arXiv subjects

Michael Langberg

Publications and source records attributed to Michael Langberg.

At least 19 recordsLinked to original sources

arXiv2026

Secret key-distribution over networks with node-based adversarial errors

We study the multiple key-cast problem in network coding under active node-based adversaries. In multiple key-cast, a source generates independent secret keys to be securely and reliably delivered to designated terminal subsets. The network adversary can observe $\ell_o$ nodes, inject additive or overwrite errors into $\ell_e$ nodes, and simultaneously observe and corrupt $\ell_{oe}$ nodes, while having full knowledge of the topology and coding operations. Adversarial models of similar nature, however, where corruption and eavesdropping is done on edges instead of nodes, have seen previous studies in the context of secure multicast network-coding. The work at hand builds on and extends these studies to address the challenges in node-based adversaries in the context of (multiple) key distribution. For single-source networks where every node is d-vertex connected from the source, we show that perfectly secure multiple key-cast under additive and overwrite error models is asymptotically achievable at the key-capacity of $d-\ell_o-\ell_e-2\ell_{oe}$. We then extend our analysis to networks where only terminal nodes satisfy this connectivity requirement, while intermediate nodes may be only partially connected. For these topologies, we develop coding schemes that achieve secure and reliable multiple key-cast capacities determined by the source vertex-connectivity and additional structural properties of the network. Finally, we show that our results generalize to multi-source settings, ensuring perfect secrecy even if the adversary observes all but one source node, and establish that our constructions apply directly to secure multicast network coding and to network secret-sharing scenarios. As part of our studies, we improve the security guarantee of a central scheme in [Zhang et al., IEEE Trans. Comm., 2023] addressing parallel-edge networks, from weak-security to perfect-security.

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arXiv2026

Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping Nodes

We study the secure multiple key-cast problem over noiseless networks under node-based eavesdroppers, where one or more source nodes participate in the generation of distinct secret keys to be shared among designated terminal subsets, while an eavesdropper observing up to $\ell$ nodes, including possibly source nodes, obtains no information about the keys. For the single-source setting, we first consider networks in which every node is $d$-vertex connected from the source. We show that a secure key rate of $d-\ell$ is achievable for all such networks. We further show that this rate is optimal by exhibiting $d$-vertex-connected networks whose secure key-cast capacity is at most $d-\ell$. We next study networks in which only the terminal nodes are $d$-vertex connected from the source, while other network nodes may not satisfy this connectivity condition and may be partially-connected. We show that secure multiple key-cast remains achievable in the presence of such partially-connected nodes, and derive coding schemes whose rate depends on the minimum network vertex-connectivity from the source and certain additional network properties. Finally, we generalize these results, for both $d$-vertex-connected networks and networks containing partially-connected nodes, to the multi-source setting; showing that secure multiple key-cast remains achievable even when the eavesdropper may observe all but one of the source nodes.

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arXiv2026

Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates

We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding.

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arXiv2025

Dynamic D2D-Assisted Federated Learning over O-RAN: Performance Analysis, MAC Scheduler, and Asymmetric User Selection

Existing studies on federated learning (FL) are mostly focused on system orchestration for static snapshots of the network and making static control decisions (e.g., spectrum allocation). However, real-world wireless networks are susceptible to temporal variations of wireless channel capacity and users' datasets. In this paper, we incorporate multi-granular system dynamics (MSDs) into FL, including (M1) dynamic wireless channel capacity, captured by a set of discrete-time events, called $\mathscr{D}$-Events, and (M2) dynamic datasets of users. The latter is characterized by (M2-a) modeling the dynamics of user's dataset size via an ordinary differential equation and (M2-b) introducing dynamic model drift}, formulated via a partial differential inequality} drawing concrete analytical connections between the dynamics of users' datasets and FL accuracy. We then conduct FL orchestration under MSDs by introducing dynamic cooperative FL with dedicated MAC schedulers (DCLM), exploiting the unique features of open radio access network (O-RAN). DCLM proposes (i) a hierarchical device-to-device (D2D)-assisted model training, (ii) dynamic control decisions through dedicated O-RAN MAC schedulers, and (iii) asymmetric user selection. We provide extensive theoretical analysis to study the convergence of DCLM. We then optimize the degrees of freedom (e.g., user selection and spectrum allocation) in DCLM through a highly non-convex optimization problem. We develop a systematic approach to obtain the solution for this problem, opening the door to solving a broad variety of network-aware FL optimization problems. We show the efficiency of DCLM via numerical simulations and provide a series of future directions.

