@inproceedings{20667,
  abstract     = {We explore the problem of mean estimation for a high-dimensional binary symmetric Gaussian mixture model, where the label (sign) follows a time-inhomogeneous Markov chain. We propose a spectral estimator based on a partition of a subset of the samples to blocks. We develop a computationally efficient algorithm to find the optimal blocks, and derive minimax lower bounds on the estimation loss of any estimator, which establish the effectiveness of our proposed estimator. The resulting minimax rate illuminates the interplay between the sample size, dimension, signal strength, and the memory on the loss.},
  author       = {El Latif Kadry, Abd and Zhang, Yihan and Weinberger, Nir},
  booktitle    = {2025 IEEE International Symposium on Information Theory Proceedings},
  isbn         = {9798331543990},
  issn         = {2157-8095},
  location     = {Ann Arbor, MI, United States},
  publisher    = {IEEE},
  title        = {{Mean estimation in high-dimensional binary timeinhomogeneous Markov Gaussian mixture models}},
  doi          = {10.1109/ISIT63088.2025.11195426},
  year         = {2025},
}

@article{20734,
  abstract     = {We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective solution. However, despite their wide use, a rigorous performance characterization, as well as a principled way to preprocess the data, are available only for unstructured (i.i.d. Gaussian and Haar orthogonal) designs. In contrast, real-world data matrices are highly structured and exhibit non-trivial correlations. To address the problem, we consider correlated Gaussian designs capturing the anisotropic nature of the features via a covariance matrix Σ. Our main result is a precise asymptotic characterization of the performance of spectral estimators. This allows us to identify the optimal preprocessing that minimizes the number of samples needed for parameter estimation. Surprisingly, such preprocessing is universal across a broad set of designs, which partly addresses a conjecture on optimal spectral estimators for rotationally invariant models. Our principled approach vastly improves upon previous heuristic methods, including for designs common in computational imaging and genetics. The proposed methodology, based on approximate message passing, is broadly applicable and opens the way to the precise characterization of spiked matrices and of the corresponding spectral methods in a variety of settings.},
  author       = {Zhang, Yihan and Ji, Hong Chang and Venkataramanan, Ramji and Mondelli, Marco},
  issn         = {2520-2324},
  journal      = {Mathematical Statistics and Learning},
  number       = {3-4},
  pages        = {193--304},
  publisher    = {EMS Press},
  title        = {{Spectral estimators for structured generalized linear models via approximate message passing}},
  doi          = {10.4171/MSL/52},
  volume       = {8},
  year         = {2025},
}

@inproceedings{19281,
  abstract     = {In this work, we consider the list-decodability and list-recoverability of codes in the zero-rate regime. Briefly, a code 𝒞 ⊆ [q]ⁿ is (p,𝓁,L)-list-recoverable if for all tuples of input lists (Y₁,… ,Y_n) with each Y_i ⊆ [q] and |Y_i| = 𝓁, the number of codewords c ∈ 𝒞 such that c_i ∉ Y_i for at most pn choices of i ∈ [n] is less than L; list-decoding is the special case of 𝓁 = 1. In recent work by Resch, Yuan and Zhang (ICALP 2023) the zero-rate threshold for list-recovery was determined for all parameters: that is, the work explicitly computes p_*: = p_*(q,𝓁,L) with the property that for all ε > 0 (a) there exist positive-rate (p_*-ε,𝓁,L)-list-recoverable codes, and (b) any (p_*+ε,𝓁,L)-list-recoverable code has rate 0. In fact, in the latter case the code has constant size, independent on n. However, the constant size in their work is quite large in 1/ε, at least |𝒞| ≥ (1/(ε))^O(q^L).
Our contribution in this work is to show that for all choices of q,𝓁 and L with q ≥ 3, any (p_*+ε,𝓁,L)-list-recoverable code must have size O_{q,𝓁,L}(1/ε), and furthermore this upper bound is complemented by a matching lower bound Ω_{q,𝓁,L}(1/ε). This greatly generalizes work by Alon, Bukh and Polyanskiy (IEEE Trans. Inf. Theory 2018) which focused only on the case of binary alphabet (and thus necessarily only list-decoding). We remark that we can in fact recover the same result for q = 2 and even L, as obtained by Alon, Bukh and Polyanskiy: we thus strictly generalize their work. 
Our main technical contribution is to (a) properly define a linear programming relaxation of the list-recovery condition over large alphabets; and (b) to demonstrate that a certain function defined on a q-ary probability simplex is maximized by the uniform distribution. This represents the core challenge in generalizing to larger q (as a binary simplex can be naturally identified with a one-dimensional interval). We can subsequently re-utilize certain Schur convexity and convexity properties established for a related function by Resch, Yuan and Zhang along with ideas of Alon, Bukh and Polyanskiy.},
  author       = {Resch, Nicolas and Yuan, Chen and Zhang, Yihan},
  booktitle    = {16th Innovations in Theoretical Computer Science Conference},
  isbn         = {9783959773614},
  issn         = {1868-8969},
  location     = {New York, NY, United States},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Tight bounds on list-decodable and list-recoverable zero-rate codes}},
  doi          = {10.4230/LIPIcs.ITCS.2025.82},
  volume       = {325},
  year         = {2025},
}

