Error Detection and Correction

We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1-D graph, namely a circle, and show how to implement discrete circular quantum walk in quantum circuits built with universal CNOT and single quit gates. We review elementary quantum gates and circuit decomposition and propose a a generalized version of the all CNOT based quantum discrete circular walk. We simulated these circuits on an IBM quantum supercomputer London IBM-Q with 5 qubits. This quantum computer has non perfect gates based on superconducting qubits, therefore we analyze the impact of errors on the fidelity of the Walker circuit.

Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional systems. In this paper, we propose a 7-qutrit errorcorrecting code for the ternary quantum system and show that this design formulation has no equivalence in qubit systems. This code is optimum in the number of qutrits required to correct a single error while maintaining the CSS structure. This degenerate CSS code can (i) correct up to seven simultaneous phase errors and a single bit error, (ii) correct two simultaneous bit errors on pre-defined pairs of qutrits on eighteen out of twenty-one possible pairs, and (iii) in terms of the cost of implementation, the depth of the circuit of this code is only two more than that of the ternary Steane code. Our proposed code shows that it is possible to design better codes explicitly for ternary quantum systems instead of simply carrying over codes from binary quantum systems.

Multi-valued quantum systems can store more information than binary ones for a given number of quantum states. For reliable operation of multi-valued quantum systems, error correction is mandated. In this paper, we propose a 5qutrit quantum error correcting code and provide its stabilizer formulation. Since 5 qutrits are necessary to correct a single error, our proposed code is optimal in the number of qutrits. We prove that the error model considered in this paper spans the entire (3 × 3) operator space. Therefore, our proposed code can correct any single error on the codeword. This code outperforms the previous 9-qutrit code in (i) the number of qutrits required for encoding, (ii) our code can correct any arbitrary (3 × 3) error, (ii) our code can readily correct bit errors in a single step as opposed to the two-step correction used previously, and (iii) phase error correction does not require correcting individual subspaces.

Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four different types of errors can occur on a qubit. Maximally entangled states are orthogonal to each other and hence can be uniquely distinguished by a measurement in the Bell basis. Thus a measurement in Bell basis and a unitary transformation is sufficient to correct error in Bell states. However, such a measurement is not possible for nonmaximally entangled states. In this work we show that the 16 possible errors for a non-maximally entangled two qubit system map to only 8 distinct error states. Hence, it is possible to correct the error without perfect knowledge of the type of error. Furthermore, we show that the possible errors can be grouped in such a way that all 4 errors can occur on one qubit, whereas only bit flip error can occur on the second qubit. As a consequence, instead of 10, only 8 qubits are sufficient to correct a single error. We propose an 8-qubit error correcting code to correct a single error in a non-maximally entangled state. We further argue that for an n-qubit non-maximally entangled state of the form α |0 ⊗n + β |1 ⊗n , it is always possible to correct a single error with fewer than 5n qubits, in fact only 3n + 2 qubits suffice.

Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional systems. In this paper, we propose a 7-qutrit error-correcting code for the ternary quantum system and show that this design formulation has no equivalence in qubit systems. This code is optimum in the number of qutrits required to correct a single error while maintaining the CSS structure. This degenerate CSS code can (i) correct up to seven simultaneous phase errors and a single bit error, (ii) correct two simultaneous bit errors on pre-defined pairs of qutrits on eighteen out of twenty-one possible pairs, and (iii) in terms of the cost of implementation, the depth of the circuit of this code is only two more than that of the ternary Steane code. Our proposed code shows that it is possible to design better codes explicitly for ternary quantum system...

Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose, although how an ML decoder will behave in a more realistic asymmetric noise model has not been studied. In this article we (i) establish a methodology to formulate the surface code decoding problem as an ML classification problem, and (ii) propose a two-level (low and high) ML-based decoding scheme, where the first (low) level corrects errors on physical qubits and the second (high) level corrects any existing logical errors, for various noise models. Our results show that our proposed decoding method achieves ∼ 10× and ∼ 2× higher values of pseudo-threshold and threshold respectively, than for those with MWPM. We also empirically establish that usage of more sophisticated ML models with higher training/testing time, do not provide significant improvement in the decoder performance.

