相关论文: Fast Codes for Large Alphabets

We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…

Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes,…

A k-query Locally Decodable Code (LDC) encodes an n-bit message x as an N-bit codeword C(x), such that one can probabilistically recover any bit x_i of the message by querying only k bits of the codeword C(x), even after some constant…

We describe a uniformly fast algorithm for generating points \vec{x} uniformly in a hypercube with the restriction that the difference between each pair of coordinates is bounded. We discuss the quality of the algorithm in the sense of its…

We present two ways in which an infinite universal alphabet may be generated using a novel rewrite system that conserves zero (a special character of the alphabet and the symbol for that character) at every step. The recursive method…

We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…

The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which…

A lossy source code $\mathcal{C}$ with rate $R$ for a discrete memoryless source $S$ is called subset-universal if for every $0<R'< R$, almost every subset of $2^{nR'}$ of its codewords achieves average distortion close to the source's…

Consider a systematic linear code where some (local) parity symbols depend on few prescribed symbols, while other (heavy) parity symbols may depend on all data symbols. Local parities allow to quickly recover any single symbol when it is…

CRCs have desirable properties for effective error detection. But their software implementation, which relies on many steps of the polynomial division, is typically slower than other codes such as weaker checksums. A relevant question is…

Consider a large database of $n$ data items that need to be stored using $m$ servers. We study how to encode information so that a large number $k$ of read requests can be performed in parallel while the rate remains constant (and ideally…

Recently, high-performing code generation systems based on large language models have surfaced. They are trained on massive corpora containing much more natural text than actual executable computer code. This work shows that current code…

In this paper we give a fast algorithm to generate all partitions of a positive integer $n$. Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. It is known that the…

An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…

In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…

Clustering problems have numerous applications and are becoming more challenging as the size of the data increases. In this paper, we consider designing clustering algorithms that can be used in MapReduce, the most popular programming…

In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…

Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code…

Large Language Models for code often entail significant computational complexity, which grows significantly with the length of the input code sequence. We propose LeanCode for code simplification to reduce training and prediction time,…

This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for…