The idea of security sharing goes back to Nakamoto's introduction of merge mining, a technique that enables Bitcoin miners to reuse their hash power to bootstrap and secure other Proof-of-Work (PoW) blockchains. However, with the rise of Proof-of-Stake (PoS) chains, there is a need for new methods of Bitcoin security sharing. We introduce Bitcoin staking, a protocol that allows Bitcoin holders to trustlessly use their idle asset to secure a PoS chain. The key challenge is to enable automatic slashing of bitcoins on the Bitcoin chain upon safety violations on the PoS chain. We achieve this using double-authentication-preventing signatures, finality gadgets and bi-directional timestamping between Bitcoin and the PoS chain. Our design is entirely modular and can be integrated with any PoS chain. A version of this protocol was deployed to secure the Babylon mainnet in April 2025 and currently has over 58,000 bitcoins staked (about 4 billion USD at current prices) while paying only 0.05

Fourteen years after the invention of Bitcoin, there has been a proliferation of many permissionless blockchains. Each such chain provides a public ledger that can be written to and read from by anyone. In this multi-chain world, a natural question arises: what is the optimal security an existing blockchain, a consumer chain, can extract by only reading and writing to k other existing blockchains, the provider chains? We design a protocol, called interchain timestamping, and show that it extracts the maximum economic security from the provider chains, as quantified by the slashable safety resilience. We observe that interchain timestamps are already provided by light-client based bridges, so interchain timestamping can be readily implemented for Cosmos chains connected by the Inter-Blockchain Communication (IBC) protocol. We compare interchain timestamping with cross-staking, the original solution to mesh security, as well as with Trustboost, another recent security sharing protocol.

We apply linear network coding (LNC) to broadcast a block of data packets from one sender to a set of receivers via lossy wireless channels, assuming each receiver already possesses a subset of these packets and wants the rest. We aim to characterize the average packet decoding delay (APDD), which reflects how soon each individual data packet can be decoded by each receiver on average, and to minimize it while achieving optimal throughput. To this end, we first derive closed-form lower bounds on the expected APDD of all LNC techniques under random packet erasures. We then prove that these bounds are NP-hard to achieve and, thus, that APDD minimization is an NP-hard problem. We then study the performance of some existing LNC techniques, including random linear network coding (RLNC) and instantly decodable network coding (IDNC). We proved that all throughput-optimal LNC techniques can approximate the minimum expected APDD with a ratio between 4/3 and 2. In particular, the ratio of RLNC is exactly 2. We then prove that all IDNC techniques are only heuristics in terms of throughput optimization and {cannot guarantee an APDD approximation ratio for at least a subset of the receivers}. Finally, we propose hyper-graphic linear network coding (HLNC), a novel throughput-optimal and APDD-approximating LNC technique based on a hypergraph model of receivers' packet reception state. We implement it under different availability of receiver feedback, and numerically compare its performance with RLNC and a heuristic general IDNC technique. The results show that the APDD performance of HLNC is better under all tested system settings, even if receiver feedback is only collected intermittently.