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A procedure is developed to automatically correct the bit flip and the arbitrary phase change errors in Generalized Bell states (GBS). The phase and parity characteristics of the GBS are encoded in ancilla bits without altering the state under consideration. The same information is then used to correct the state at a different point, through appropriate unitrary control operations. It is also shown that the distributed/indirect measurements on ancilla can yield the error syndrome. The restricted error correction circuit obtained for N-qubit entangled states of the Bell type, are generalized for the corresponding higher dimensions, thus opening up the possibility of designing of task specific error correction circuits.

Quantum error correcting codes (QECC) are the key ingredients both for fault-tolerant quantum computation and quantum communication. Teleportation-based error correction (TEC) helps in detecting and correcting operational and erasure errors by performing X and Z measurements during teleportation. Here we demonstrate the TEC protocol for the detection and correction of a single bit-flip error by proposing a new quantum circuit. A single phase-flip error can also be detected and corrected using the above protocol. For the first time, we illustrate detection and correction of erasure error in the superconducting qubitbased IBM's 14-qubit quantum computer.

The Klein Gordon equation was the first attempt at unifying special relativity and quantum mechanics. While initially discarded this equation of "many fathers" can be used in understanding spinless particles that consequently led to the discovery of pions and other subatomic particles. The equation leads to the development of Dirac equation and hence quantum field theory. It shows interesting quantum relativistic phenomena like Klein Paradox and "Zitterbewegung", a rapid vibrating movement of quantum relativistic particles. The simulation of such quantum equations initially motivated Feynman to propose the idea of quantum computation. While many such simulations have been done till date in various physical setups, this is the first time a digital quantum simulation of Klein Gordon equation is proposed on IBM's quantum computer. Here we simulate the time-dependent Klein Gordon equation in a barrier potential and clearly observe the tunnelling of the particle a...

Experimental realization of automated error correction is demonstrated through IBM Quantum Experience for Bell and GHZ states using a measurement based approach upon ancilla qubits. The measurement automatically activates error correcting unitary operations to restore the system to its original entangled state. We illustrate the algorithm for the maximally entangled qudit case by applying appropriate Hadamard and Controlled-NOT gates.

In this letter, we conceive a multi-layered coding scheme for the recently proposed Layered Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing (LACO-OFDM) system, which exploits its layered structure for protecting the information bits transmitted in the base layer. Explicitly, we intrinsically integrate error correction into the layered structure of the LACO-OFDM system and invoke soft iterative decoding between the layers at the receiver. Our system operates within 2 dB of the capacity limit at a BER of 10 -4 .

Based on internal predictions, action-errors can be detected relatively early. Different kinds of sensory feedback further provide information about the occurrence of errors later on. To investigate the mechanisms underlying error detection in copy-typing, ten-finger-typists and hunt-and-peck-typists copy typed with and without visibility of the screen and keyboard. We expected that error detection evolves in slower typing before, during, and after an error. Results showed that more errors were reported with visible screen than with covered screen in both groups underpinning the importance of distal action-effects for error detection. Importantly, ten-finger-typists showed pre-error-slowing in the inter-keystroke-intervals (IKIs) before reported errors, but hunt-and-peck-typists did not. In both groups, error-slowing was observed in the last IKI before both reported and unreported errors. Hence, internal predictions play a role in error detection in both groups, but in ten-finger-ty...

The parameters of the codes in Section 4 of our article are not correctly stated. The inequality in Proposition 5 should be with respect to the dual code C ⊥ s . The correct statement of Proposition 5 is Proposition 5 Assume that a positive integer c satisfies 2c ≤ d H (C ⊥ s \ {0}) -1, then dim F q P(C) = dim F q C, and dim F q P(C) ∩ P(C) ⊥ s = dim F q S(C) = dim F q C -2c.

