Related papers: Introduction to Dynamic Unary Encoding
Concurrent coding is an encoding scheme with "holographic" type properties that are shown here to be robust against a significant amount of noise and signal loss. This single encoding scheme is able to correct for random errors and burst…
Decoupling systems into independently evolving components has a long history of simplifying seemingly complex systems. They enable a better understanding of the underlying dynamics and causal structures while providing more efficient means…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
Coherence has been used as a resource for optical communications since its earliest days. It is widely used for multiplexing of data, but not for encoding of data. Here we introduce a coding scheme, which we call \textit{mutual coherence…
Digital humanities are rooted in text analysis. However, most visualization paradigms use only categoric, ordered or quantitative data. Literal text must be considered a base data type to encode into visualizations. Literal text offers…
A universal cycle (u-cycle) is a compact listing of a collection of combinatorial objects. In this paper, we use natural encodings of these objects to show the existence of u-cycles for collections of subsets, matroids, restricted…
Conventional scattering-based encryption systems that operate based on a static complex medium which is used by all users are vulnerable to learning-based attacks that exploit ciphertext-plaintext pairs to model and reverse-engineer the…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this…
This paper presents a convenient graphical tool for encoding visual patterns (such as image patches and image atoms) as point constellations in a space spanned by perceptual features and with a clear geometrical interpretation. General…
For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall…
We propose two dynamical models with delay taking advantage of their complex dynamics for information processing tasks. The first model incorporates coupled delayed dynamics of multiple bits, which is shown to have desirable properties as…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
A new approach for designing bilayer and multi-layer LDPC codes is proposed and studied in the asymptotic regime. The ensembles are defined through individual uni-variate degree distributions, one for each layer. We present a construction…
The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the…
A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous…
Motivated by signal processing, we present a new class of channel codes, called signal codes, for continuous-alphabet channels. Signal codes are lattice codes whose encoding is done by convolving an integer information sequence with a fixed…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
We consider distributed computations between two parties carried out over a noisy channel that may erase messages. Following a noise model proposed by Dani et al. (2018), the noise level observed by the parties during the computation in our…