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arXiv2025

From Federated Learning to X-Learning: Breaking the Barriers of Decentrality Through Random Walks

We provide our perspective on X-Learning (XL), a novel distributed learning architecture that generalizes and extends the concept of decentralization. Our goal is to present a vision for XL, introducing its unexplored design considerations and degrees of freedom. To this end, we shed light on the intuitive yet non-trivial connections between XL, graph theory, and Markov chains. We also present a series of open research directions to stimulate further research.

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arXiv2025

Hierarchical Federated Foundation Models over Wireless Networks for Multi-Modal Multi-Task Intelligence: Integration of Edge Learning with D2D/P2P-Enabled Fog Learning Architectures

The rise of foundation models (FMs) has reshaped the landscape of machine learning. As these models continued to grow, leveraging geo-distributed data from wireless devices has become increasingly critical, giving rise to federated foundation models (FFMs). More recently, FMs have evolved into multi-modal multi-task (M3T) FMs (e.g., GPT-4) capable of processing diverse modalities across multiple tasks, which motivates a new underexplored paradigm: M3T FFMs. In this paper, we unveil an unexplored variation of M3T FFMs by proposing hierarchical federated foundation models (HF-FMs), which in turn expose two overlooked heterogeneity dimensions to fog/edge networks that have a direct impact on these emerging models: (i) heterogeneity in collected modalities and (ii) heterogeneity in executed tasks across fog/edge nodes. HF-FMs strategically align the modular structure of M3T FMs, comprising modality encoders, prompts, mixture-of-experts (MoEs), adapters, and task heads, with the hierarchical nature of fog/edge infrastructures. Moreover, HF-FMs enable the optional usage of device-to-device (D2D) communications, enabling horizontal module relaying and localized cooperative training among nodes when feasible. Through delving into the architectural design of HF-FMs, we highlight their unique capabilities along with a series of tailored future research directions. Finally, to demonstrate their potential, we prototype HF-FMs in a wireless network setting and release the open-source code for the development of HF-FMs with the goal of fostering exploration in this untapped field (GitHub: https://github.com/payamsiabd/M3T-FFM).

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arXiv2025

Switched Feedback for the Multiple-Access Channel

A mechanism called switched feedback is introduced; under switched feedback, each channel output goes forward to the receiver(s) or back to the transmitter(s) but never both. By studying the capacity of the Multiple-Access Channel (MAC) with switched feedback, this work investigates the benefits of feedback, seeking to maximize that benefit under reliable and unreliable feedback scenarios. The study is used to explore the tradeoffs between cooperation and transmission in the context of communication systems. Results include upper and lower bounds on the capacity region of the MAC with switched feedback.

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arXiv2025

Sliding Window Adversarial Channels

In an arbitrarily varying channel (AVC), the channel has a state which is under the control of an adversarial jammer and the corresponding capacities are often functions of the "power" constraints on the transmitter and jammer. In this paper we propose a model in which the constraints must hold almost surely over contiguous subsequences of the codeword and state, which we call a sliding window constraint. We study oblivious jammers and codes with stochastic encoding under maximum probability of error. We show that this extra limitation on the jammer is beneficial for the transmitter: in some cases, the capacity for unique decoding with a sliding window constraint is equal to the capacity for list decoding in the standard model without sliding windows, roughly implying that the addition of window constraints reduces list decoding to unique decoding. The list decoding capacity in the standard model can be strictly larger than the unique decoding capacity.

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arXiv2025

On Subset Retrieval and Group Testing Problems with Differential Privacy Constraints

This paper focuses on the design and analysis of privacy-preserving techniques for group testing and infection status retrieval. Our work is motivated by the need to provide accurate information on the status of disease spread among a group of individuals while protecting the privacy of the infection status of any single individual involved. The paper is motivated by practical scenarios, such as controlling the spread of infectious diseases, where individuals might be reluctant to participate in testing if their outcomes are not kept confidential. The paper makes the following contributions. First, we present a differential privacy framework for the subset retrieval problem, which focuses on sharing the infection status of individuals with administrators and decision-makers. We characterize the trade-off between the accuracy of subset retrieval and the degree of privacy guaranteed to the individuals. In particular, we establish tight lower and upper bounds on the achievable level of accuracy subject to the differential privacy constraints. We then formulate the differential privacy framework for the noisy group testing problem in which noise is added either before or after the pooling process. We establish a reduction between the private subset retrieval and noisy group testing problems and show that the converse and achievability schemes for subset retrieval carry over to differentially private group testing.