This paper studies the problem of increasing the efficiency in controlling burst errors that are caused by external noise in the context of digital data transmission. For this purpose, the utilization of special weighted check sum modification has been proposed. Indeed, an algorithm for burst error control is presented and its use is illustrated via the presentation of an example in order to show that the technique proposed in this paper ensures superior data transmission error control effectiveness compared with already known codes.

Spectral Minutiae (SM) representation enables the combination of minutiae-based fingerprint recognition systems with template protection schemes based on fuzzy commitment, but it requires error-correcting codes that can handle high bit error rates (i.e. above 40%). In this paper, we propose a 3-Layer coding scheme based on erasure codes for the SM-based biometric recognition system. Our approach is inspired by the fact that the Packet Error Rate (PER) is proportional to the Bit Error Rate (BER). Each packet is encoded by an Error Detection Code (EDC) and an Error Correction Code (ECC). The packet can only survive if it successfully passes the ECC and EDC decoder. With the erasure code, the system can reconstruct the secret key by only using the survived packets. By applying SM to the FVC2000-DB2 fingerprint database, the unprotected system achieves an EER of around 6% while our proposed coding scheme reaches an EER of approximately 6.5% with a 1032-bit secret key.

The current error correction layer of IEEE 802.11a WLAN is designed for worst case scenarios, which often do not apply. In this paper, we propose a new opportunistic error correction layer based on Fountain codes and a resolution adaptive ADC. The key part in the new proposed system is that only packets are processed by the receiver chain which have encountered "good" channel conditions. Others are discarded. With this new approach, around 2 3 of the energy consumption can be saved compared with the conventional IEEE 802.11a WLAN system under the same channel conditions and throughput.

Traditional Optical Character Recognition (OCR) systems that generate text of highly inflectional Indic languages like Hindi tend to suffer from poor accuracy due to a wide alphabet set, compound characters and difficulty in segmenting characters in a word. Automatic spelling error detection and context-sensitive error correction can be used to improve accuracy by post-processing the text generated by these OCR systems. A majority of previously developed language models for error correction of Hindi spelling have been context-free. In this paper, we present Vartani Spellcheck a context-sensitive approach for spelling correction of Hindi text using a state-of-the-art transformer -BERT in conjunction with the Levenshtein distance algorithm, popularly known as Edit Distance. We use a lookup dictionary and context-based named entity recognition (NER) for detection of possible spelling errors in the text. Our proposed technique has been tested on a large corpus of text generated by the widely used Tesseract OCR on the Hindi epic Ramayana. With an accuracy of 81%, the results show a significant improvement over some of the previously established context-sensitive error correction mechanisms for Hindi. We also explain how Vartani Spellcheck may be used for on-the-fly autocorrect suggestion during continuous typing in a text editor environment.

A system for soft error detection and correction is proposed for digital Integrated Circuit (IC) implementation of convolution. The convolution is implemented in a Residue Number System using Fermat Number Theoretic Transforms. The flexibility afforded by the Modified Overlap Technique in allowing transforms of differing lengths in a convolution makes it possible to easily detect and correct soft errors by means of a Single Redundant Channel and pattern matching technique. The proposed system gives area reductions in the majority of cases examined, when compared with Triple Modular Redundancy. In the case of large (e.g. 28 and 32 bit) word lengths, the proposed system provides area reductions of up to 30%.

One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic errors, i.e., errors represented by arbitrary combinations of Pauli X, Y and Z operators, in this paper we investigate the design of stabilizer QECC able to correct a given number eg of generic Pauli errors, plus eZ Pauli errors of a specified type, e.g., Z errors. These codes can be of interest when the quantum channel is asymmetric in that some types of error occur more frequently than others. We first derive a generalized quantum Hamming bound for such codes, then propose a design methodology based on syndrome assignments. For example, we found a [[9, 1]] quantum error-correcting code able to correct up to one generic qubit error plus one Z error in arbitrary positions. This, according to the generalized quantum Hamming bound, is the shortest code with the specified error correction capability. Finally, we evaluate analytically the performance of the new codes over asymmetric channels.

