Error correction in nonbinary words

A simple error detecting and correcting procedure is described for nonbinary symbol words; here, the error position is located using the Hamming method and the correct symbol is substituted using a modulo-check procedure.

Bootstrapping the Error Correction Model Cointegration Test

This paper is concerned with using the bootstrap to obtain improved critical values for the error correction model (ECM) cointegration test in dynamic models. In the paper we investigate the effects of dynamic specification on the size and power of the ECM cointegration test with bootstrap critical values. The results from a Monte Carlo study show that the size of the bootstrap ECM cointegration test is close to the nominal significance level. We find that overspecification of the lag length results in a loss of power. Underspecification of the lag length results in size distortion. The performance of the bootstrap ECM cointegration test deteriorates if the correct lag length is not used in the ECM. The bootstrap ECM cointegration test is therefore not robust to model misspecification.

Convolutional Codes for Network-Error Correction

In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors are separated by a certain interval. We also give some bounds on the field size and the number of errors that can get corrected in a certain interval. Compared to previous network error correction schemes, using convolutional codes is seen to have advantages in field size and decoding technique. Some examples are discussed which illustrate the several possible situations that arise in this context.

Network Error Correction for Unit-Delay, Memory-Free Networks Using Convolutional Codes

A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their outgoing edges. In this work, we introduce network-error correction for single source, acyclic, unit-delay, memory-free networks with coherent network coding for multicast. A convolutional code is designed at the source based on the network code in order to correct network- errors that correspond to any of a given set of error patterns, as long as consecutive errors are separated by a certain interval which depends on the convolutional code selected. Bounds on this interval and the field size required for constructing the convolutional code with the required free distance are also obtained. We illustrate the performance of convolutional network error correcting codes (CNECCs) designed for the unit-delay networks using simulations of CNECCs on an example network under a probabilistic error model.

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.

Burst error correction using partial fourier matrices and block sparse representation

There is a strong relation between sparse signal recovery and error control coding. It is known that burst errors are block sparse in nature. So, here we attempt to solve burst error correction problem using block sparse signal recovery methods. We construct partial Fourier based encoding and decoding matrices using results on difference sets. These constructions offer guaranteed and efficient error correction when used in conjunction with reconstruction algorithms which exploit block sparsity.

Layered Exact-Repair Regenerating Codes via Embedded Error Correction and Block Designs

A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the help-by-transfer property where the helper nodes simply transfer part of the stored data directly, without performing any computation. This embedded error correction structure makes the decoding process straightforward, and in some cases the complexity is very low. We show that this construction is able to achieve performance better than space-sharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes, and it is the first class of codes to achieve this performance. In fact, it is shown that the proposed construction can achieve a nontrivial point on the optimal functional-repair tradeoff, and it is asymptotically optimal at high rate, i.e., it asymptotically approaches the minimum storage and the minimum repair-bandwidth simultaneously.

crossmodal error correction of continuous handwriting recognition by speech

In recognition-based user interface, users’ satisfaction is determined not only by recognition accuracy but also by effort to correct recognition errors. In this paper, we introduce a crossmodal error correction technique, which allows users to correct errors of Chinese handwriting recognition by speech. The focus of the paper is a multimodal fusion algorithm supporting the crossmodal error correction. By fusing handwriting and speech recognition, the algorithm can correct errors in both character extraction and recognition of handwriting. The experimental result indicates that the algorithm is effective and efficient. Moreover, the evaluation also shows the correction technique can help users to correct errors in handwriting recognition more efficiently than the other two error correction techniques.

Hybrid error correction and de novo assembly of single-molecule sequencing reads.

Single-molecule sequencing instruments can generate multikilobase sequences with the potential to greatly improve genome and transcriptome assembly. However, the error rates of single-molecule reads are high, which has limited their use thus far to resequencing bacteria. To address this limitation, we introduce a correction algorithm and assembly strategy that uses short, high-fidelity sequences to correct the error in single-molecule sequences. We demonstrate the utility of this approach on reads generated by a PacBio RS instrument from phage, prokaryotic and eukaryotic whole genomes, including the previously unsequenced genome of the parrot Melopsittacus undulatus, as well as for RNA-Seq reads of the corn (Zea mays) transcriptome. Our long-read correction achieves >99.9% base-call accuracy, leading to substantially better assemblies than current sequencing strategies: in the best example, the median contig size was quintupled relative to high-coverage, second-generation assemblies. Greater gains are predicted if read lengths continue to increase, including the prospect of single-contig bacterial chromosome assembly.

Real-time error detection but not error correction drives automatic visuomotor adaptation

We investigated the role of visual feedback of task performance in visuomotor adaptation. Participants produced novel two degrees of freedom movements (elbow flexion-extension, forearm pronation-supination) to move a cursor towards visual targets. Following trials with no rotation, participants were exposed to a 60A degrees visuomotor rotation, before returning to the non-rotated condition. A colour cue on each trial permitted identification of the rotated/non-rotated contexts. Participants could not see their arm but received continuous and concurrent visual feedback (CF) of a cursor representing limb position or post-trial visual feedback (PF) representing the movement trajectory. Separate groups of participants who received CF were instructed that online modifications of their movements either were, or were not, permissible as a means of improving performance. Feedforward-mediated performance improvements occurred for both CF and PF groups in the rotated environment. Furthermore, for CF participants this adaptation occurred regardless of whether feedback modifications of motor commands were permissible. Upon re-exposure to the non-rotated environment participants in the CF, but not PF, groups exhibited post-training aftereffects, manifested as greater angular deviations from a straight initial trajectory, with respect to the pre-rotation trials. Accordingly, the nature of the performance improvements that occurred was dependent upon the timing of the visual feedback of task performance. Continuous visual feedback of task performance during task execution appears critical in realising automatic visuomotor adaptation through a recalibration of the visuomotor mapping that transforms visual inputs into appropriate motor commands.