arXiv subjects

Yihan Zhang

Publications and source records attributed to Yihan Zhang.

63 records · Page 4Linked to original sources

arXiv2021

Network Coding with Myopic Adversaries

We consider the problem of reliable communication over a network containing a hidden {\it myopic} adversary who can eavesdrop on some $z_{ro}$ links, jam some $z_{wo}$ links, and do both on some $z_{rw}$ links. We provide the first information-theoretically tight characterization of the optimal rate of communication possible under all possible settings of the tuple $(z_{ro},z_{wo},z_{rw})$ by providing a novel coding scheme/analysis for a subset of parameter regimes. In particular, our vanishing-error schemes bypass the Network Singleton Bound (which requires a zero-error recovery criteria) in a certain parameter regime where the capacity had been heretofore open. As a direct corollary we also obtain the capacity of the corresponding problem where information-theoretic secrecy against eavesdropping is required in addition to reliable communication.

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arXiv2021

Zero-Error Communication over Adversarial MACs

We consider zero-error communication over a two-transmitter deterministic adversarial multiple access channel (MAC) governed by an adversary who has access to the transmissions of both senders (hence called omniscient) and aims to maliciously corrupt the communication. None of the encoders, jammer and decoder is allowed to randomize using private or public randomness. This enforces a combinatorial nature of the problem. Our model covers a large family of channels studied in the literature, including all deterministic discrete memoryless noisy or noiseless MACs. In this work, given an arbitrary two-transmitter deterministic omniscient adversarial MAC, we characterize when the capacity region 1) has nonempty interior (in particular, is two-dimensional); 2) consists of two line segments (in particular, has empty interior); 3) consists of one line segment (in particular, is one-dimensional); 4) or only contains $ (0,0) $ (in particular, is zero-dimensional). This extends a recent result by Wang, Budkuley, Bogdanov and Jaggi (2019) from the point-to-point setting to the multiple access setting. Indeed, our converse arguments build upon their generalized Plotkin bound and involve delicate case analysis. One of the technical challenges is to take care of both "joint confusability" and "marginal confusability". In particular, the treatment of marginal confusability does not follow from the point-to-point results by Wang et al. Our achievability results follow from random coding with expurgation.

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arXiv2020

MG-GCN: Fast and Effective Learning with Mix-grained Aggregators for Training Large Graph Convolutional Networks

Graph convolutional networks (GCNs) have been employed as a kind of significant tool on many graph-based applications recently. Inspired by convolutional neural networks (CNNs), GCNs generate the embeddings of nodes by aggregating the information of their neighbors layer by layer. However, the high computational and memory cost of GCNs due to the recursive neighborhood expansion across GCN layers makes it infeasible for training on large graphs. To tackle this issue, several sampling methods during the process of information aggregation have been proposed to train GCNs in a mini-batch Stochastic Gradient Descent (SGD) manner. Nevertheless, these sampling strategies sometimes bring concerns about insufficient information collection, which may hinder the learning performance in terms of accuracy and convergence. To tackle the dilemma between accuracy and efficiency, we propose to use aggregators with different granularities to gather neighborhood information in different layers. Then, a degree-based sampling strategy, which avoids the exponential complexity, is constructed for sampling a fixed number of nodes. Combining the above two mechanisms, the proposed model, named Mix-grained GCN (MG-GCN) achieves state-of-the-art performance in terms of accuracy, training speed, convergence speed, and memory cost through a comprehensive set of experiments on four commonly used benchmark datasets and a new Ethereum dataset.

cs.LG↗

arXiv2020

Tight List-Sizes for Oblivious AVCs under Constraints

We study list-decoding over adversarial channels governed by oblivious adversaries (a.k.a. oblivious Arbitrarily Varying Channels (AVCs)). This type of adversaries aims to maliciously corrupt the communication without knowing the actual transmission from the sender. For any oblivious AVCs potentially with constraints on the sender's transmitted sequence and the adversary's noise sequence, we determine the exact value of the minimum list-size that can support a reliable communication at positive rate. This generalizes a classical result by Hughes (IEEE Transactions on Information Theory, 1997) and answers an open question posed by Sarwate and Gastpar (IEEE Transactions on Information Theory, 2012). A lower bound on the list-decoding capacity (whenever positive) is presented. Under a certain combinatorial conjecture, we also prove a matching upper bound. En route to a tight characterization of the list-decoding capacity, we propose a method for subcode construction towards the resolution of the combinatorial conjecture.

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arXiv2020

Quadratically Constrained Myopic Adversarial Channels

We study communication in the presence of a jamming adversary where quadratic power constraints are imposed on the transmitter and the jammer. The jamming signal is allowed to be a function of the codebook, and a noncausal but noisy observation of the transmitted codeword. For a certain range of the noise-to-signal ratios (NSRs) of the transmitter and the jammer, we are able to characterize the capacity of this channel under deterministic encoding or stochastic encoding, i.e., with no common randomness between the encoder/decoder pair. For the remaining NSR regimes, we determine the capacity under the assumption of a small amount of common randomness (at most $2\log(n)$ bits in one sub-regime, and at most $Ω(n)$ bits in the other sub-regime) available to the encoder-decoder pair. Our proof techniques involve a novel myopic list-decoding result for achievability, and a Plotkin-type push attack for the converse in a subregion of the NSRs, both of which which may be of independent interest. We also give bounds on the secrecy capacity of this channel assuming that the jammer is simultaneously eavesdropping.

