In a recent paper, Jaggi et al. (INFOCOM 2007), presented a distributed polynomial-time rate-optimal network-coding scheme that works in the presence of Byzantine faults. We revisit their adversarial models and augment them with three, arguably realistic, models. In each of the models, we present a distributed scheme that demonstrates the usefulness of the model. In particular, all of the schemes obtain optimal rate $C-z$, where $C$ is the network capacity and $z$ is a bound on the number of links controlled by the adversary.
In this paper we close the gap between end-to-end diversity coding and intra-session network coding for unicast connections resilient against single link failures. In particular, we show that coding operations are sufficient to perform at the source and receiver if the user data can be split into at most two parts over the filed GF(2). Our proof is purely combinatorial and based on standard graph and network flow techniques. It is a linear time construction that defines the route of subflows A, B and A+B between the source and destination nodes. The proposed resilient flow decomposition method…
In this paper we study the problem of storing reliably an archive of versioned data. Specifically, we focus on systems where the differences (deltas) between subsequent versions rather than the whole objects are stored - a typical model for storing versioned data. For reliability, we propose erasure encoding techniques that exploit the sparsity of information in the deltas while storing them reliably in a distributed back-end storage system, resulting in improved I/O read performance to retrieve the whole versioned archive. Along with the basic techniques, we propose a few optimization heurist…
An interactive error correcting code ($\mathsf{iECC}$) is an interactive protocol with the guarantee that the receiver can correctly determine the sender's message, even in the presence of noise. This generalizes the concept of an error correcting code ($\mathsf{ECC}$), which is a non-interactive $\mathsf{iECC}$ that is known to have erasure resilience capped at $\frac12$. The work of \cite{GuptaTZ21} constructed the first $\mathsf{iECC}$ resilient to $> \frac12$ adversarial erasures. However, their $\mathsf{iECC}$ has communication complexity quadratic in the message size. In our work, we con…
This paper provides a source coding theorem for multi-dimensional information signals when, at a given instant, the distribution associated with one arbitrary component of the signal to be compressed is not known and a side information is available at the destination. This new framework appears to be both of information-theoretical and game-theoretical interest: it provides a new type of constraints to compress an information source; it is useful for designing certain types of mediators in games and characterize utility regions for games with signals. Regarding the latter aspect, we apply the …
An error correcting code ($\mathsf{ECC}$) allows a sender to send a message to a receiver such that even if a constant fraction of the communicated bits are corrupted, the receiver can still learn the message correctly. Due to their importance and fundamental nature, $\mathsf{ECC}$s have been extensively studied, one of the main goals being to maximize the fraction of errors that the $\mathsf{ECC}$ is resilient to. For adversarial erasure errors (over a binary channel) the maximal error resilience of an $\mathsf{ECC}$ is $\frac12$ of the communicated bits. In this work, we break this $\frac12$…
This paper considers rateless network error correction codes for reliable multicast in the presence of adversarial errors. Most existing network error correction codes are designed for a given network capacity and maximum number of errors known a priori to the encoder and decoder. However, in certain practical settings it may be necessary to operate without such a priori knowledge. We present rateless coding schemes for two adversarial models, where the source sends more redundancy over time, until decoding succeeds. The first model assumes there is a secret channel between the source and the …
Given a noiseless protocol $π_0$ computing a function $f(x, y)$ of Alice and Bob's private inputs $x, y$, the goal of interactive coding is to construct an error-resilient protocol $π$ computing $f$ such that even if some fraction of the communication is adversarially corrupted, both parties still learn $f(x, y)$. Ideally, the resulting scheme $π$ should be positive rate, computationally efficient, and achieve optimal error resilience. While interactive coding over large alphabets is well understood, the situation over the binary alphabet has remained evasive. At the present moment, the known …
In large scale distributed storage systems (DSS) deployed in cloud computing, correlated failures resulting in simultaneous failure (or, unavailability) of blocks of nodes are common. In such scenarios, the stored data or a content of a failed node can only be reconstructed from the available live nodes belonging to the available blocks. To analyze the resilience of the system against such block failures, this work introduces the framework of Block Failure Resilient (BFR) codes, wherein the data (e.g., a file in DSS) can be decoded by reading out from a same number of codeword symbols (nodes) …