@article{14665,
  abstract     = {We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. For any N > 0 and L ∈ Z ≥2 , a multiple packing is a set C of points in R n such that any point in R n lies in the intersection of at most L - 1 balls of radius √ nN around points in C . This is a natural generalization of the sphere packing problem. We study the multiple packing problem for both bounded point sets whose points have norm at most √ nP for some constant P > 0, and unbounded point sets whose points are allowed to be anywhere in R n . Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied over finite fields. We derive the best known lower bounds on the optimal multiple packing density. This is accomplished by establishing an inequality which relates the list-decoding error exponent for additive white Gaussian noise channels, a quantity of average-case nature, to the list-decoding radius, a quantity of worst-case nature. We also derive novel bounds on the list-decoding error exponent for infinite constellations and closed-form expressions for the list-decoding error exponents for the power-constrained AWGN channel, which may be of independent interest beyond multiple packing.},
  author       = {Zhang, Yihan and Vatedka, Shashank},
  issn         = {1557-9654},
  journal      = {IEEE Transactions on Information Theory},
  number       = {2},
  pages        = {1008--1039},
  publisher    = {IEEE},
  title        = {{Multiple packing: Lower bounds via error exponents}},
  doi          = {10.1109/TIT.2023.3334032},
  volume       = {70},
  year         = {2024},
}

@inproceedings{17895,
  abstract     = {We propose a concatenated code construction for a class of discrete-alphabet oblivious arbitrarily varying channels (AVCs) with cost constraints. The code has time and space complexity polynomial in the blocklength n . It uses a Reed-Solomon outer code, logarithmic blocklength random inner codes, and stochastic encoding by permuting the codeword before transmission. When the channel satisfies a condition called strong DS-nonsymmetrizability (a modified version of nonsymmetrizability originally due to Dobrushin and Stambler), we show that the code achieves a rate that for a variety of oblivious AVCs (such as classically studied error/erasure channels) match the known capacities.},
  author       = {Dey, B. K. and Jaggi, S. and Langberg, M. and Sarwate, A. D. and Zhang, Yihan},
  booktitle    = {Proceedings of the 2024 IEEE International Symposium on Information Theory },
  isbn         = {9798350382846},
  issn         = {2157-8095},
  location     = {Athens, Greece},
  pages        = {1586--1591},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{Computationally efficient codes for strongly Dobrushin-Stambler nonsymmetrizable oblivious AVCs}},
  doi          = {10.1109/ISIT57864.2024.10619362},
  year         = {2024},
}

@article{18652,
  abstract     = {Over the last 70 years, information theory and coding has enabled communication technologies that have had an astounding impact on our lives. This is possible due to the match between encoding/decoding strategies and corresponding channel models. Traditional studies of channels have taken one of two extremes: Shannon-theoretic models are inherently average-case in which channel noise is governed by a memoryless stochastic process, whereas coding-theoretic (referred to as “Hamming”) models take a worst-case, adversarial, view of the noise. However, for several existing and emerging communication systems the Shannon/average-case view may be too optimistic, whereas the Hamming/worstcase view may be too pessimistic. This monograph takes up the challenge of studying adversarial channel models that lie between the Shannon and Hamming extremes.},
  author       = {Dey, Bikash Kumar and Jaggi, Sidharth and Langberg, Michael and Sarwate, Anand D. and Zhang, Yihan},
  issn         = {1567-2328},
  journal      = {Foundations and Trends in Communications and Information Theory},
  number       = {3-4},
  pages        = {300--588},
  publisher    = {Now Publishers},
  title        = {{Codes for adversaries: Between worst-case and average-case jamming}},
  doi          = {10.1561/0100000112},
  volume       = {21},
  year         = {2024},
}