We apply linear network coding (LNC) to broadcast a block of data packets from one sender to a set of receivers via lossy wireless channels, assuming that each receiver already possesses a subset of these packets (through previous systematic transmissions) and wants the rest. We aim to characterize the average packet decoding delay (APDD), which reflects how soon each data packet can be decoded by each receiver on average, and to minimize it without sacrificing throughput. To this end, we first derive closed-form lower bounds on the expected APDD of LNC techniques. We then prove that determining whether these lower bounds are tight is NP-hard and so is APDD minimization. We then prove that every throughput-optimal LNC technique can approximate the minimum expected APDD with a ratio between 4/3 and 2 and that this ratio is exactly 2 for random LNC (RLNC). We also show that instantly decodable network coding (IDNC) techniques cannot approximate APDD due to suboptimal throughput. Finally, we propose hypergraphic LNC (HLNC), a novel throughput-optimal and APDD-approximating technique based on a hypergraphic model of receivers. Our simulations show that the APDD of HLNC significantly outperforms existing techniques, including RLNC, under all considered settings without any sacrifice on throughput. Résumé—Nous appliquons le codage linéaire de réseau (LNC) pour diffuser un bloc de paquets de données d’un émetteur à un ensemble de récepteurs via des canaux sans fil avec pertes, en supposant que chaque récepteur possède déjà un sous-ensemble de ces paquets (par des transmissions systématiques précédentes) et veut le reste. Nous cherchons à caractériser le délai moyen de décodage des paquets (APDD), qui reflète la rapidité avec laquelle chaque paquet de données peut être décodé par chaque récepteur en moyenne, et à le minimiser sans sacrifier le débit. À cette fin, nous dérivons d’abord des limites inférieures en forme fermée sur l’APDD attendu des techniques LNC. Nous prouvons ensuite déterminer si ces limites inférieures sont serrées, NP-hard et que la minimisation de l’APDD l’est aussi. Nous prouvons ensuite que chaque technique LNC optimale en termes de débit peut approximer l’APDD minimum attendu avec un rapport entre 4/3 et 2 et que ce rapport est exactement 2 pour les LNC aléatoires (RLNC). Nous montrons également que les techniques de codage de réseau instantanément décodable (IDNC) ne peuvent pas approximer l’APDD en raison d’un débit sous-optimal. Enfin, nous proposons le LNC hypergraphique (HLNC), une nouvelle technique d’optimisation du débit et d’approximation de l’APDD basée sur un modèle hypergraphique des récepteurs. Nos simulations montrent que l’APDD de HLNC surpasse de manière significative les techniques existantes, y compris RLNC, dans tous les paramètres considérés sans aucun sacrifice sur le débit.

Today's blockchain designs suffer from a trilemma claiming that no blockchain system can simultaneously achieve decentralization, security, and performance scalability. For current blockchain systems, as more nodes join the network, the efficiency of the system (computation, communication, and storage) stays constant at best. A leading idea for enabling blockchains to scale efficiency is the notion of sharding: different subsets of nodes handle different portions of the blockchain, thereby reducing the load for each individual node. However, existing sharding proposals achieve efficiency scaling by compromising on trust - corrupting the nodes in a given shard will lead to the permanent loss of the corresponding portion of data. In this paper, we settle the trilemma by demonstrating a new protocol for coded storage and computation in blockchains. In particular, we propose PolyShard: “polynomially coded sharding” scheme that achieves information-theoretic upper bounds on the efficiency of the storage, system throughput, as well as on trust, thus enabling a truly scalable system. We provide simulation results that numerically demonstrate the performance improvement over state of the arts, and the scalability of the PolyShard system. Finally, we discuss potential enhancements, and highlight practical considerations in building such a system.

In this paper, we propose coded Merkle tree (CMT), a novel hash accumulator that offers a constant-cost protection against data availability attacks in blockchains, even if the majority of the network nodes are malicious. A CMT is constructed using a family of sparse erasure codes on each layer, and is recovered by iteratively applying a peeling-decoding technique that enables a compact proof for data availability attack on any layer. Our algorithm enables any node to verify the full availability of any data block generated by the system by just downloading a (1) byte block hash commitment and randomly sampling (log b) bytes, where b is the size of the data block. With the help of only one connected honest node in the system, our method also allows any node to verify any tampering of the coded Merkle tree by just downloading (log b) bytes. We provide a modular library for CMT in Rust and Python and demonstrate its efficacy inside the Parity Bitcoin client.

We introduce Coded State Machine (CSM), an information-theoretic framework to securely and efficiently execute multiple state machines on Byzantine nodes. The standard method of solving this problem is using State Machine Replication, which achieves high security at the cost of low efficiency. CSM simultaneously achieves the optimal linear scaling in storage, throughput, and security with increasing network size. The storage is scaled via the design of Lagrange coded states and coded input commands that require the same storage size as their origins. The computational efficiency is scaled using a novel delegation algorithm, called INTERMIX, which is an information-theoretically verifiable matrix-vector multiplication algorithm of independent interest.

