Related papers: Simultaneous Code/Error-Trellis Reduction for Conv…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
We present in this paper a special class of unit memory convolutional codes (UMCCs), called semi-random UMCCs (SRUMCCs), where the information block is first encoded by a short block code and then transmitted in a block Markov (random)…
For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various…
Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for computation at the agents is affected by the availability of local resources…
We show how real-number codes can be used to compress correlated sources, and establish a new framework for lossy distributed source coding, in which we quantize compressed sources instead of compressing quantized sources. This change in…
A convolutional code $\C$ over $\ZZ[D]$ is a $\ZZ[D]$-submodule of $\ZZN[D]$ where $\ZZ[D]$ stands for the ring of polynomials with coefficients in $\ZZ$. In this paper, we study the list decoding problem of these codes when the…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
An asynchronous multiple access error exponent result implicates a new result for time invariant trellis codes of memory 1.
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…
In this paper a framework to study the dual of skew cyclic codes is proposed. The transposed Hamming ring extensions are based in the existence of an anti-isomorphism of algebras between skew polynomial rings. Our construction is applied to…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Recently, Transformer-based encoder-decoder models have demonstrated strong performance in multilingual speech recognition. However, the decoder's autoregressive nature and large size introduce significant bottlenecks during inference.…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a…
We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement-assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and…
Achieving fault-tolerance will require a strong relationship between the hardware and the protocols used. Different approaches will therefore naturally have tailored proof-of-principle experiments to benchmark progress. Nevertheless,…
We will study convolutional codes with the help of state space realizations. It will be shown that two such minimal realizations belong to the same code if and only if they are equivalent under the full state feedback group. This result…