@article{17330,
  abstract     = {In this work we consider the list-decodability and list-recoverability of arbitrary q -ary codes, for all integer values of q ⩾ 2. A code is called ( p , L ) q -list-decodable if every radius pn Hamming ball contains less than L codewords; ( p , ℓ, L ) q -recoverability is a generalization where we place radius pn Hamming balls on every point of a combinatorial rectangle with side length ℓ and again stipulate that there be less than L codewords. Our main contribution is to precisely calculate the maximum value of p for which there exist infinite families of positive rate ( p , ℓ, L ) q -list-recoverable codes, the quantity we call the zero-rate threshold . Denoting this value by p *, we in fact show that codes correcting a p * + ε fraction of errors must have size O ε (1), i.e., independent of n . Such a result is typically referred to as a “Plotkin bound.” To complement this, a standard random code with expurgation construction shows that there exist positive rate codes correcting a p * − ε fraction of errors. We also follow a classical proof template (typically attributed to Elias and Bassalygo) to derive from the zero-rate threshold other tradeoffs between rate and decoding radius for list-decoding and list-recovery. Technically, proving the Plotkin bound boils down to demon-strating the Schur convexity of a certain function defined on the q -simplex as well as the convexity of a univariate function derived from it. We remark that an earlier argument claimed similar results for q -ary list-decoding; however, we point out that this earlier proof is flawed.},
  author       = {Resch, Nicolas and Yuan, Chen and Zhang, Yihan},
  issn         = {1557-9654},
  journal      = {IEEE Transactions on Information Theory},
  number       = {9},
  pages        = {6211--6238},
  publisher    = {IEEE},
  title        = {{Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery}},
  doi          = {10.1109/TIT.2024.3430842},
  volume       = {70},
  year         = {2024},
}

@inproceedings{14083,
  abstract     = {In this work we consider the list-decodability and list-recoverability of arbitrary q-ary codes, for all integer values of q ≥ 2. A code is called (p,L)_q-list-decodable if every radius pn Hamming ball contains less than L codewords; (p,𝓁,L)_q-list-recoverability is a generalization where we place radius pn Hamming balls on every point of a combinatorial rectangle with side length 𝓁 and again stipulate that there be less than L codewords.
Our main contribution is to precisely calculate the maximum value of p for which there exist infinite families of positive rate (p,𝓁,L)_q-list-recoverable codes, the quantity we call the zero-rate threshold. Denoting this value by p_*, we in fact show that codes correcting a p_*+ε fraction of errors must have size O_ε(1), i.e., independent of n. Such a result is typically referred to as a "Plotkin bound." To complement this, a standard random code with expurgation construction shows that there exist positive rate codes correcting a p_*-ε fraction of errors. We also follow a classical proof template (typically attributed to Elias and Bassalygo) to derive from the zero-rate threshold other tradeoffs between rate and decoding radius for list-decoding and list-recovery.
Technically, proving the Plotkin bound boils down to demonstrating the Schur convexity of a certain function defined on the q-simplex as well as the convexity of a univariate function derived from it. We remark that an earlier argument claimed similar results for q-ary list-decoding; however, we point out that this earlier proof is flawed.},
  author       = {Resch, Nicolas and Yuan, Chen and Zhang, Yihan},
  booktitle    = {50th International Colloquium on Automata, Languages, and Programming},
  isbn         = {9783959772785},
  issn         = {1868-8969},
  location     = {Paderborn, Germany},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery}},
  doi          = {10.4230/LIPIcs.ICALP.2023.99},
  volume       = {261},
  year         = {2023},
}