The component-wise or Schur product C ∗C of two linear error correcting codes C and C over certain finite field is the linear code spanned by all component-wise products of a codeword in C with a codeword in C. When C = C, we call the product the square of C and denote it C. Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrixproduct codes, a general construction that allows to obtain new longer codes from several “constituent” codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known (u, u+v)-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the ...

A new strategy is proposed for implementing computationally intensive high-throughput decoders based on the long length irregular LDPC codes adopted in the DVB-S2 standard. It is supported on manycore graphics processing unit (GPU) architectures, for performing parallel multi-threaded decoding of multiple codewords with reduced accesses to global memory. This novel approach is flexible and scalable, and achieves throughputs superior to the 90 Mbit/s required by the DVB-S2 standard, while at the same time it improves error-correcting performances such as BER and error floors regarding conventional VLSI-based decoders.

The authors present a new hybrid method for performing modular exponentiation using a hybrid ternaryquinary number system. A recent result concerning performing modular exponentiation with precomputation was presented by Dimitrov and Cooklev: their average number of modular multiplications is 0.3381n, where n is the length of the modulus, while the authors' proposed method only needs 0.3246~ modular multiplications. Furthermore, compared to Dimitrov and Cooklev's approach, the authors' method reduces the amount of storage by 56.8% if the modulus is a 512bit number.

The error-resilient for video transmission over the Internet in which regarded as the packet erasure channel is always a tough task and has gained lots of attentions. The main contradictory problem lies between error-resilient and bandwidth usage. Additional redundant data has to be added to achieve robust transmission which leads to huge bandwidth usage. In this paper, an error-resilient scheme called Wyner-Ziv Error-Resilient (WZER) based on a receiver driven layered Wyner-Ziv (WZ) coding framework is proposed. The WZER purposely emphasizes on the protection of the Region of Interest (ROI) area in the frame thus to achieve the better tradeoff between the bandwidth usage and error-resilience. WZER is designed to work for the scenario of wavelet based video coding over packet erasure channel, where several techniques including automatic ROI detection, ROI mask generation, Rate distortion optimization (RDO) quantization, WZ coding with layer design, and packet level Low Density Parity Check (LDPC) code are used. The performances of the proposed WZER are simulated based on average PSNR of luminance, perceptual reconstruction and bandwidth usage and compared with normal Forward Error Correction (FEC) full protection scheme and no protection scheme. The results show the advantages of the proposed WZER over traditional FEC protection, especially in the aspects of the recovery of the subject area and bandwidth efficiency.

Next Generation Sequencing (NGS) technologies produce massive amount of low cost data that is very much useful in genomic study and research. However, data produced by NGS is affected by different errors such as substitutions, deletions or insertion. It is essential to differentiate between true biological variants and alterations occurred due to errors for accurate downstream analysis. Many types of methods and tools have been developed for NGS error correction. Some of these methods only correct substitutions errors whereas others correct multi types of data errors. In this article, a comprehensive evaluation of three types of methods (k-spectrum based, Multisequencing alignment and Hybrid based) is presented which are implemented and adopted by different tools. Experiments have been conducted to compare the performance based on runtime and error correction rate. Two different computing platforms have been used for the experiments to evaluate effectiveness of runtime and error correction rate. The mission and aim of this comparative evaluation is to provide recommendations for selection of suitable tools to cope with the specific needs of users and practitioners. It has been noticed that k-mer spectrum based methodology generated superior results as compared to other methods. Amongst all the tools being utilized, Racer has shown eminent performance in terms of error correction rate and execution time for both small as well as large data sets. In multisequence alignment based tools, Karect depicts excellent error correction rate whereas Coral shows better execution time for all data sets. In hybrid based tools, Jabba shows better error correction rate and execution time as compared to brownie. Computing platforms mostly affect execution time but have no general effect on error correction rate.

