Related papers: Coding for Combined Block-Symbol Error Correction
Concatenated forward error correction is studied using an outer KP4 Reed-Solomon code with hard-decision decoding and inner single parity check (SPC) codes with Chase/Wagner soft-decision decoding. Analytical expressions are derived for the…
In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node.…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
This paper explores the possibilities and limitations of error correction by the structural simplicity of error mechanisms. Specifically, we consider channel models, called \emph{samplable additive channels}, in which (a) errors are…
We consider a problem in which a source is encoded into N packets, an unknown number of which are subject to adversarial errors en route to the decoder. We seek code designs for which the decoder is guaranteed to be able to reproduce the…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
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…
In this paper, the design of irregular turbo codes for the binary erasure channel is investigated. An analytic expression of the erasure probability of punctured recursive systematic convolutional codes is derived. This exact expression…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
Erasures, or errors with known locations, are a more favorable type of error for quantum error-correcting codes than Pauli errors. Converting physical noise into erasures can significantly improve the performance of quantum error…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
We construct two-dimensional codes for correcting burst errors using the finite field Fourier transform. The encoding procedure is performed in the transformed domain using the conjugacy property of the finite field Fourier transform. The…
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…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…
We present a scheme able to protect k >= 3 qubits of information against the occurrence of multiple erasures, based on the code proposed by Yang et al. (2004 JETP Letters 79 236). In this scheme redundant blocks are used and we restrict to…