Training a machine learning model is both compute and data-intensive. Most of the model training is performed on high performance compute nodes and the training data is stored near these nodes for faster training. But there is a growing interest in enabling training near the data. For instance, mobile devices are rich sources of training data. It may not be feasible to consolidate the data from mobile devices into a cloud service, due to bandwidth and data privacy reasons. Training at mobile devices is however fraught with challenges. First mobile devices may join or leave the distributed setting, either voluntarily or due to environmental uncertainties, such as lack of power. Tolerating uncertainties is critical to the success of distributed mobile training. One proactive approach to tolerate computational uncertainty is to store data in a coded format and perform training on coded data. Encoding data is a challenging task since erasure codes require multiple devices to exchange their data to create a coded data partition, which places a significant bandwidth constraint. Furthermore, coded computing traditionally relied on a central node to encode and distribute data to all the worker nodes, which is not practical in a distributed mobile setting. In this paper, we tackle the uncertainty in distributed mobile training using a bandwidth-efficient encoding strategy. We use a Random Linear Network coding (RLNC) which reduces the need to exchange data partitions across all participating mobile devices, while at the same time preserving the property of coded computing to tolerate uncertainties. We implement gradient descent for logistic regression and SVM to evaluate the effectiveness of our mobile training framework. We demonstrate a 50% reduction in total required communication bandwidth compared to MDS coded computation, one of the popular erasure codes.

We study the interplay between the throughput and average packet decoding delay (APDD) of linear network coded (LNC) wireless broadcast systems through studying the approximation of throughput and APDD. We first define strong and weak approximations (based on whether the approximation holds for every receiver or not). We then prove that LNC techniques that strongly approximate throughput can also strongly approximate APDD, but those that weakly approximate throughput do not necessarily weakly approximate APDD. We prove that all throughput-optimal LNC techniques, including random linear network coding, strongly approximate APDD with a ratio between 4/3 and 2. We also prove that all memoryless LNC techniques, including instantly decodable network coding techniques, cannot strongly or weakly approximate throughput, nor strongly approximate APDD.

Data parallelism can boost the training speed of convolutional neural networks (CNN), but could suffer from significant communication costs caused by gradient aggregation. To alleviate this problem, several scalar quantization techniques have been developed to compress the gradients. But these techniques could perform poorly when used together with decentralized aggregation protocols like ring all-reduce (RAR), mainly due to their inability to directly aggregate compressed gradients. In this paper, we empirically demonstrate the strong linear correlations between CNN gradients, and propose a gradient vector quantization technique, named GradiVeQ, to exploit these correlations through principal component analysis (PCA) for substantial gradient dimension reduction. GradiVeQ enables direct aggregation of compressed gradients, hence allows us to build a distributed learning system that parallelizes GradiVeQ gradient compression and RAR communications. Extensive experiments on popular CNNs demonstrate that applying GradiVeQ slashes the wall-clock gradient aggregation time of the original RAR by more than 5X without noticeable accuracy loss, and reduces the end-to-end training time by almost 50%. The results also show that GradiVeQ is compatible with scalar quantization techniques such as QSGD (Quantized SGD), and achieves a much higher speed-up gain under the same compression ratio.

In this paper, we introduce the k× n (with k≤ n) truncated, supplemented Pascal matrix which has the property that any k columns form a linearly independent set. This property is also present in Reed-Solomon codes; however, Reed-Solomon codes are completely dense, whereas the truncated, supplemented Pascal matrix has multiple zeros. If the maximal-distance separable code conjecture is correct, then our matrix has the maximal number of columns (with the aformentioned property) that the conjecture allows. This matrix has applications in coding, network coding, and matroid theory.