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arXiv2025

Bounds on Box Codes

Let $n_q(M,d)$ be the minimum length of a $q$-ary code of size $M$ and minimum distance $d$. Bounding $n_q(M,d)$ is a fundamental problem that lies at the heart of coding theory. This work considers a generalization $n^\bx_q(M,d)$ of $n_q(M,d)$ corresponding to codes in which codewords have \emph{protected} and \emph{unprotected} entries; where (analogs of) distance and of length are measured with respect to protected entries only. Such codes, here referred to as \emph{box codes}, have seen prior studies in the context of bipartite graph covering. Upper and lower bounds on $n^\bx_q(M,d)$ are presented.

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arXiv2024

Competitive Analysis of Arbitrary Varying Channels

Arbitrary varying channels (AVC) are used to model communication settings in which a channel state may vary arbitrarily over time. Their primary objective is to circumvent statistical assumptions on channel variation. Traditional studies on AVCs optimize rate subject to the worst-case state sequence. While this approach is resilient to channel variations, it may result in low rates for state sequences that are associated with relatively good channels. This paper addresses the analysis of AVCs through the lens of competitive analysis, where solution quality is measured with respect to the optimal solution had the state sequence been known in advance. Our main result demonstrates that codes constructed by a single input distribution do not achieve optimal competitive performance over AVCs. This stands in contrast to the single-letter capacity formulae for AVCs, and it indicates, in our setting, that even though the encoder cannot predict the subsequent channel states, it benefits from varying its input distribution as time proceeds.

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arXiv2024

Characterizing positive-rate key-cast (and multicast network coding) with eavesdropping nodes

In multi-source multi-terminal key-dissemination, here called ``key-cast,'' introduced by the authors in [ITW2022], network nodes hold independent random bits, and one seeks a communication scheme that allows all terminal nodes to share a secret key K. The work at hand addresses positive (albeit, arbitrarily small) rate key-cast under the security requirement that no single non-terminal network node can gain information about the shared key K; this scenario is useful in cryptographic settings. Specifically, key-dissemination protocols based on secure multicast network coding are designed. The analysis presented yields two combinatorial characterizations. In each, we assume a network in which an eavesdropper may access any individual network node. The first characterization captures all networks that support positive-rate secure multicast; computing the secure-multicast capacity in the setting studied is a known open problem. The second characterizes all networks that support positive-rate secure key-cast.

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arXiv2024

Nobody Expects a Differential Equation: Minimum Energy-Per-Bit for the Gaussian Relay Channel with Rank-1 Linear Relaying

Motivated by the design of low-complexity low-power coding solutions for the Gaussian relay channel, this work presents an upper bound on the minimum energy-per-bit achievable on the Gaussian relay channel using rank-1 linear relaying. Our study addresses high-dimensional relay codes and presents bounds that outperform prior known bounds using 2-dimensional schemes. A novelty of our analysis ties the optimization problem at hand to the solution of a certain differential equation which, in turn, leads to a low energy-per-bit achievable scheme.

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arXiv2023

Competitive Channel-Capacity

We consider communication over channels whose statistics are not known in full, but can be parameterized as a finite family of memoryless channels. A typical approach to address channel uncertainty is to design codes for the worst channel in the family, resulting in the well-known compound channel capacity. Although this approach is robust, it may suffer a significant loss of performance if the capacity-achieving distribution of the worst channel attains low rates over other channels. In this work, we cope with channel uncertainty through the lens of {\em competitive analysis}. The main idea is to optimize a relative metric that compares the performance of the designed code and a clairvoyant code that has access to the true channel. To allow communication rates that adapt to the channel at use, we consider rateless codes with a fixed number of message bits and random decoding times. We propose two competitive metrics: the competitive ratio between the expected rates of the two codes, and a regret defined as the difference between the expected rates. The competitive ratio, for instance, provides a percentage guarantee on the expected rate of the designed code when compared to the rate of the clairvoyant code that knows the channel at hand. Our main results are single-letter expressions for the optimal {\em competitive-ratio} and {\em regret}, expressed as a max-min or min-max optimization. Several examples illustrate the benefits of the competitive analysis approach to code design compared to the compound channel.

