Automatic-repeat-request error control schemes

Error detection incorporated with automatic-repeat-request (ARQ) is widely used for error control in data communication systems. This method of error control is simple and provides high system reliability. If a properly chosen code is used for error detection, virtually error-free data transmission can be attained. Various types of ARQ and hybrid ARQ schemes, and error detection using linear block codes are surveyed

Engineering autonomous error correction in stabilizer codes at finite temperature

We present an error correcting protocol that enhances the lifetime of stabilizer code based qubits which are susceptible to the creation of pairs of localized defects (due to string-like error operators) at finite temperature, such as the toric code. The primary tool employed is dynamic application of a local, unitary operator which exchanges defects and thereby translates localized excitations. Crucially, the protocol does not require any measurements of stabilizer operators, and therefore can be used to enhance the lifetime of a qubit in the absence of such experimental resources.Comment: 14 pages, 13 figures. Comments welcome, APS March Meeting session K44.0000

Continuous quantum error correction by cooling

We describe an implementation of quantum error correction that operates continuously in time and requires no active interventions such as measurements or gates. The mechanism for carrying away the entropy introduced by errors is a cooling procedure. We evaluate the effectiveness of the scheme by simulation, and remark on its connections to some recently proposed error prevention procedures.Comment: 8 pages, 5 figures. Published version. Minor change in conten

Design of Raptor Codes in the Low SNR Regime with Applications in Quantum Key Distribution

The focus of this work is on the design of Raptor codes for continuous variable Quantum key distribution (CV-QKD) systems. We design a highly efficient Raptor code for very low signal to noise ratios (SNRs), which enables CV-QKD systems to operate over long distances with a significantly higher secret key rate compared to conventional fixed rate codes. The degree distribution design of Raptor codes in the low SNR regime is formulated as a linear program, where a set of optimized degree distributions are also obtained through linear programming. Simulation results show that the designed code achieves efficiencies higher than 94\% for SNRs as low as -20 dB and -30 dB. We further propose a new error reconciliation protocol for CV-QKD systems by using Raptor codes and show that it can achieve higher secret key rates over long distances compared to existing protocols.Comment: The paper has been submitted to IEEE International Communications Conference (ICC), Kuala Lumpur, Malaysia, May 201

Tailored codes for small quantum memories

We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly outperforms the well-studied Steane code across the full range of parameters of the noise model, including for unbiased noise. In fact, this tailored code performs almost optimally when compared with 10,000 randomly selected stabilizer codes of comparable experimental complexity. Tailored codes can even outperform the Steane code with realistic experimental noise, and without any increase in the experimental complexity, as we demonstrate by comparison in the observed error model in a recent 7-qubit trapped ion experiment.Comment: 6 pages, 2 figures, supplementary material; v2 published versio

Energy Aware Error Control in Cooperative Communication in Wireless Sensor Networks

Due to small size of sensor nodes deployed in Wireless Sensor Networks (WSNs), energy utilization is a key issue. Poor channel conditions lead to retransmissions and hence, result in energy wastage. Error control strategies are usually utilized to accommodate channel impairments like noise and fading in order to optimize energy consumption for network lifetime enhancement. Meanwhile, cooperative communication also emerges to be an appropriate candidate to combat the effects of channel fading. Energy efficiency of cooperative scheme when applied with Automatic Repeat Request (ARQ), Hybrid-ARQ (HARQ) and Forward Error Correction (FEC) is investigated in this work. Moreover, the expressions for energy efficiency of Direct Transmission, Single Relay Cooperation and Multi Relay Cooperation are also derived. In all, our work is focused towards energy optimal communication in WSNs. Our results show that error control strategies with cooperative schemes can significantly enhance system performance in form of energy optimization.Comment: ACM Research in Adaptive and Convergent Systems (RACS 2013), Montreal, Canad

Coping with qubit leakage in topological codes

Many physical systems considered promising qubit candidates are not, in fact, two-level systems. Such systems can leak out of the preferred computational states, leading to errors on any qubits that interact with leaked qubits. Without specific methods of dealing with leakage, long-lived leakage can lead to time-correlated errors. We study the impact of such time-correlated errors on topological quantum error correction codes, which are considered highly practical codes, using the repetition code as a representative case study. We show that, under physically reasonable assumptions, a threshold error rate still exists, however performance is significantly degraded. We then describe simple additional quantum circuitry that, when included in the error detection cycle, restores performance to acceptable levels.Comment: 5 pages, 8 figures, comments welcom

Probability of undetected error after decoding for a concatenated coding scheme

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed

Embedding Noise Prediction into List-Viterbi Decoding using Error Detection Codes for Magnetic Tape Systems

A List Viterbi detector produces a rank ordered list of the N globally best candidates in a trellis search. A List Viterbi detector structure is proposed that incorporates the noise prediction with periodic state-metric updates based on outer error detection codes (EDCs). More specifically, a periodic decision making process is utilized for a non-overlapping sliding windows of P bits based on the use of outer EDCs. In a number of magnetic recording applications, Error Correction Coding (ECC) is adversely effected by the presence of long and dominant error events. Unlike the conventional post processing methods that are usually tailored to a specific set of dominant error events or the joint modulation code trellis architectures that are operating on larger state spaces at the expense of increased implementation complexity, the proposed detector does not use any a priori information about the error event distributions and operates at reduced state trellis. We present pre ECC bit error rate performance as well as the post ECC codeword failure rates of the proposed detector using perfect detection scenario as well as practical detection codes as the EDCs are not essential to the overall design. Furthermore, it is observed that proposed algorithm does not introduce new error events. Simulation results show that the proposed algorithm gives improved bit error and post ECC codeword failure rates at the expense of some increase in complexity.Comment: 4 pages, 3 figures, Proceedings of the ASME 2013 Conference on information storage and processing systems (ISPS 2013

CodeNet: Training Large Scale Neural Networks in Presence of Soft-Errors

This work proposes the first strategy to make distributed training of neural networks resilient to computing errors, a problem that has remained unsolved despite being first posed in 1956 by von Neumann. He also speculated that the efficiency and reliability of the human brain is obtained by allowing for low power but error-prone components with redundancy for error-resilience. It is surprising that this problem remains open, even as massive artificial neural networks are being trained on increasingly low-cost and unreliable processing units. Our coding-theory-inspired strategy, "CodeNet," solves this problem by addressing three challenges in the science of reliable computing: (i) Providing the first strategy for error-resilient neural network training by encoding each layer separately; (ii) Keeping the overheads of coding (encoding/error-detection/decoding) low by obviating the need to re-encode the updated parameter matrices after each iteration from scratch. (iii) Providing a completely decentralized implementation with no central node (which is a single point of failure), allowing all primary computational steps to be error-prone. We theoretically demonstrate that CodeNet has higher error tolerance than replication, which we leverage to speed up computation time. Simultaneously, CodeNet requires lower redundancy than replication, and equal computational and communication costs in scaling sense. We first demonstrate the benefits of CodeNet in reducing expected computation time over replication when accounting for checkpointing. Our experiments show that CodeNet achieves the best accuracy-runtime tradeoff compared to both replication and uncoded strategies. CodeNet is a significant step towards biologically plausible neural network training, that could hold the key to orders of magnitude efficiency improvements.Comment: Currently under revie