Related papers: Error Correction Capacity of Unary Coding
Synthetic DNA can in principle be used for the archival storage of arbitrary data. Because errors are introduced during DNA synthesis, storage, and sequencing, an error-correcting code (ECC) is necessary for error-free recovery of the data.…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
Decoder diversity is a powerful error correction framework in which a collection of decoders collaboratively correct a set of error patterns otherwise uncorrectable by any individual decoder. In this paper, we propose a new approach to…
We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby, d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff parameter…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we…
Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different…
Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of…
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.…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
Adaptive coding faces the following problem: given a collection of source classes such that each class in the collection has non-trivial minimax redundancy rate, can we design a single code which is asymptotically minimax over each class in…
In this paper, we show that the single deletion correcting Varshamov-Tenengolts code, with minor modifications, can also correct an ordered deletion-erasure pattern where one deletion and at most one erasure occur and the deletion always…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the…
In this paper, we shed light on how an adaptive, efficient error coding in the transport layer helps ensure the application requirements. We recap the use of MDS codes and show that binary coding can significantly reduce the complexity and…