Distributed training of deep nets is an important technique to address some of the present day computing challenges like memory consumption and computational demands. Classical distributed approaches, synchronous or asynchronous, are based on the parameter server architecture, i.e., worker nodes compute gradients which are communicated to the parameter server while updated parameters are returned. Recently, distributed training with AllReduce operations gained popularity as well. While many of those operations seem appealing, little is reported about wall-clock training time improvements. In this paper, we carefully analyze the AllReduce based setup, propose timing models which include network latency, bandwidth, cluster size and compute time, and demonstrate that a pipelined training with a width of two combines the best of both synchronous and asynchronous training. Specifically, for a setup consisting of a four-node GPU cluster we show wall-clock time training improvements of up to 5.4x compared to conventional approaches.

The paper focuses on the reliable delivery of a stream of packets from a sender to a set of receivers over a lossy broadcast channel with limited receiver feedback. To facilitate efficient data transfer, the packets are grouped into generations. For each generation, we employ a two-phase coding scheme that transmits uncoded packets in the first phase and coded packets in the second phase. We assume that the packet reception status of receivers after the first phase is known through feedback. To enable tunable tradeoff between throughput, computational load, and packet decoding delay, we partition each generation into sub-generations, such that each coded packet is a linear combination of packets that belong to the same sub-generation. We focus on the optimal sub-generation partitioning problem which limits the number of transmissions required to deliver all packets that belong to each sub-generation. We show that this problem is NP-complete and present a heuristic algorithm for its solution. Our simulation results indicate that the proposed algorithm outperforms existing alternative solutions.

One novel Gram-stain-negative, long rod-shaped, non-spore-forming, non-motile, non-flagellated and strictly aerobic strain, designated M124T, was isolated from diseased Pacific white shrimp Litopenaeus vannamei larvae. Growth occurred at 16-37 °C (optimum 28 °C), in the presence of 2-5 % (w/v) NaCl (optimum 3 %) and at pH 7-8 (optimum pH 7). Phylogenetic analysis based on 16S rRNA gene sequences indicated that strain M124T belonged to the genus Aquimarina and showed highest sequence similarity to Aquimarina penaei P3-1T (96.4 %). The dominant fatty acids of the isolate were iso-C15 : 0 and iso-C17 : 0 3-OH. The major polar lipids comprised phosphatidylethanolamine, one unknown aminolipid, three unknown phospholipids, two unknown glycolipids and one unknown polar lipid. The major respiratory quinone was menaquinone 6 (MK-6). The DNA G+C content of strain M124T was 33.7 mol%. Based on the polyphasic analyses in this study, strain M124T is considered to represent a novel species of the genus Aquimarina, for which the name Aquimarina hainanensis sp. nov. is proposed. The type strain is M124T ( = KCTC 42423T = MCCC 1K00498T).

We consider a setting in which a sender wishes to broadcast a block of K data packets to a set of wireless receivers, where each of the receivers already has a subset of the data packets available to it (e.g., from prior transmissions) and wants to obtain the rest of the packets in the block. Our goal is to find a linear network coding scheme that yields the minimum average packet decoding delay (APDD), i.e., the average time it takes for a receiver to decode a data packet. Our contributions can be summarized as follows. First, we prove that this problem is NP-hard by presenting a reduction from the hypergraph coloring problem. Next, we show that the random linear network coding (RLNC) technique provides an approximate solution to this problem with approximation ratio of 2 with high probability. Next, we present a methodology for designing specialized approximation algorithms for this problem that outperform RLNC solutions while maintaining the same throughput. In a special case of practical interest in which each receiver wants a small number of packets, our solution can achieve an approximation ratio of 4-2/K 3. Finally, we conduct an experimental study that demonstrates the advantages of the presented methodology.