In an attempt to enrich the lives of billions of people by providing proper information, security and a way of communicating with others, the need for efficient and improved satellites is constantly growing. Thus, there is an increasing demand for better error detection and correction (EDAC) schemes, which are capable of protecting the data onboard the satellites. The paper is aimed towards detecting and correcting such errors using a special algorithm called the Hamming Code, which uses the concept of parity and parity bits to prevent single-bit errors onboard a satellite in Low Earth Orbit. This paper focuses on the study of Low Earth Orbit satellites and the process of generating the Hamming Code matrix to be used for EDAC using computer programs. The most effective version of Hamming Code generated was the Hamming (16, 11, 4) version using MATLAB, and the paper compares this particular scheme with other EDAC mechanisms, including other versions of Hamming Codes and Cyclic Redundancy Check (CRC), and the limitations of this scheme. This particular version of the Hamming Code guarantees single-bit error corrections as well as double-bit error detections. Furthermore, this version of Hamming Code has proved to be fast with a checking time of 5.669 nanoseconds, that has a relatively higher code rate and lower bit overhead compared to the other versions and can detect a greater percentage of errors per length of code than other EDAC schemes with similar capabilities. In conclusion, with the proper implementation of the system, it is quite possible to ensure a relatively uncorrupted satellite storage system.

The error recovery problem in wireless sensor networks is studied from a generic resource‐constrained energy‐optimization perspective. To characterize the features of error recovery schemes that suit the majority of applications, an energy model is developed and inferences are drawn based on a suitable performance metric. For applications that require error control coding, an efficient scheme is proposed based on an interesting observation related to shortened Reed–Solomon (RS) codes for packet reliability. It is shown that multiple instances (γ) of RS codes defined on a smaller alphabet combined with interleaving results in smaller resource usage, while the performance exceeds the benefits of a shortened RS code defined over a larger alphabet. In particular, the proposed scheme can have an error correction capability of up to γ times larger than that of the conventional RS scheme without changing the rate of the code with much lower power, timing and memory requirements. Implementa...

Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and real-time feedback. Autonomous quantum error correction (AQEC) instead uses steady-state bath engineering to perform the correction in a hardware-efficient manner. We realize an AQEC scheme, implemented with only two transmon qubits in a 2D scalable architecture, that actively corrects single-photon loss and passively suppresses low-frequency dephasing using six microwave drives. Compared to uncorrected encoding, factors of 2.0, 5.1, and 1.4 improvements are experimentally witnessed for the logical zero, one, and superposition states. Our results show the potential of implementing hardware-efficient AQEC to enhance the reliability of a transmon-based quantum information processor.

Processing quantum information using quantum three-level systems or qutrits as the fundamental unit is an alternative to contemporary qubit-based architectures with the potential to provide significant computational advantages. We demonstrate a fully programmable two-qutrit quantum processor by utilizing the third energy eigenstates of two transmons. We develop a parametric coupler to achieve excellent connectivity in the nine-dimensional Hilbert space enabling efficient implementations of two-qutrit gates. We characterize our processor by realizing several algorithms like Deutsch-Jozsa, Bernstein-Vazirani, and Grover's search. Our hardware-efficient protocols allow us to show that two stages of Grover's amplification can improve the success rates of an unstructured search with quantum advantage. Our results pave the way for building fully programmable ternary quantum processors using transmons as building blocks for a universal quantum computer.

Processing quantum information using quantum three-level systems or qutrits as the fundamental unit is an alternative to contemporary qubit-based architectures with the potential to provide significant computational advantages. We demonstrate a fully programmable two-qutrit quantum processor by utilizing the third energy eigenstates of two transmons. We develop a parametric coupler to achieve excellent connectivity in the nine-dimensional Hilbert space enabling efficient implementations of two-qutrit gates. We characterize our processor by realizing several algorithms like Deutsch-Jozsa, Bernstein-Vazirani, and Grover's search. Our efficient ancilla-free protocols allow us to show that two stages of Grover's amplification can improve the success rates of an unstructured search with quantum advantage. Our results pave the way for building fully programmable ternary quantum processors using transmons as building blocks for a universal quantum computer.

Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and real-time feedback. Autonomous quantum error correction (AQEC) instead uses steady-state bath engineering to perform the correction in a hardware-efficient manner. We develop and realize an AQEC scheme with transmons, that actively corrects single-photon loss and passively suppresses low-frequency dephasing. Compared to uncorrected encoding, factors of 2.0, 5.1, and 1.4 improvements are experimentally witnessed for the logical zero, one, and superposition states. Our results show the potential of implementing hardware-efficient AQEC to enhance the reliability of a transmon-based quantum information processor.

Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. Given that the overhead of such error correction is often formidable, autonomous quantum error correction (AQEC) proposals offer a promising near-term alternative. AQEC schemes work by transforming error states into excitations that can be efficiently removed through engineered dissipation. The recently proposed AQEC scheme by Li et al., called the Star code, can autonomously correct or suppress all single qubit error channels using two transmons as encoders with a tunable coupler and two lossy resonators as a cooling source. The Star code requires only two-photon interactions and can be realized with linear coupling elements, avoiding experimentally challenging higher-order terms needed in many other AQEC proposals, but needs carefully selected parameters to achieve quadratic improvements in logical states' lifetimes. Here, we theoretically and numerically demonstrate the optimal parameter choices in the Star Code. We further discuss adapting the Star code to other planar superconducting circuits, which offers a scalable alternative to single qubits for incorporation in larger quantum computers or error correction codes.

The P-Bigram method is a string comparison methods base on an internal two characters-based similarity measure. The edit distance between two strings is the minimal number of elementary editing operations required to transform one string into the other. The elementary editing operations include deletion, insertion, substitution two characters. In this paper, we address the P-Bigram method to sole the similarity problem in DNA sequence. This method provided an efficient algorithm that locates all minimum operation in a string. We have been implemented algorithm and found that our program calculated that smaller distance than one string. We develop PBigram edit distance and show that edit distance or the similarity and implementation using dynamic programming. The performance of the proposed approach is evaluated using number edit and percentage similarity measures.

A n ecient multicast hybrid ARQ scheme is proposed by incorporating the generalized minimum distance (GMD) decoding of maximum distance separable (MDS) codes with Metzner's scheme . Erroneous frames are stored in the receiver buer and recovered after receiving one or more redundant frames. The throughput and the average transmission delay of the proposed scheme are analyzed on memoryless symmetric channels. The proposed scheme can circumvent the degradation of the throughput due to an increase of the number of receivers, which is the most serious defect in the conventional multicast ARQ schemes, at the expense of the transmission delay. Keywords| Multicast ARQ, MDS codes, GMD decoding, Memoryless symmetric channels, Throughput, Average transmission delay. I. Introduction M ULTICAST is a common scenario in various com- munication systems such as satellite communications, mobile telephony and local area networks. The performance of plain ARQ schemes including stop-andwait (SAW), go-back-N (GBN) and selective repeat (SR) schemes has been evaluated over multicast communication systems. Calo and Easton examined a multicast ARQ scheme based on a SAW scheme [1]. Mase et al. [2] and Gopal and Jae [3] discussed some multicast ARQ schemes employing a GBN principle. Two multicast SR ARQ schemes are studied by Sabnani and Schwartz [4]. Chandran and Lin [5] presented a multicast ARQ s c heme based on hybrid ARQ schemes [6]. Deng evaluated the performance of a multicast hybrid ARQ scheme on nonstationary channels [7]. It has been veried, however, that the performance of such m ulticast communication systems is deteriorated signicantly as the number of receivers increases [3]. It necessitates the development of ecient m ulticast ARQ s c hemes. Metzner [8] proposed an ecient m ulticast ARQ s c heme taking advantage of the following features of maximum distance separable (MDS) codes [9]; Lemma 1: For any codewords of [n; k] MDS codes 1 , if at least k symbols are correct, then the codeword can be K. Sakakibara was with

In this paper, we introduced a new type of Encryption and Error Correction scheme, which is called "A Combined Encryption and Turbo Coding Scheme: AES-TURBO". Although in previous studies error correction and encryption are handled independently, we combined error correction and Encryption functionality into one single step. This combined System's performances are evaluated in AWGN (Additive White Gaussian Noise) channel type. The results are compared with the system employing ideal encryption and decryption.

