Related papers: New Constructions for Query-Efficient Locally Deco…
We present an explicit and efficient algebraic construction of capacity-achieving list decodable codes with both constant alphabet and constant list sizes. More specifically, for any $R \in (0,1)$ and $\epsilon>0$, we give an algebraic…
Locally Decodable Codes (LDCs) are error correcting codes which permit the recovery of any single message symbol with a low number of queries to the codeword (the locality). Traditional LDC tradeoffs between the rate, locality, and error…
In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that…
We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
A new construction for constant weight codes is presented. The codes are constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These subspaces form a constant dimension code in the Grassmannian space $\cG_q(n,k)$. Some of…
We study the problem of efficiently computing on encoded data. More specifically, we study the question of low-bandwidth computation of functions $F:\mathbb{F}^k \to \mathbb{F}$ of some data $x \in \mathbb{F}^k$, given access to an encoding…
Flash memory is a non-volatile computer memory comprised of blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomplished only by…
We introduce randomized Limited View (LV) adversary codes that provide protection against an adversary that uses their partial view of the communication to construct an adversarial error vector to be added to the channel. For a codeword of…
The long code is a central tool in hardness of approximation, especially in questions related to the unique games conjecture. We construct a new code that is exponentially more efficient, but can still be used in many of these applications.…
We study codes that are list-decodable under insertions and deletions. Specifically, we consider the setting where a codeword over some finite alphabet of size $q$ may suffer from $\delta$ fraction of adversarial deletions and $\gamma$…
An observed $K$-dimensional series $\left\{ y_{n}\right\} _{n=1}^{N}$ is expressed in terms of a lower $p$-dimensional latent series called factors $f_{n}$ and random noise $\varepsilon_{n}$. The equation, $y_{n}=Qf_{n}+\varepsilon_{n}$ is…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet…
An index code for a broadcast channel with receiver side information is 'locally decodable' if every receiver can decode its demand using only a subset of the codeword symbols transmitted by the sender instead of observing the entire…
A multi-user private data compression problem is studied. A server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is connected to an encoder. The encoder is connected through an unsecured link to a user.…
Function-Correcting Codes (FCCs) enable reliable computation of a function of a $k$-bit message over noisy channels without requiring full message recovery. In this work, we study optimal single-error correcting FCCs (SEFCCs) for…
We show an essentially tight bound on the number of adaptively chosen statistical queries that a computationally efficient algorithm can answer accurately given $n$ samples from an unknown distribution. A statistical query asks for the…
V. Guruswami and N. Resch prove that the list decodability of $\mathbb{F}_q$-linear rank metric codes is as good as that of random rank metric codes in~\cite{venkat2017}. Due to the potential applications of self-orthogonal rank metric…
Both performance and efficiency are important to semantic segmentation. State-of-the-art semantic segmentation algorithms are mostly based on dilated Fully Convolutional Networks (dilatedFCN), which adopt dilated convolutions in the…
The rapid scaling of Large Language Models (LLMs) elevates inference costs and compounds substantial deployment barriers. While quantization to 8 or 4 bits mitigates this, sub-3-bit methods face severe accuracy, scalability, and efficiency…