Related papers: Pearson codes
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the…
For any prime power $q$, Mori and Tanaka introduced a family of $q$-ary polar codes based on $q$~by~$q$ Reed-Solomon polarization kernels. For transmission over a $q$-ary erasure channel, they also derived a closed-form recursion for the…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
A flag is a sequence of nested subspaces of a given ambient space F_q^n over a finite field F_q. In network coding, a flag code is a set of flags, all of them with the same sequence of dimensions, the type vector. In this paper, we…
This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
This article examines the queueing performance of communication systems that transmit encoded data over unreliable channels. A fading formulation suitable for wireless environments is considered where errors are caused by a discrete channel…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…
Developing computationally-efficient codes that approach the Shannon-theoretic limits for communication and compression has long been one of the major goals of information and coding theory. There have been significant advances towards this…
Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding…
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a…
An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if the vertex codes have minimum distance $\ge 3$, the overall…
Symbol-pair code is a new coding framework which is proposed to correct errors in the symbol-pair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible…
We study quantum communication in the presence of adversarial noise. In this setting, communicating with perfect fidelity requires using a quantum code of bounded minimum distance, for which the best known rates are given by the quantum…
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum…
The paper establishes the capacity region of the Gaussian interference channel with many transmitter-receiver pairs constrained to use point-to-point codes. The capacity region is shown to be strictly larger in general than the achievable…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…