The universal secure network coding presented by Silva et al. realizes secure and reliable transmission of a secret message over any underlying network code, by using maximum rank distance codes. Inspired by their result, this paper considers the secure network coding based on arbitrary linear codes, and investigates its security performance and error correction capability that are guaranteed independently of the underlying network code. The security performance and error correction capability are said to be universal when they are independent of underlying network codes. This paper introduces new code parameters, the relative dimension/intersection profile (RDIP) and the relative generalized rank weight (RGRW) of linear codes. We reveal that the universal security performance and universal error correction capability of secure network coding are expressed in terms of the RDIP and RGRW of linear codes. The security and error correction of existing schemes are also analyzed as applications of the RDIP and RGRW.

Transferring data is one of the key operations performed by millions of users every day. Users do this by issuing direct commands, such as file transfer commands, or indirectly as a feature invoked by numerous end-user applications. The most important security characteristic of a successful data exchange is the integrity of that data. The receiver user desires to acquire data that has not been modified through malicious acts, or simple human or machine error. Applications that rely on the Transfer Control Protocol (TCP) as the main mechanism to provide end-to-end reliability, including error and sequence control, do not check the integrity of the file being transmitted prior to the transfer. In this paper, we present an overview of current data transfer mechanisms and their security provisions and propose an internal integrity mechanism that provides a triangulation means of error control through the use of one-way hash functions based on the original file being transferred; and a discussion of the implications and limitations that such a mechanism imparts on data transfer mechanisms.

DRAMs are used as the main memory in most computing systems today. Studies show that DRAMs contribute to a significant part of overall system power consumption. One of the main challenges in low-power DRAM design is the inevitable refresh process. Due to process variation, memory cells exhibit retention time variations. Current DRAMs use a single refresh period determined by the cell with the largest leakage. Since prolonging refresh intervals introduces retention errors, a set of previous works adopt conventional error-correcting code (ECC) to correct retention errors. However, these approaches introduce significant area and energy overheads. In this article, we propose a novel error correction framework for retention errors in DRAMs, called SECRET (selective error correction for refresh energy reduction). The key observations we make are that retention errors are hard errors rather than soft errors, and only few DRAM cells have large leakage. Therefore, instead of equipping error ...

In this paper, we propose an Automatic Repeat reQuest (ARQ) technique for enhancing the reliability and throughput of broadband wireless Internet access applications, and provide examples of its performance. ARQ is a method for making a link and flow more robust to errors. Other than enhancing link quality, ARQ provides early error recovery, so that the transport layer does not lower the data throughput. The cost of these enhancements is additional overhead. In this work, we have extensively analyzed our proposed ARQ scheme along with realistic wireless channel and protocol stack models. We have quantified the performance gains of our ARQ scheme as reduced end-to-end delay, increased throughput, SNR gain and fade margin, also providing the overhead costs. We have proposed and analyzed enhanced features, namely, Segmentation and Reassembly (SAR) and Bitmap Compression. We showed that these features reduce the overhead, the extent of which depends on the nature of the errors.

Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the communication overhead for regeneration (called MBR). In this work, we propose new encoding schemes for [n, d] error-correcting MSR and MBR codes that generalize our earlier work on error-correcting regenerating codes. We show that by choosing a suitable diagonal matrix, any generator matrix of the [n, α] Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR codes with the least update complexity can be found. By using the coefficients of generator polynomials of [n, k] and [n, d] RS codes, we present a least-update-complexity encoding scheme for MBR codes. A decoding scheme is proposed that utilizes the [n, α] RS code to perform data reconstruction for MSR codes. The proposed decoding scheme has better error correction capability and incurs the least number of node accesses when errors are present. A new decoding scheme is also proposed for MBR codes that can correct more error-patterns.

