Related papers: Elder-Rule-Staircodes for Augmented Metric Spaces
We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
We propose four finite-length scaling laws to predict the frame error rate (FER) performance of spatially-coupled low-density parity-check codes under full belief propagation (BP) decoding with a limit on the number of decoding iterations…
Unsourced random access (URA) has emerged as a pragmatic framework for next-generation distributed sensor networks. Within URA, concatenated coding structures are often employed to ensure that the central base station can accurately recover…
High-rate product codes (PCs) and staircase codes (SCs) are ubiquitous codes in high-speed optical communication achieving near-capacity performance on the binary symmetric channel. Their success is mostly due to very efficient iterative…
Single encoder-decoder methodologies for semantic segmentation are reaching their peak in terms of segmentation quality and efficiency per number of layers. To address these limitations, we propose a new architecture based on a decoder…
Given a metric space $(X,d)$, a set of terminals $K\subseteq X$, and a parameter $t\ge 1$, we consider metric structures (e.g., spanners, distance oracles, embedding into normed spaces) that preserve distances for all pairs in $K\times X$…
Within the realm of advanced code retrieval, existing methods have primarily relied on intricate matching and attention-based mechanisms. However, these methods often lead to computational and memory inefficiencies, posing a significant…
In this paper, we generalize the method of using two parallel versions of the lifted MRD code from the existing work [1]. The Delsarte theorem of the rank distribution of MRD codes is an important part to count codewords in our…
Subcode-ensemble decoders improve iterative decoding by running multiple decoders in parallel over carefully chosen subcodes, increasing the likelihood that at least one decoder avoids the dominant trapping structures. Achieving strong…
This paper introduces Claycode, a novel 2D scannable code designed for extensive stylization and deformation. Unlike traditional matrix-based codes (e.g., QR codes), Claycodes encode their message in a tree structure. During the encoding…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We develop the first algorithms for computing the Skyscraper Invariant [FJNT24]. This is a filtration of the classical rank invariant for multiparameter persistence modules defined by the Harder-Narasimhan filtrations along every central…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
Aperiodic tilings support two classically studied but hitherto separately presented structures: matching rules, which enforce global order via local constraints, and height functions, which encode global geometry through integer-valued…
We consider the numbers of positive and negative eigenvalues of matrices of squared distances between randomly sampled i.i.d. points in a given metric measure space. These numbers and their limits, as the number of points grows, in fact…
We describe a new parameterized family of symmetric error-correcting codes with low-density parity-check matrices (LDPC). Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are…
We propose two variants of staircase codes that resolve the issue of parity-propagation in their encoding process. The proposed codes provide a systematic way of terminating a staircase code after an arbitrary number of blocks. The class of…
In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare…
One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics -…