相关论文: Construction C*: an inter-level coded version of C…
Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…
We present a new method of establishing a bijective correspondence - in fact, a lattice isomorphism - between action- and coaction-invariant ideals of C*-algebras and their crossed products by a fixed locally compact group. It is known that…
We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level…
For a complexity class $C$ and language $L$, a constructive separation of $L \notin C$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every $C$-algorithm attempting to decide $L$. We study the…
The so-called min-sum algorithm has been applied for decoding lattices constructed by Construction D'. We generalize this iterative decoding algorithm to decode lattices constructed by Construction D. An upper bound on the decoding…
Standard optical potentials use off-resonant laser standing wave induced AC-Stark shift. In a recent development [Phys. Rev. Lett. {\bf 117}, 233001 (2016)] a three-level scheme in $\Lambda$ configuration coupled coherently by resonant…
We propose a method to substantially improve the signal-to-noise ratio of lattice correlation functions for bosonic operators or other operator combinations with disconnected contributions. The technique is applicable for correlations…
In this paper, we analyse asymptotically a new class of LDPC codes called Non-binary Hybrid LDPC codes, which has been recently introduced. We use density evolution techniques to derive a stability condition for hybrid LDPC codes, and prove…
We propose a construction of lattices from codes corresponding to lattices of type $A_n$, $D_n$ and $E_n$. This construction is a generalization of construction A of lattices from $p$-ary codes corresponding to a lattice of type $A_{p-1}$.…
Recently, the mysterious In-Context Learning (ICL) ability exhibited by Transformer architectures, especially in large language models (LLMs), has sparked significant research interest. However, the resilience of Transformers' in-context…
Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable…
We consider the problem of transmitting correlated data after independent encoding to a central receiver through orthogonal channels. We assume that the channel state information is not known at the transmitter. The receiver has access to…
A recent line of work on lattice codes for Gaussian wiretap channels introduced a new lattice invariant called secrecy gain as a code design criterion which captures the confusion that lattice coding produces at an eavesdropper. Following…
Ultra-reliable low-latency communication is essential in mission-critical settings, including military applications, where persistent and asymmetric link blockages caused by mobility, jamming, or adversarial attacks can disrupt…
In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.
We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability,…
Constant dimension codes (CDCs) have become an important object in coding theory due to their application in random network coding. The multilevel construction is one of the most effective ways to construct constant dimension codes. The…
We investigate iterating the construction of $C^{*}$, the $L$-like inner model constructed using first order logic augmented with the "cofinality $\omega$" quantifier. We first show that $\left(C^{*}\right)^{C^{*}}=C^{*}\ne L$ is…
The dichotomy between noise-stable and (completely) noise-sensitive stochastic models is of recent interest in probability theory. Of particular interest is the study of lattice models coming from statistical physics. The Fourier transform…
Learning structured representations of visual scenes is currently a major bottleneck to bridging perception with reasoning. While there has been exciting progress with slot-based models, which learn to segment scenes into sets of objects,…