@article{12838,
  abstract     = {We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let N > 0 and L ∈ Z ≽2 . A multiple packing is a set C of points in R n such that any point in R n lies in the intersection of at most L – 1 balls of radius √ nN around points in C . Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied for finite fields. In this paper, we derive the best known lower bounds on the optimal density of list-decodable infinite constellations for constant L under a stronger notion called average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory.},
  author       = {Zhang, Yihan and Vatedka, Shashank},
  issn         = {1557-9654},
  journal      = {IEEE Transactions on Information Theory},
  number       = {7},
  pages        = {4513--4527},
  publisher    = {IEEE},
  title        = {{Multiple packing: Lower bounds via infinite constellations}},
  doi          = {10.1109/TIT.2023.3260950},
  volume       = {69},
  year         = {2023},
}

@article{13269,
  abstract     = {This paper is a collection of results on combinatorial properties of codes for the Z-channel . A Z-channel with error fraction τ takes as input a length- n binary codeword and injects in an adversarial manner up to n τ asymmetric errors, i.e., errors that only zero out bits but do not flip 0’s to 1’s. It is known that the largest ( L - 1)-list-decodable code for the Z-channel with error fraction τ has exponential size (in n ) if τ is less than a critical value that we call the ( L - 1)- list-decoding Plotkin point and has constant size if τ is larger than the threshold. The ( L -1)-list-decoding Plotkin point is known to be L -1/L-1 – L -L/ L-1 , which equals 1/4 for unique-decoding with L -1 = 1. In this paper, we derive various results for the size of the largest codes above and below the list-decoding Plotkin point. In particular, we show that the largest ( L -1)-list-decodable code ε-above the Plotkin point, for any given sufficiently small positive constant ε > 0, has size Θ L (ε -3/2 ) for any L - 1 ≥ 1. We also devise upper and lower bounds on the exponential size of codes below the list-decoding Plotkin point.},
  author       = {Polyanskii, Nikita and Zhang, Yihan},
  issn         = {1557-9654},
  journal      = {IEEE Transactions on Information Theory},
  number       = {10},
  pages        = {6340--6357},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{Codes for the Z-channel}},
  doi          = {10.1109/TIT.2023.3292219},
  volume       = {69},
  year         = {2023},
}

@article{14751,
  abstract     = {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 et al. (201 9) 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.},
  author       = {Zhang, Yihan},
  issn         = {1557-9654},
  journal      = {IEEE Transactions on Information Theory},
  keywords     = {Computer Science Applications, Information Systems},
  number       = {7},
  pages        = {4093--4127},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{Zero-error communication over adversarial MACs}},
  doi          = {10.1109/tit.2023.3257239},
  volume       = {69},
  year         = {2023},
}

@article{11639,
  abstract     = {We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints P and N respectively, the list decoding capacity is equal to 1/2logP/N. Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain conjecture that originates in analytic number theory is true, then the list size grows as a polynomial function of the gap-to-capacity.},
  author       = {Zhang, Yihan and Vatedka, Shashank},
  issn         = {1557-9654},
  journal      = {IEEE Transactions on Information Theory},
  number       = {12},
  pages        = {7753--7786},
  publisher    = {IEEE},
  title        = {{List decoding random Euclidean codes and Infinite constellations}},
  doi          = {10.1109/TIT.2022.3189542},
  volume       = {68},
  year         = {2022},
}

@inproceedings{12011,
  abstract     = {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.},
  author       = {Zhang, Yihan and Jaggi, Sidharth and Langberg, Michael and Sarwate, Anand D.},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {2523--2528},
  publisher    = {IEEE},
  title        = {{The capacity of causal adversarial channels}},
  doi          = {10.1109/ISIT50566.2022.9834709},
  volume       = {2022},
  year         = {2022},
}