The relationships between microbial communities and aquatic animals have drawn attention. In this study, samples collected from different health statuses (diseased and healthy) and growth stages (zoea, mysis and postlarvae period) of Pacific white shrimp (Litopenaeus vannamei) were obtained from a shrimp hatchery. A total of 240 cultivable bacterial strains were isolated and characterized using 16S rRNA gene sequencing, and three isolates were identified as potential novel species. It was found that Proteobacteria and Bacteroidetes were widely distributed in healthy shrimp at all growth stages, but varied in relative abundance among different stages. Many opportunistic pathogens, such as genera Vibrio and Nautella, were isolated from the diseased samples. Five dominant strains isolated from the diseased samples were selected to test their virulence and four of them (Nautella italica, Pseudoalteromonas piscicida, Vibrio sinaloensis and Vibrio campbellii), especially V. campbellii, were shown to be pathogenic to Artemia. Additionally, 18 out of 143 isolates from the healthy samples, displayed N-acyl-homoserine lactone (AHL) degrading activity, and two species (Tenacibaculum mesophilum and Microbacterium aquimaris) possessed strong degrading activity. These isolates could be applied as probiotic candidates to shrimp hatcheries for controlling diseases caused by quorum sensing dependent pathogens. Overall, this study demonstrates that the bacterial community associated with Pacific white shrimp larvae was highly dynamic under different health statuses and growth stages.Statement of relevance: Provide scientific guidance to commercial shrimp producers. (C) 2015 Elsevier B.V. All rights reserved.

We consider broadcasting a block of packets to multiple wireless receivers under random packet erasures using instantly decodable network coding (IDNC). The sender first broadcasts each packet uncoded once, then generates coded packets according to receivers’ feedback about their missing packets. We focus on strict IDNC (S-IDNC), where each coded packet includes at most one missing packet of every receiver. But, we will also study its relation with generalized IDNC (G-IDNC), where this condition is relaxed. We characterize two fundamental performance limits of S-IDNC: (1) the number of transmissions to complete the broadcast, which measures throughput and (2) average packet decoding delay, which measures how fast each packet is decoded at each receiver on average. We derive a closed-form expression for the expected minimum number of transmissions in terms of the number of packets and receivers and the erasure probability. We prove that it is NP-hard to minimize the average packet decoding delay of S-IDNC. We also prove that the graph models of S- and G-IDNC share the same chromatic number. Next, we design efficient S-IDNC transmission schemes and coding algorithms with full/intermittent receiver feedback. We present simulation results to corroborate the developed theory and compare our schemes with existing ones.

Deterministic linear network coding (DLNC) is an important family of network coding techniques for wireless packet broadcast. In this paper, we show that DLNC is strongly related to and can be effectively studied using matroid theory without bridging index coding. We prove the equivalence between the DLNC solution and matrix matroid. We use this equivalence to study the performance limits of DLNC in terms of the number of transmissions and its dependence on the finite field size. Specifically, we derive the sufficient and necessary condition for the existence of perfect DLNC solutions and prove that such solutions may not exist over certain finite fields. We then show that identifying perfect solutions over any finite field is still an open problem in general. To fill this gap, we develop a heuristic algorithm which employs graphic matroids to find perfect DLNC solutions over any finite field. Numerical results show that its performance in terms of minimum number of transmissions is close to the lower bound, and is better than random linear network coding when the field size is not so large.

Our primary goal in this paper is to better understand and extend the achievable tradeoffs between the throughput and decoding delay performance of network coded wireless broadcast. To this end, we traverse the performance gap between two linear network coding schemes: random linear network coding (RLNC) and instantly decodable network coding (IDNC). Our approach is to appropriately partition a block of partially received data packets into subgenerations and broadcast them separately using RLNC. Through analyzing the factors that affect the performance of a generic partitioning scheme, we are led to develop a coding framework in which subgenerations are created from IDNC coding sets in an IDNC solution. This coding framework consists of a series of coding schemes, with classic RLNC and IDNC identified as two extreme schemes. We develop two basic partitioning guidelines, including disjoint partitioning and even partitioning. We design various implementations of this coding framework, such as partitioning algorithms and generation scheduling strategies, to further improve its throughput and decoding delay, to manage feedback frequency and coding complexity, or to achieve in-block performance adaption. Their effectiveness is verified through extensive simulations, and their performance is compared with an existing work in the literature.