Related papers: A Note on Comparison of Error Correction Codes
We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…
This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…
We derive the optimum second-order coding rates, known as second-order capacities, for erasure and list decoding. For erasure decoding for discrete memoryless channels, we show that second-order capacity is $\sqrt{V}\Phi^{-1}(\epsilon_t)$…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
We consider analog error-correcting codes (analog ECCs) that are designed to correct/detect outlying errors arising in analog implementations of vector-matrix multiplication. The error-correction/detection capability of an analog ECC can be…
The problem of software fault localization may be viewed as an approach for finding hidden faults or bugs in the existing program codes which are syntactically correct and give fault free output for some input instances but fail for all…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Quantum error correction codes based on continuous variables play an important role for the implementation of quantum communication systems. A natural application of such codes occurs within quantum repeater systems which are used to combat…
The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method,…
Extrapolating physical error rates to logical error rates requires many assumptions and thus can radically under- or overestimate the performance of an error correction implementation. We introduce logical randomized benchmarking, a…
Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with…
The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This…
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
This paper presents a new paradigm for image transmission through analog error correction codes. Conventional schemes rely on digitizing images through quantization (which inevitably causes significant bandwidth expansion) and transmitting…
I formulate the problem of closing the detection loophole as a constrained optimization problem. Numerical methods can then be used to maximize the detector efficiency subject to the constraint that there exists a local realist explanation…
Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error…
Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without…
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…
Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…