@inproceedings{12013,
  abstract     = {We consider the problem of communication over adversarial channels with feedback. Two parties comprising sender Alice and receiver Bob seek to communicate reliably. An adversary James observes Alice's channel transmission entirely and chooses, maliciously, its additive channel input or jamming state thereby corrupting Bob's observation. Bob can communicate over a one-way reverse link with Alice; we assume that transmissions over this feedback link cannot be corrupted by James. Our goal in this work is to study the optimum throughput or capacity over such channels with feedback. We first present results for the quadratically-constrained additive channel where communication is known to be impossible when the noise-to-signal (power) ratio (NSR) is at least 1. We present a novel achievability scheme to establish that positive rate communication is possible even when the NSR is as high as 8/9. We also present new converse upper bounds on the capacity of this channel under potentially stochastic encoders and decoders. We also study feedback communication over the more widely studied q-ary alphabet channel under additive noise. For the q -ary channel, where q > 2, it is well known that capacity is positive under full feedback if and only if the adversary can corrupt strictly less than half the transmitted symbols. We generalize this result and show that the same threshold holds for positive rate communication when the noiseless feedback may only be partial; our scheme employs a stochastic decoder. We extend this characterization, albeit partially, to fully deterministic schemes under partial noiseless feedback. We also present new converse upper bounds for q-ary channels under full feedback, where the encoder and/or decoder may privately randomize. Our converse results bring to the fore an interesting alternate expression for the well known converse bound for the q—ary channel under full feedback which, when specialized to the binary channel, also equals its known capacity.},
  author       = {Joshi, Pranav and Purkayastha, Amritakshya and Zhang, Yihan and Budkuley, Amitalok J. and Jaggi, Sidharth},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {504--509},
  publisher    = {IEEE},
  title        = {{On the capacity of additive AVCs with feedback}},
  doi          = {10.1109/ISIT50566.2022.9834850},
  volume       = {2022},
  year         = {2022},
}

@inproceedings{12014,
  abstract     = {We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let N > 0 and L∈Z≥2. A multiple packing is a set C of points in Rn such that any point in Rn lies in the intersection of at most L – 1 balls of radius nN−−−√ around points in C. Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied for finite fields. In this paper, we exactly pin down the asymptotic density of (expurgated) Poisson Point Processes under a stronger notion called average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory. This gives rise to the best known lower bound on the largest multiple packing density. Our result corrects a mistake in a previous paper by Blinovsky [Bli05].},
  author       = {Zhang, Yihan and Vatedka, Shashank},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {2559--2564},
  publisher    = {IEEE},
  title        = {{List-decodability of Poisson Point Processes}},
  doi          = {10.1109/ISIT50566.2022.9834512},
  volume       = {2022},
  year         = {2022},
}

@inproceedings{12015,
  abstract     = {We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let P, N > 0 and L∈Z≥2. A multiple packing is a set C of points in Bn(0–,nP−−−√) such that any point in ℝ n lies in the intersection of at most L – 1 balls of radius nN−−−√ around points in C. 1 In this paper, we derive two lower bounds on the largest possible density of a multiple packing. These bounds are obtained through a stronger notion called average-radius multiple packing. Specifically, we exactly pin down the asymptotics of (expurgated) Gaussian codes and (expurgated) spherical codes under average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory. The bound for spherical codes matches the previous best known bound which was obtained for the standard (weaker) notion of multiple packing through a curious connection with error exponents [Bli99], [ZV21]. The bound for Gaussian codes suggests that they are strictly inferior to spherical codes.},
  author       = {Zhang, Yihan and Vatedka, Shashank},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {3085--3090},
  publisher    = {IEEE},
  title        = {{Lower bounds for multiple packing}},
  doi          = {10.1109/ISIT50566.2022.9834443},
  volume       = {2022},
  year         = {2022},
}

