroneous packets are randomly chosen and injected into the network. Upper and lower bounds on capacity are obtained for any channel parameters, and asymptotic expressions are provided in the limit of large field or matrix size. A simple coding scheme is presented that achieves capacity in both limiting cases. The scheme has decoding complexityO(n2m) and a probability of error that decreases exponentially both in the packet length and in the field size in bits. Extensions of these results for coherent network coding are also presented.

While network coding can be an efficient means of information dissemination in networks, it is highly susceptible to “pollution attacks,” as the injection of even a single erroneous packet has the potential to corrupt each and every packet received by a given destination. Even when suitable error-control coding is applied, an adversary can, in many interesting practical situations, overwhelm the error-correcting capability of the code. To limit the power of potential adversaries, a broadcast transformation is introduced, in which nodes are limited to just a single (broadcast) transmission per generation. Under this broadcast transformation, the multicast capacity of a network is changed (in general reduced) from the number of edge-disjoint paths between source and sink to the number of internally disjoint paths. Exploiting this fact, a family of networks is proposed whose capacity is largely unaffected by a broadcast transformation. This results in a significant achievable transmission rate for such networks, even in the presence of adversaries.

Gabidulin codes are the rank-metric analogs of Reed-Solomon codes and have a major role in practical error control for network coding. This paper presents new encoding and decoding algorithms for Gabidulin codes based on low-complexity normal bases. In addition, a new decoding algorithm is proposed based on a transform-domain approach. Together, these represent the fastest known algorithms for encoding and decoding Gabidulin codes.

This paper considers the problem of secure network coding under the weak (and practically appealing) security requirements of Bhattad and Narayanan. Weak security allows communication at maximum rate while ensuring that only meaningless information is leaked to a wiretapper. Differently from the approach of Bhattad and Narayanan, which requires a joint design of the underlying network code and the outer security scheme, we propose a universal approach that is completely independent of the network code. In particular, the field size for linear network coding operations does not need to be enlarged. The scheme is also compatible with random network coding.

The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and destination nodes, the error correction capability of an (outer) code is succinctly described by the rank metric; as a consequence, it is shown that universal network error correcting codes achieving the Singleton bound can be easily constructed and efficiently decoded. For noncoherent network coding, where knowledge of the network topology and network code is not assumed, the error correction capability of a (subspace) code is given exactly by a new metric, called theinjection metric, which is closely related to, but different than, the subspace metric of KOumltter and Kschischang. In particular, in the case of a non-constant-dimension code, the decoder associated with the injection metric is shown to correct more errors then a minimum-subspace-distance decoder. All of these results are based on a general approach to adversarial error correction, which could be useful for other adversarial channels beyond network coding.

The problem of securing a network coding communication system against a wiretapper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the wiretapper can eavesdrop on mu arbitrarily chosen links. A coding scheme is proposed that can achieve the maximum possible rate of k = n - mu packets that are information-theoretically secure from the adversary. A distinctive feature of our scheme is that it is universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying network code. In fact, even a randomized network code can be used. Our approach is based on Rouayheb-Soljaninpsilas formulation of a wiretap network as a generalization of the Ozarow-Wyner wiretap channel of type II. Essentially, the linear MDS code in Ozarow-Wynerpsilas coset coding scheme is replaced by a maximum-rank-distance code over an extension of the field in which linear network coding operations are performed.

The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of KÖtter and Kschischang. A large class of constant-dimension subspace codes is investigated. It is shown that codes in this class can be easily constructed from rank-metric codes, while preserving their distance properties. Moreover, it is shown that minimum distance decoding of such subspace codes can be reformulated as a generalized decoding problem for rank-metric codes where partial information about the error is available. This partial information may be in the form of erasures (knowledge of an error location but not its value) anddeviations(knowledge of an error value but not its location). Taking erasures and deviations into account (when they occur) strictly increases the error correction capability of a code: if$\mu$erasures and$\delta$deviations occur, then errors of rank$t$can always be corrected provided that$2t \leq d - 1 + \mu + \delta$, where$d$is the minimum rank distance of the code. For Gabidulin codes, an important family of maximum rank distance codes, an efficient decoding algorithm is proposed that can properly exploit erasures and deviations. In a network coding application, where$n$packets of length$M$over$\BBF _{q}$are transmitted, the complexity of the decoding algorithm is given by$O(dM)$operations in an extension field$\BBF _{q^{n}}$.

It is shown that the error correction problem in random network coding is closely related to a generalized decoding problem for rank-metric codes. This result enables many of the rich tools devised for the rank metric to be naturally applied to random network coding. The generalized decoding problem introduced in this paper allows partial information about the error to be supplied. This partial information can be either in the form of erasures (knowledge of an error location but not its value) or deviations (knowledge of an error value but not its location). For Gabidulin codes, an efficient decoding algorithm is proposed that can correct e errors, mu erasures and v deviations, provided 2isin + mu + v les d - 1, where d is the minimum distance of the code.

The problem of error control in random network coding is considered, and a formulation of the problem is given in terms of rank-metric codes. This formulation allows many of the tools developed for rank-metric codes to be applied to random network coding. A random network code induces a generalized decoding problem for rank-metric codes in which the channel may supply partial information about the error in the form of erasures (knowledge of an error location not its values) and deviations (knowledge of an error value but not its location).