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arXiv2020

Improved efficiency for covering codes matching the sphere-covering bound

A covering code is a subset $\mathcal{C} \subseteq \{0,1\}^n$ with the property that any $z \in \{0,1\}^n$ is close to some $c \in \mathcal{C}$ in Hamming distance. For every $ε,δ>0$, we show a construction of a family of codes with relative covering radius $δ+ ε$ and rate $1 - \mathrm{H}(δ) $ with block length at most $\exp(O((1/ε) \log (1/ε)))$ for every $ε> 0$. This improves upon a folklore construction which only guaranteed codes of block length $\exp(1/ε^2)$. The main idea behind this proof is to find a distribution on codes with relatively small support such that most of these codes have good covering properties.

cs.IT↗

arXiv2020

Quadratically Constrained Two-way Adversarial Channels

We study achievable rates of reliable communication in a power-constrained two-way additive interference channel over the real alphabet where communication is disrupted by a power-constrained jammer. This models the wireless communication scenario where two users Alice and Bob, operating in the full duplex mode, wish to exchange messages with each other in the presence of a jammer, James. Alice and Bob simultaneously transmit their encodings $ \underline{x}_A $ and $\underline{x}_B $ over $ n $ channel uses. It is assumed that James can choose his jamming signal $ \underline{s} $ as a noncausal randomized function of $ \underline{x}_A $ and $ \underline{x}_B $, and the codebooks used by Alice and Bob. Alice and Bob observe $ \underline{x}_A+\underline{x}_B +\underline{s}$, and must recover each others' messages reliably. In this article, we provide upper and lower bounds on the capacity of this channel which match each other and equal $ \frac{1}{2}\log\left(\frac{1}{2} + \mathsf{SNR}\right) $ in the high-$\mathsf{SNR}$ regime (where $\mathsf{SNR}$, signal to noise ratios, is defined as the ratio of the power constraints of the users to the power constraint of the jammer). We give a code construction based on lattice codes, and derive achievable rates for large $\mathsf{SNR}$. We also present upper bounds based on two specific attack strategies for James. Along the way, sumset property of lattices for the achievability and general properties of capacity-achieving codes for memoryless channels for the converse are proved, which might be of independent interest.

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arXiv2020

List Decoding for Oblivious Arbitrarily Varying MACs: Constrained and Gaussian

This paper provides upper and lower bounds on list sizes of list decoding for two-user oblivious arbitrarily varying multiple access channels (AVMACs). An oblivious AVMAC consists of two users who wish to transmit messages (without cooperation) to a remote receiver, a malicious jammer who only has access to the codebooks of both users (which are also known to every party), and a receiver who is required to decode the message pair sent by both users. The transmitters send codewords which encode messages subject to input constraints. The jammer, without knowing the transmitted codeword pair, injects adversarial noise subject to state constraints so as to actively corrupt the communication from both users to the receiver. It was left as an open question by Cai (2016) to nail down the smallest list sizes for constrained AVMACs. Our inner and outer bounds are based on a judicious notion of symmetrizability for AVMACs introduced by Cai (2016) with twists to incorporate input and state constraints. The analysis follows techniques by Csiszár and Narayan (1988). When no constraints are imposed, our bound collapse to prior results by Cai (2016) which characterized the list-decoding capacity region of unconstrained AVMACs. Techniques used in this paper can also be extended to the Gaussian case and we characterize the list-decoding capacity region for Gaussian AVMACs. The converse argument relies on a bounding technique recently used by Hosseinigoki and Kosut (2019).

cs.IT↗

arXiv2019

Generalized List Decoding

This paper concerns itself with the question of list decoding for general adversarial channels, e.g., bit-flip ($\textsf{XOR}$) channels, erasure channels, $\textsf{AND}$ ($Z$-) channels, $\textsf{OR}$ channels, real adder channels, noisy typewriter channels, etc. We precisely characterize when exponential-sized (or positive rate) $(L-1)$-list decodable codes (where the list size $L$ is a universal constant) exist for such channels. Our criterion asserts that: "For any given general adversarial channel, it is possible to construct positive rate $(L-1)$-list decodable codes if and only if the set of completely positive tensors of order-$L$ with admissible marginals is not entirely contained in the order-$L$ confusability set associated to the channel." The sufficiency is shown via random code construction (combined with expurgation or time-sharing). The necessity is shown by 1. extracting equicoupled subcodes (generalization of equidistant code) from any large code sequence using hypergraph Ramsey's theorem, and 2. significantly extending the classic Plotkin bound in coding theory to list decoding for general channels using duality between the completely positive tensor cone and the copositive tensor cone. In the proof, we also obtain a new fact regarding asymmetry of joint distributions, which be may of independent interest. Other results include 1. List decoding capacity with asymptotically large $L$ for general adversarial channels; 2. A tight list size bound for most constant composition codes (generalization of constant weight codes); 3. Rederivation and demystification of Blinovsky's [Bli86] characterization of the list decoding Plotkin points (threshold at which large codes are impossible); 4. Evaluation of general bounds ([WBBJ]) for unique decoding in the error correction code setting.

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