相关论文: Ulam Sphere Size Analysis for Permutation and Mult…

The classical rank aggregation problem seeks to combine a set X of n permutations into a single representative "consensus" permutation. In this paper, we investigate two fundamental rank aggregation tasks under the well-studied Ulam metric:…

The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel…

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…

Exploiting permutation invariance to reduce the exponential scaling of semidefinite programs in quantum information has emerged as a powerful computational technique. In this work, we develop a systematic framework for using this reduction…

The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…

The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of…

Deploying Large Language Models (LLMs) on mobile devices faces the challenge of insufficient performance in smaller models and excessive resource consumption in larger ones. This paper highlights that mobile Neural Processing Units (NPUs)…

Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with…

In this paper we study the hard sphere packing problem in the Hamming space by the cavity method. We show that both the replica symmetric and the replica symmetry breaking approximations give maximum rates of packing that are asymptotically…

Channel permutation is a powerful technique for enhancing the accuracy of N:M sparse models by reordering the channels of weight matrices to prioritize the retention of important weights. However, traditional channel permutation methods…

In Multiple-Input Multiple-Output (MIMO) systems, Sphere Decoding (SD) can achieve performance equivalent to full search Maximum Likelihood (ML) decoding, with reduced complexity. Several researchers reported techniques that reduce the…

Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…

Multi-mode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication, sensing…

A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…

This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…

Existing fixed-length feedback communication schemes are either specialized to particular channels (Schalkwijk--Kailath, Horstein), or apply to general channels but either have high coding complexity (block feedback schemes) or are…

We investigate the memory effects under oscillatory shear deformation of amorphous solids through computer simulations. Applications of shear deformations in all orthogonal directions show that encoded memories via this protocol are more…

Recent works on compression of large language models (LLM) using quantization considered reparameterizing the architecture such that weights are distributed on the sphere. This demonstratively improves the ability to quantize by increasing…

This paper derives an improved sphere-packing (ISP) bound for finite-length codes whose transmission takes place over symmetric memoryless channels. We first review classical results, i.e., the 1959 sphere-packing (SP59) bound of Shannon…

For applications in concatenated coding for optical communications systems, we examine soft-demapping of short spherical codes constructed as constant-energy shells of the Cartesian power of pulse amplitude modulation constellations. These…