Related papers: Systematic Codes for Rank Modulation
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
As sensing and instrumentation play an increasingly important role in systems controlled over wired and wireless networks, the need to better understand delay-sensitive communication becomes a prime issue. Along these lines, this article…
This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n \times n$ arrays affected by $t$-criss-cross deletions defined as any combination…
In this paper we present a new Turbo analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This Turbo code improves Donoho's deterministic construction by using a probabilistic approach. More…
Reed-Muller codes are some of the oldest and most widely studied error-correcting codes, of interest for both their algebraic structure as well as their many algorithmic properties. A recent beautiful result of Saptharishi, Shpilka and Volk…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as…
We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite…
In learning-to-rank for information retrieval, a ranking model is automatically learned from the data and then utilized to rank the sets of retrieved documents. Therefore, an ideal ranking model would be a mapping from a document set to a…
Autoregressive language models accumulate errors due to their fixed, irrevocable left-to-right token generation. To address this, we propose a new sampling method called Resample-Previous-Tokens (RPT). RPT mitigates error accumulation by…
In-Memory Computing (IMC) introduces a new paradigm of computation that offers high efficiency in terms of latency and power consumption for AI accelerators. However, the non-idealities and defects of emerging technologies used in advanced…
We introduce a novel method to enhance cross-language code translation from Fortran to C++ by integrating task-specific embedding alignment into a Retrieval-Augmented Generation (RAG) framework. Unlike conventional retrieval approaches that…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
Cross-modal retrieval aims to search for instances, which are semantically related to the query through the interaction of different modal data. Traditional solutions utilize a single-tower or dual-tower framework to explicitly compute the…
Instruction Tuning involves finetuning a language model on a collection of instruction-formatted datasets in order to enhance the generalizability of the model to unseen tasks. Studies have shown the importance of balancing different task…
We propose a new interpolation-based error decoding algorithm for $(n,k)$ Reed-Solomon (RS) codes over a finite field of size $q$, where $n=q-1$ is the length and $k$ is the dimension. In particular, we employ the fast Fourier transform…
Data quality is critical for multimedia tasks, while various types of systematic flaws are found in image benchmark datasets, as discussed in recent work. In particular, the existence of the semantic gap problem leads to a many-to-many…
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our…
We give new lower bounds for $M(n,d)$, for various positive integers $n$ and $d$ with $n>d$, where $M(n,d)$ is the largest number of permutations on $n$ symbols with pairwise Hamming distance at least $d$. Large sets of permutations on $n$…
Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over $\mathbb{Z}_{2^{k}r}$ and which are based on so called $B_{1}[4](2^{k}r)$…