We introduce the paradigm of validated decentralized learning for undirected networks with heterogeneous data and possible adversarial infiltration. We require ($a$) convergence to a global empirical loss minimizer when adversaries are absent, and$(\boldsymbol{b})$either detection of adversarial presence or convergence to an admissible consensus model in their presence. This contrasts sharply with the traditional byzantine-robustness requirement of convergence to an admissible consensus irrespective of the adversarial configuration. To this end, we propose the Valid protocol which, to the best of our knowledge, is the first to achieve a validated learning guarantee. Moreover, Valid offers an$O(1/T)$convergence rate (under pertinent regularity assumptions), and computational and communication complexities comparable to non-adversarial distributed stochastic gradient descent. Remarkably, Valid retains optimal performance metrics in adversary-free environments, sidestepping the robustness penalties observed in prior byzantine-robust methods. A distinctive aspect of our study is a heterogeneity metric based on the norms of individual agents' gradients computed at the global empirical loss minimizer. This not only provides a natural statistic for detecting significant byzantine disruptions but also allows us to prove the optimality of Valid in wide generality. Lastly, our numerical results reveal that, in the absence of adversaries, Validcon-verges faster than state-of-the-art byzantine robust algorithms, while when adversaries are present, Valid terminates with each honest agent either converging to an admissible consensus or declaring adversarial presence in the network.

In this work we propose RELDEC, a novel approach for sequential decoding of moderate length low-density parity-check (LDPC) codes. The main idea behind RELDEC is that an optimized decoding policy is subsequently obtained via reinforcement learning based on a Markov decision process (MDP). In contrast to our previous work, where an agent learns to schedule only a single check node (CN) within a group (cluster) of CNs per iteration, in this work we train the agent to schedule all CNs in a cluster, and all clusters in every iteration. That is, in each learning step of RELDEC an agent learns to schedule CN clusters sequentially depending on a reward associated with the outcome of scheduling a particular cluster. We also modify the state space representation of the MDP, enabling RELDEC to be suitable for larger block length LDPC codes than those studied in our previous work. Furthermore, to address decoding under varying channel conditions, we propose agile meta-RELDEC (AM-RELDEC) that employs meta-reinforcement learning. The proposed RELDEC scheme significantly outperforms standard flooding and random sequential decoding for a variety of LDPC codes, including codes designed for 5G new radio.

We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal framework and a series of techniques to obtain upper and lower bounds on the network’s (1-shot) capacity, improving on the best currently known results. In particular, we show that traditional cut-set bounds are not tight in general in the presence of a restricted adversary, and that the non-tightness of these is caused precisely by the restrictions imposed on the noise (and not, as one may expect, by the alphabet size). We also show that, in sharp contrast with the typical situation within network coding, capacity cannot be achieved in general by combining linear network coding with end-to-end channel coding, not even when the underlying network has a single source and a single terminal. We finally illustrate how network decoding techniques are necessary to achieve capacity in the scenarios we examine, exhibiting capacity-achieving schemes and lower bounds for various classes of networks.

This work establishes that the physical layer can be used to perform information-theoretic authentication in additive white Gaussian noise (AWGN) channels, as long as the adversary is not omniscient. The model considered consists of an encoder, decoder, and adversary, where the adversary knows the message given to the encoder, has a non-causal noisy observation of the encoder’s transmission and may use unlimited transmission power, while the decoder observes a noisy version of the sum of the encoder and adversary’s outputs. A method to modify a generic existing channel code to enable authentication is presented. This method relies on injecting message-dependent noise into the transmission and accepting the transmission as authentic only if the correct noise levels for the decoded message are observed. One drawback to this method is that the encoder must still transmit a low-power signal in the case where there is no message to send. It is shown that this modification costs an asymptotically negligible amount of the coding rate, while still enabling authentication as long as the adversary’s observation is not noiseless. Also notable is that this modification is not (asymptotically) a function of the statistical characterization of the adversary’s channel and no secret key is required. We believe these features will pave the way for a robust practical implementation. Using these results, the channel-authenticated capacity is calculated and shown to be equal to the non-adversarial channel capacity. As our results will show, information-theoretic authentication in AWGN channels is possible without the need for the legitimate party to have a model-based advantage over the adversary. While this modular scheme is designed for use in the given channel model, it is applicable to a wide range of settings.

In this paper, we consider approaches to designing Tanner codes to protect against symbol loss from multiple erasures. First, we note that Tanner codes inherit locality and availability from their inner codes, allowing one to design longer codes with specified locality and availability. Availability is desirable in that multiple disjoint repair groups increase the likelihood that symbols are available to repair erased ones. Even so, particular patterns of erasures well-distributed across the repair groups may prevent recovery. Hence, we consider an alternative using hierarchical locality which implements tiered recovery, where the tier utilized depends on the number of erasures. Finally, we define hierarchical stopping sets to characterize local message-passing decoder failure at the various repair levels.

In unsecured communications settings, ascertaining the trustworthiness of received information, called authentication, is paramount. We consider keyless authentication over an arbitrarily-varying channel, where channel states are chosen by a malicious adversary with access to noisy versions of transmitted sequences. We have shown previously that a channel condition termed U-overwritability is a sufficient condition for zero authentication capacity over such a channel, and also that with a deterministic encoder, a sufficiently clear-eyed adversary is essentially omniscient. In this paper, we show that even if the authentication capacity with a deterministic encoder and an essentially omniscient adversary is zero, allowing a stochastic encoder can result in a positive authentication capacity. Furthermore, the authentication capacity with a stochastic encoder can be equal to the no-adversary capacity of the underlying channel in this case. We illustrate this for a binary channel model, which provides insight into the more general case.

The multi-armed bandit (MAB) problem refers to the dilemma encountered by a gambler when deciding which arm of a multi-armed slot machine to pull in order to maximize the total reward earned in a sequence of pulls. In this paper, we model the scheduling of a node-wise sequential LDPC decoder as a Markov decision process, where the underlying Tanner graph is viewed as a slot machine with multiple arms corresponding to the check nodes. A fictitious gambler decides which check node to pull (schedule) next by observing a reward associated with each pull. This interaction enables the gambler to discover an optimized scheduling policy that aims to reach a codeword output by propagating the fewest possible messages. Based on this policy, we contrive a novel MAB-based node-wise scheduling (MABNS) algorithm to perform sequential decoding of LDPC codes. Simulation results show that the MAB-NS scheme, aided by an appropriate scheduling policy, outperforms traditional scheduling schemes in terms of complexity and bit error probability.

Absorbing sets are combinatorial structures in a Tanner graph that have been shown to characterize iterative decoder failure, and particularly error floor behavior, of LDPC codes. In this paper, we examine the connection between absorbing sets and the syndromes of their support vectors. Using this framework, we provide a new characterization of fully absorbing sets, which have been considered the most harmful for iterative decoders. We also show how the sets of absorbing set support vectors appear as translates of codewords in subspaces of the code. These techniques are used to derive new search methods for absorbing sets.

We show in this work that reinforcement learning can be successfully applied to decoding short to moderate length sparse graph-based channel codes. Specifically, we focus on low-density parity check (LDPC) codes, which for example have been standardized in the context of 5G cellular communication systems due to their excellent error correcting performance. These codes are typically decoded via belief propagation iterative decoding on the corresponding bipartite (Tanner) graph of the code via flooding, i.e., all check and variable nodes in the Tanner graph are updated at once. In contrast, in this paper we utilize a sequential update policy which selects the optimum check node (CN) scheduling in order to improve decoding performance. In particular, we model the CN update process as a multi-armed bandit process with dependent arms and employ a Q-learning scheme for optimizing the CN scheduling policy. In order to reduce the learning complexity, we propose a novel graph-induced CN clustering approach to partition the state space in such a way that dependencies between clusters are minimized. Our results show that compared to other decoding approaches from the literature, the proposed reinforcement learning scheme not only significantly improves the decoding performance, but also reduces the decoding complexity dramatically once the scheduling policy is learned.

Authentication in the presence of a malicious adversary consists of either recovering the legitimate transmission or declaring that the adversary has interfered with the transmission. In this work, we present a structured coding scheme for keyless authentication over a discrete memoryless binary-input, symmetric adversarial channel. Our scheme allows for coding rates up to the non-adversarial capacity of the underlying channel, as well as bounded-complexity decoding.

We construct a modular scheme which extends codes for wiretap channels of type I for use in wiretap channels of type II. This is done by using a concatenate and permute strategy, wherein multiple uses of the wiretap type I code are concatenated and then the joint sequence of symbols permuted. The choice of permutation is then encoded with a short code and appended to the transmitted sequence. Analysis shows essentially no degradation in operational parameters (rate, error rate, leakage) for the new code over the wiretap type II channel when compared to those of multiple uses of the original code over the wiretap type I channel.