We analyze a wireless line network employing wireless network coding. The two end nodes exchange their packets through relays. While a packet at a relay might not find its coding pair upon arrival, a transmission cost can be reduced by waiting for coding with a packet from the other side. To strike a balance between the reduced transmission cost and the cost incurred by the delay, a scheduling algorithm determining either to transmit an uncoded packet or to wait for coding is needed. Because of highly uncertain traffic injections, scheduling with no assumption of the traffic is critical. This …
A combinatorial framework for adversarial network coding is presented. Channels are described by specifying the possible actions that one or more (possibly coordinated) adversaries may take. Upper bounds on three notions of capacity (the one-shot capacity, the zero-error capacity, and the compound zero-error capacity) are obtained for point-to-point channels, and generalized to corresponding capacity regions appropriate for multi-source networks. A key result of this paper is a general method by which bounds on these capacities in point-to-point channels may be ported to networks. This techniq…
The adversarial wiretap channel (AWTC) model is a secure communication model in which adversary can directly read and write the transmitted bits in legitimate communication with fixed fractions. In this paper we propose a secure polar coding scheme to provide secure and reliable communication over the AWTC model. For the adversarial reading and writing action, we present a $ρ$ equivalent channel block and study its transformation under the channel polarization operation. We find that the generated channels are polarized in the sense that part of them are full-noise channels with probability al…
Distributed implementations of gradient-based methods, wherein a server distributes gradient computations across worker machines, suffer from slow running machines, called 'stragglers'. Gradient coding is a coding-theoretic framework to mitigate stragglers by enabling the server to recover the gradient sum in the presence of stragglers. 'Approximate gradient codes' are variants of gradient codes that reduce computation and storage overhead per worker by allowing the server to approximately reconstruct the gradient sum. In this work, our goal is to construct approximate gradient codes that are …
A major hurdle in machine learning is scalability to massive datasets. Approaches to overcome this hurdle include compression of the data matrix and distributing the computations. \textit{Leverage score sampling} provides a compressed approximation of a data matrix using an importance weighted subset. \textit{Gradient coding} has been recently proposed in distributed optimization to compute the gradient using multiple unreliable worker nodes. By designing coding matrices, gradient coded computations can be made resilient to stragglers, which are nodes in a distributed network that degrade syst…
Distributed model training is vulnerable to byzantine system failures and adversarial compute nodes, i.e., nodes that use malicious updates to corrupt the global model stored at a parameter server (PS). To guarantee some form of robustness, recent work suggests using variants of the geometric median as an aggregation rule, in place of gradient averaging. Unfortunately, median-based rules can incur a prohibitive computational overhead in large-scale settings, and their convergence guarantees often require strong assumptions. In this work, we present DRACO, a scalable framework for robust distri…
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 …
A major hurdle in machine learning is scalability to massive datasets. One approach to overcoming this is to distribute the computational tasks among several workers. \textit{Gradient coding} has been recently proposed in distributed optimization to compute the gradient of an objective function using multiple, possibly unreliable, worker nodes. By designing distributed coded schemes, gradient coded computations can be made resilient to \textit{stragglers}, nodes with longer response time comparing to other nodes in a distributed network. Most such schemes rely on operations over the real or co…
We study the information leakage to a guessing adversary in zero-error source coding. The source coding problem is defined by a confusion graph capturing the distinguishability between source symbols. The information leakage is measured by the ratio of the adversary's successful guessing probability after and before eavesdropping the codeword, maximized over all possible source distributions. Such measurement under the basic adversarial model where the adversary makes a single guess and allows no distortion between its estimator and the true sequence is known as the maximum min-entropy leakage…
Berger's paper `The Source Coding Game', IEEE Trans. Inform. Theory, 1971, considers the problem of finding the rate-distortion function for an adversarial source comprised of multiple known IID sources. The adversary, called the `switcher', was allowed only causal access to the source realizations and the rate-distortion function was obtained through the use of a type covering lemma. In this paper, the rate-distortion function of the adversarial source is described, under the assumption that the switcher has non-causal access to all source realizations. The proof utilizes the type covering le…