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arXiv2023

Perfect vs. Independent Feedback in the Multiple-Access Channel

The multiple access channel (MAC) capacity with feedback is considered under feedback models designed to tease out which factors contribute to the MAC feedback capacity benefit. Comparing the capacity of a MAC with ``perfect'' feedback, which causally delivers to the transmitters the true channel output, to that of a MAC with ``independent'' feedback, which causally delivers to the transmitters an independent instance of that same channel output, allows separation of effects like cooperation from alternative feedback benefits such as knowledge of the channel instance. Proving that the Cover-Leung (CL) achievability bound, which is known to be loose for some channels, is achievable also under (shared or distinct) independent feedback at the transmitters shows that the CL bound does not require transmitter knowledge of the channel instance. Proving that each transmitter's maximal rate under independent feedback exceeds that under perfect feedback highlights the potential power of an independent look at the channel output.

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arXiv2023

Multiple Key-cast over Networks

The multicast key-dissemination problem over noiseless networks, introduced by Langberg and Effros [ITW 2022], here called the ``key-cast'' problem, captures the task of disseminating a shared secret random key to a set of terminals over a given network. Unlike traditional communication, where messages must be delivered from source to destination(s) unchanged, key-cast is more flexible since key-cast need not require source reconstruction at destination nodes. For example, the distributed keys can be mixtures of sources from which the sources themselves may be unrecoverable. The work at hand considers key dissemination in the single-source, multiple-multicast network coding setting, i.e., the ``multiple key-cast'' problem. Here, distinct keys are to be simultaneously transmitted from a single source node to multiple terminal sets, one shared random key per multicast set. Scenarios include the secure setting, in which only the source and intended destinations gain information about a given key; and the non-secure setting in which the only requirement is that the knowledge of one key does not reveal information about another. In both settings, we present combinatorial conditions for key dissemination and design corresponding multiple key-cast schemes. In addition, we compare the multiple key-cast rate with and without the restriction of source reconstruction, the former corresponding to traditional forms of communication; key-cast achieves a strict advantage in rate when source reconstruction is relaxed.

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arXiv2022

Network Coding Multicast Key-Capacity

For a multi-source multi-terminal noiseless network, the key-dissemination problem involves the task of multicasting a secret key K from the network sources to its terminals. As in secure multicast network-coding, in the key-dissemination problem the source nodes have access to independent randomness and, as the network is noiseless, the resulting key K is a function of the sources' information. However, different from traditional forms of multicast, in key-dissemination the key K need not consist of source messages, but rather may be any function of the information generated at the sources, as long as it is shared by all terminals. Allowing the shared key K to be a mixture of source information grants a flexibility to the communication process which gives rise to the potential of increased key-rates when compared to traditional secure multicast. The multicast key-capacity is the supremum of achievable key-rates, subject to the security requirement that the shared key is not revealed to an eavesdropper with predefined eavesdropping capabilities. The key-dissemination problem (termed also, secret key-agreement) has seen significant studies over the past decades in memoryless network structures. In this work, we initiate the study of key-dissemination in the context of noiseless networks, i.e., network coding. In this context, we study similarities and differences between traditional secure-multicast and the more lenient task of key-dissemination.

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arXiv2022

The Capacity of Causal Adversarial Channels

We characterize the capacity for the discrete-time arbitrarily varying channel with discrete inputs, outputs, and states when (a) the encoder and decoder do not share common randomness, (b) the input and state are subject to cost constraints, (c) the transition matrix of the channel is deterministic given the state, and (d) at each time step the adversary can only observe the current and past channel inputs when choosing the state at that time. The achievable strategy involves stochastic encoding together with list decoding and a disambiguation step. The converse uses a two-phase "babble-and-push" strategy where the adversary chooses the state randomly in the first phase, list decodes the output, and then chooses state inputs to symmetrize the channel in the second phase. These results generalize prior work on specific channels models (additive, erasure) to general discrete alphabets and models.

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