Related papers: MacWilliams type identities for some new $m$-spott…
This study presents a methodology for anticounterfeiting of Non-Volatile Memory (NVM) chips. In particular, we experimentally demonstrate a generalized methodology for detecting (i) Integrated Circuit (IC) origin, (ii) recycled or used NVM…
Variational mutual information (MI) estimators are widely used in unsupervised representation learning methods such as contrastive predictive coding (CPC). A lower bound on MI can be obtained from a multi-class classification problem, where…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
Let $\mathbb{F}_q$ be a finite field of characteristic not equal to $2$ or $3$. We compute the weight enumerators of some projective and affine Reed-Muller codes of order $3$ over $\mathbb{F}_q$. These weight enumerators answer enumerative…
Efficient low complexity error correcting code(ECC) is considered as an effective technique for mitigation of multi-bit upset (MBU) in the configuration memory(CM)of static random access memory (SRAM) based Field Programmable Gate Array…
Computing-in-memory (CIM) has attracted significant attentions in recent years due to its massive parallelism and low power consumption. However, current CIM designs suffer from large area overhead of small CIM macros and bad programmablity…
We introduce a general class of codes which includes several well-known classes of deletion/insertion correcting codes as special cases. For example, the Helberg code, the Levenshtein code, the Varshamov--Tenengolts code, and most variants…
We introduce a class of regularized M-estimators of multivariate scatter and show, analogous to the popular spatial sign covariance matrix (SSCM), that they possess high breakdown points. We also show that the SSCM can be viewed as an…
In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering coverings that are not connected, we classify the metrics satisfying the…
Improvements in main memory storage density are primarily driven by process technology scaling, which negatively impacts reliability by exacerbating various circuit-level error mechanisms. To compensate for growing error rates, both memory…
Emerging memristor computing systems have demonstrated great promise in improving the energy efficiency of neural network (NN) algorithms. The NN weights stored in memristor crossbars, however, may face potential theft attacks due to the…
We introduce a general class of regular weight functions on finite abelian groups, and study the combinatorics, the duality theory, and the metric properties of codes endowed with such functions. The weights are obtained by composing a…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
As DRAM technology continues to evolve towards smaller feature sizes and increased densities, faults in DRAM subsystem are becoming more severe. Current servers mostly use CHIPKILL based schemes to tolerate up-to one/two symbol errors per…
The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes…
Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
This work develops new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal number of generators to measure the size of codes. We prove a…
This paper investigates the relationship between the rank weight distribution of a linear code and that of its dual code. The main result of this paper is that, similar to the MacWilliams identity for the Hamming metric, the rank weight…
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial…