Related papers: Optimal Binary Coding for $q^+$ -state Data Embedd…
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…
In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or…
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…
Lossy compression algorithms aim to compactly encode images in a way which enables to restore them with minimal error. We show that a key limitation of existing algorithms is that they rely on error measures that are extremely sensitive to…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Learning compact binary codes for image retrieval problem using deep neural networks has recently attracted increasing attention. However, training deep hashing networks is challenging due to the binary constraints on the hash codes. In…
We introduce the notion of entanglement of subspaces as a measure that quantify the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces…
We examine dense coding with an arbitrary pure entangled state sharing between the sender and the receiver. Upper bounds on the average success probability in approximate dense coding and on the probability of conclusive results in…
We give a complete answer to the following basic question: "What is the maximal fraction of deletions or insertions tolerable by $q$-ary list-decodable codes with non-vanishing information rate?" This question has been open even for binary…
Word embeddings are commonly used as a starting point in many NLP models to achieve state-of-the-art performances. However, with a large vocabulary and many dimensions, these floating-point representations are expensive both in terms of…
An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming…
Lossless image compression is required in various applications to reduce storage or transmission costs of images, while requiring the reconstructed images to have zero information loss compared to the original. Existing lossless image…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be…
Data compression is a well-studied (and well-solved) problem in the setup of long coding blocks. But important emerging applications need to compress data to memory words of small fixed widths. This new setup is the subject of this paper.…
For a required payload, the existing reversible data hiding (RDH) methods always expect to reduce the embedding distortion as much as possible, such as by utilizing a well-designed predictor, taking into account the carrier-content…
In steganography, selecting an optimal cover image, referred to as cover selection, is pivotal for effective message concealment. Traditional methods have typically employed exhaustive searches to identify images that conform to specific…