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Recent DEtection TRansformer-based (DETR) models have obtained remarkable performance. Its success cannot be achieved without the re-introduction of multi-scale feature fusion in the encoder. However, the excessively increased tokens in…
In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
We illustrate the utility of the recently developed loop calculus for improving the Belief Propagation (BP) algorithm. If the algorithm that minimizes the Bethe free energy fails we modify the free energy by accounting for a critical loop…
We initiate a study of locally decodable codes with randomized encoding. Standard locally decodable codes are error correcting codes with a deterministic encoding function and a randomized decoding function, such that any desired message…
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
Gated Linear Units (GLUs) have become a common building block in modern foundation models. Bilinear layers drop the non-linearity in the "gate" but still have comparable performance to other GLUs. An attractive quality of bilinear layers is…
The minimum-weight perfect matching (MWPM) decoder is a standard decoding strategy for surface codes, but its performance degrades considerably under biased noise. In this paper, a modified surface code, termed the XYZ planar code, is…
All utility-scale quantum computers will require some form of Quantum Error Correction in which logical qubits are encoded in a larger number of physical qubits. One promising encoding is known as the colour code which has broad…
Higher-order Fourier analysis, developed over prime fields, has been recently used in different areas of computer science, including list decoding, algorithmic decomposition and testing. We extend the tools of higher-order Fourier analysis…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
We present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
Generalized Goppa codes are defined by a code locator set $\mathcal{L}$ of polynomials and a Goppa polynomial $G(x)$. When the degree of all code locator polynomials in $\mathcal{L}$ is one, generalized Goppa codes are classical Goppa…
In 1994, Frieze and Teng proposed an integer linear programming formulation of the NP-Complete Exact Partition problem, whose LP-relaxation they claimed was non-degenerate. Contrary to their claim, we show how an instance of Exact Partition…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…