Related papers: Comparing quaternary and binary multipliers
Highly accurate alpha blending can be performed entirely with integer operations, and no divisions. To reduce the number of integer multiplications, multiple color components can be blended in parallel in the same 32-bit or 64-bit register.…
Binary embedding of high-dimensional data aims to produce low-dimensional binary codes while preserving discriminative power. State-of-the-art methods often suffer from high computation and storage costs. We present a simple and fast…
Approximate circuits have been developed to provide good tradeoffs between power consumption and quality of service in error resilient applications such as hardware accelerators of deep neural networks (DNN). In order to accelerate the…
This letter proposes superposing two Generalized Quadratic Noise Modulators (GQNM) by simply adding their outputs. It creates a 16-ary noise modulator that resembles QAM modulators in classical communication. It modulates the information…
Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…
In many practical communication systems, one binary encoder/decoder pair is used to communicate over a set of parallel channels. Examples of this setup include multi-carrier transmission, rate-compatible puncturing of turbo-like codes, and…
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits.…
Revisiting an approach by Conway and Sloane we investigate a collection of optimal non-linear binary codes and represent them as (non-linear) codes over Z4. The Fourier transform will be used in order to analyze these codes, which leads to…
This paper shows that, for matrix multiplications and convolutions, it is possible to asymptotically replace each real multiplication with a single squaring operation. Similarly, a single complex multiplication can be replaced with 3…
There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
In the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. The classical set of gates such as AND, OR, and EXOR are not…
Discrimination of unitary operations is a fundamental quantum information processing task. Assisted with linear optical elements, we experimentally demonstrate perfect discrimination between single-bit unitary operations using two…
Binary convolutional networks have lower computational load and lower memory foot-print compared to their full-precision counterparts. So, they are a feasible alternative for the deployment of computer vision applications on limited…
Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed…
This paper presents a ternary half adder and a 1-trit multiplier using carbon nanotube transistors. The proposed circuits are designed using pass transistor logic and dynamic logic. Ternary logic uses less connections than binary logic, and…
As is well-known, the real quaternion division algebra $ {\cal H}$ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra ${\cal O}$ can not be algebraically isomorphic to any matrix algebras…
Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in…
Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of…
The creation of practical deep learning data-products often requires parallelization across processors and computers to make deep learning feasible on large data sets, but bottlenecks in communication bandwidth make it difficult to attain…