Related papers: Coding Theory: the unit-derived methodology
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
Starting from a practical use of Reed-Solomon codes in a cryptographic scheme published in Indocrypt'09, this paper deals with the threshold of linear $q$-ary error-correcting codes. The security of this scheme is based on the…
This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded…
Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both…
Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Matching algorithms can be used for identifying errors in quantum systems, being the most famous the Blossom algorithm. Recent works have shown that small distance quantum error correction codes can be efficiently decoded by employing…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
Code super-optimization is the task of transforming any given program to a more efficient version while preserving its input-output behaviour. In some sense, it is similar to the paraphrase problem from natural language processing where the…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with 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…
Algebraic systems are constructed from which series of maximum distance separable (mds) codes are derived. The methods use unit and idempotent schemes.
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Algorithms can be used to prove and to discover new theorems. This paper shows how algorithmic skills in general, and the notion of invariance in particular, can be used to derive many results from Euclid's algorithm. We illustrate how to…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
We consider a distributed source coding system in which several observations are communicated to the decoder using limited transmission rate. The observations must be separately coded. We introduce a robust distributed coding scheme which…
This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…