@inproceedings{12017,
  abstract     = {In the classic adversarial communication problem, two parties communicate over a noisy channel in the presence of a malicious jamming adversary. The arbitrarily varying channels (AVCs) offer an elegant framework to study a wide range of interesting adversary models. The optimal throughput or capacity over such AVCs is intimately tied to the underlying adversary model; in some cases, capacity is unknown and the problem is known to be notoriously hard. The omniscient adversary, one which knows the sender’s entire channel transmission a priori, is one of such classic models of interest; the capacity under such an adversary remains an exciting open problem. The myopic adversary is a generalization of that model where the adversary’s observation may be corrupted over a noisy discrete memoryless channel. Through the adversary’s myopicity, one can unify the slew of different adversary models, ranging from the omniscient adversary to one that is completely blind to the transmission (the latter is the well known oblivious model where the capacity is fully characterized).In this work, we present new results on the capacity under both the omniscient and myopic adversary models. We completely characterize the positive capacity threshold over general AVCs with omniscient adversaries. The characterization is in terms of two key combinatorial objects: the set of completely positive distributions and the CP-confusability set. For omniscient AVCs with positive capacity, we present non-trivial lower and upper bounds on the capacity; unlike some of the previous bounds, our bounds hold under fairly general input and jamming constraints. Our lower bound improves upon the generalized Gilbert-Varshamov bound for general AVCs while the upper bound generalizes the well known Elias-Bassalygo bound (known for binary and q-ary alphabets). For the myopic AVCs, we build on prior results known for the so-called sufficiently myopic model, and present new results on the positive rate communication threshold over the so-called insufficiently myopic regime (a completely insufficient myopic adversary specializes to an omniscient adversary). We present interesting examples for the widely studied models of adversarial bit-flip and bit-erasure channels. In fact, for the bit-flip AVC with additive adversarial noise as well as random noise, we completely characterize the omniscient model capacity when the random noise is sufficiently large vis-a-vis the adversary’s budget.},
  author       = {Yadav, Anuj Kumar and Alimohammadi, Mohammadreza and Zhang, Yihan and Budkuley, Amitalok J. and Jaggi, Sidharth},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {2535--2540},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{New results on AVCs with omniscient and myopic adversaries}},
  doi          = {10.1109/ISIT50566.2022.9834632},
  volume       = {2022},
  year         = {2022},
}

@inproceedings{12018,
  abstract     = {We study the problem of characterizing the maximal rates of list decoding in Euclidean spaces for finite list sizes. For any positive integer L ≥ 2 and real N > 0, we say that a subset C⊂Rn is an (N,L – 1)-multiple packing or an (N,L– 1)-list decodable code if every Euclidean ball of radius nN−−−√ in ℝ n contains no more than L − 1 points of C. We study this problem with and without ℓ 2 norm constraints on C, and derive the best-known lower bounds on the maximal rate for (N,L−1) multiple packing. Our bounds are obtained via error exponents for list decoding over Additive White Gaussian Noise (AWGN) channels. We establish a curious inequality which relates the error exponent, a quantity of average-case nature, to the list-decoding radius, a quantity of worst-case nature. We derive various bounds on the error exponent for list decoding in both bounded and unbounded settings which could be of independent interest beyond multiple packing.},
  author       = {Zhang, Yihan and Vatedka, Shashank},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {1324--1329},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{Lower bounds on list decoding capacity using error exponents}},
  doi          = {10.1109/ISIT50566.2022.9834815},
  volume       = {2022},
  year         = {2022},
}

@inproceedings{12019,
  abstract     = {This paper studies combinatorial properties of codes for the Z-channel. A Z-channel with error fraction τ takes as input a length-n binary codeword and injects in an adversarial manner up to nτ asymmetric errors, i.e., errors that only zero out bits but do not flip 0’s to 1’s. It is known that the largest (L − 1)-list-decodable code for the Z-channel with error fraction τ has exponential (in n) size if τ is less than a critical value that we call the Plotkin point and has constant size if τ is larger than the threshold. The (L−1)-list-decoding Plotkin point is known to be L−1L−1−L−LL−1. In this paper, we show that the largest (L−1)-list-decodable code ε-above the Plotkin point has size Θ L (ε −3/2 ) for any L − 1 ≥ 1.},
  author       = {Polyanskii, Nikita and Zhang, Yihan},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {2553--2558},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{List-decodable zero-rate codes for the Z-channel}},
  doi          = {10.1109/ISIT50566.2022.9834829},
  volume       = {2022},
  year         = {2022},
}

@article{12273,
  abstract     = {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 2log(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 may be of independent interest. We also give bounds on the strong secrecy capacity of this channel assuming that the jammer is simultaneously eavesdropping.},
  author       = {Zhang, Yihan and Vatedka, Shashank and Jaggi, Sidharth and Sarwate, Anand D.},
  issn         = {1557-9654},
  journal      = {IEEE Transactions on Information Theory},
  number       = {8},
  pages        = {4901--4948},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{Quadratically constrained myopic adversarial channels}},
  doi          = {10.1109/tit.2022.3167554},
  volume       = {68},
  year         = {2022},
}