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In light of recent hardware advances, it is striking that real arithmetic in balanced ternary logic has received almost no attention in the literature. This is particularly surprising given ternary logic's promising properties, which could…
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a numerically stable binary coding method which overcomes the drawbacks of the \textit{Fractional…
This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation $Ax =…
This correspondence proposes a new rotated codebook for three-dimensional (3D) multi-input-multi-output (MIMO) system under spatially correlated channel. To avoid the problem of high dimensionality led by large antenna array, the rotation…
We study the 2N-dimensional canonical systems and discuss some properties of its fundamental solution. We then discuss the Floquet theory of periodic canonical systems and observe the asymptotic behavior of its solution. Some important…
We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can…
Unary representation is straightforward, error tolerant and requires simple logic while its latency is a concern. On the other hand, positional representation (like binary) is compact and requires less space, but it is sensitive to errors.…
As the dimensions and operating voltages of computer electronics shrink to cope with consumers' demand for higher performance and lower power consumption, circuit sensitivity to soft errors increases dramatically. Recently, a new data-type…
Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
The computation of select eigenvalues and eigenvectors of large, sparse matrices is fundamental to a wide range of applications. Accordingly, evaluating the numerical performance of emerging alternatives to the IEEE 754 floating-point…
The canonical partition function is related to the grand canonical one through the fugacity expansion and is known to have no sign problem. In this paper we perform the fugacity expansion by a method of the hopping parameter expansion in…
The introduction of posit reopened the debate about the utility of IEEE754 in specific domains. In this context, we propose a high-level language (Scala) library that aims to reduce the effort of designing and testing new number…
This paper proposes a channel estimation method for Multiple-Input Multiple-Output (MIMO) systems based on Canonical Polyadic (CP) decomposition applied to a mode-factorized tensor representation of the channel. The proposed approach…
Conversion between binary and decimal floating-point representations is ubiquitous. Floating-point radix conversion means converting both the exponent and the mantissa. We develop an atomic operation for FP radix conversion with simple…
With streaming floating-point numbers being increasingly prevalent, effective and efficient compression of such data is critical. Compression schemes must be able to exploit the similarity, or smoothness, of consecutive numbers and must be…
Positional encodings are employed to capture the high frequency information of the encoded signals in implicit neural representation (INR). In this paper, we propose a novel positional encoding method which improves the reconstruction…
Even orthogonal time frequency space (OTFS) has been shown as a promising modulation scheme for high mobility doubly-selective fading channels, its attainability of full diversity order in either time or frequency selective fading channels…
We propose a new instruction (FPADDRE) that computes the round-off error in floating-point addition. We explain how this instruction benefits high-precision arithmetic operations in applications where double precision is not sufficient.…