Related papers: Nonuniform Codes for Correcting Asymmetric Errors …
Function-correcting codes are an innovative class of codes that are designed to protect a function evaluation of the data against errors or corruptions. Due to its usefulness in machine learning applications and archival data storage, where…
Surface codes are quantum error correcting codes normally defined on 2D arrays of qubits. In this paper, we introduce a surface code design based on the fact that the severity of bit flip and phase flip errors in the physical quantum…
In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of…
We propose efficient coding schemes for two communication settings: 1. asymmetric channels, and 2. channels with an informed encoder. These settings are important in non-volatile memories, as well as optical and broadcast communication. The…
Computation of the undetected error probability for error correcting codes over the Z-channel is an important issue, explored only in part in previous literature. In this paper we consider the case of Varshamov-Tenengol'ts codes, by…
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…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
We study a form of unequal error protection that we term "unequal message protection" (UMP). The message set of a UMP code is a union of $m$ disjoint message classes. Each class has its own error protection requirement, with some classes…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar…
We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances…
The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{N}$ is considered. The sequence of channels is assumed to be completely known to both the…
Recently, the theory of quantum error control codes has been extended to subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Unary coding has found applications in data compression, neural network training, and in explaining the production mechanism of birdsong. Unary coding is redundant; therefore it should have inherent error correction capacity. An expression…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
We consider a new fundamental question regarding the point-to-point memoryless channel. The source-channel separation theorem indicates that random codebook construction for lossy source compression and channel coding can be independently…