We describe a new way to organize a full search vector quantization codebook so that images encoded with it can be sent progressively and have resilience to channel noise. The codebook organization guarantees that the most signicant bits (MSB's) of the codeword index are most important to the overall image quality and are highly correlated. Simulations show that the eective channel error rates of the MSB's can be substantially lowered by implementing a Maximum A Posteriori (MAP) detector similar to one suggested by Phamdo and Farvardin . The performance of the scheme is close to that of coding at lower bit error rates and outperforms it at higher error rates. No extra bits are used for channel error correction.

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in . Initial results showed that decoders which employ a group of these algorithms operating in parallel can offer low error floor decoding for high-speed applications. As the number of two-bit bit flipping algorithms is large, designing such a decoder is not a trivial task. In this paper, we describe a procedure to select collections of algorithms that work well together. This procedure relies on a recursive process which enumerates error configurations that are uncorrectable by a given algorithm. The error configurations uncorrectable by a given algorithm form its trapping set profile. Based on their trapping set profiles, algorithms are selected so that in parallel, they can correct a fixed number of errors with high probability.

A new class of bit flipping algorithms for lowdensity parity-check codes over the binary symmetric channel is proposed. Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit allows an increase in the guaranteed error correction capability. An additional bit is also employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis and selection of two-bit bit flipping algorithms is provided. The main component of this framework is the (re)definition of trapping sets, which are the most "compact" Tanner graphs that cause decoding failures of an algorithm. A recursive procedure to enumerate trapping sets is described. This procedure is the basis for selecting a collection of algorithms that work well together. It is demonstrated that decoders which employ a properly selected group of the proposed algorithms operating in parallel can offer high speed and low error floor decoding.

Novel bitwise retransmission schemes are devised which retransmit only the bits received with small reliability. The retransmissions are used to accumulate the reliabilities of individual bits. Unlike the conventional automatic repeat request (ARQ) schemes, the proposed scheme does not require a checksum for the error detection. The bits to be retransmitted are reported as a combination number, or two synchronized random number generators (RNGs) at the transmitter and receiver are used to greatly compress the feedback message. The bitwise retransmission decisions and/or combining can be performed after the demodulation or after the channel decoding at the receiver. The bit-error rate (BER) expressions are derived for the case of one and two retransmissions, and verified by computer simulations. Assuming three specific retransmission strategies, the scheme parameters are optimized to minimize the overall BER. For the same number of retransmissions and packet length, the proposed schemes always outperform the frequently used stop-and-wait ARQ. The impact of feedback errors is also considered. Finally, practical designs of the bitwise retransmissions for data fusion from sensor nodes in Zigbee, Wifi and Bluetooth networks are presented.

Novel bitwise retransmission schemes are devised which retransmit only the bits received with small reliability. The retransmissions are used to accumulate the reliabilities of individual bits. Unlike the conventional automatic repeat request (ARQ) schemes, the proposed scheme does not require a checksum for the error detection. The bits to be retransmitted are reported as a combination number, or two synchronized random number generators (RNGs) at the transmitter and receiver are used to greatly compress the feedback message. The bitwise retransmission decisions and/or combining can be performed after the demodulation or after the channel decoding at the receiver. The bit-error rate (BER) expressions are derived for the case of one and two retransmissions, and verified by computer simulations. Assuming three specific retransmission strategies, the scheme parameters are optimized to minimize the overall BER. For the same number of retransmissions and packet length, the proposed sche...

This paper experimentally evaluates and models the error-caused security vulnerabilities and the resulting security violations on two Linux kernel firewalls: IPChains and Netfilter. There are two major aspects to this work: to conduct extensive error injection experiments on the Linux kernel and to quantify the possibility of error-caused security violations using a Stochastic Activity Network (SAN) model. The error injection experiments show that about 2% of errors injected into the firewall code segment cause security vulnerabilities. Two types of error-caused security vulnerabilities are distinguished: temporary, which disappear when the error disappears, and permanent, which persist even after the error is removed, as long as the system is not rebooted. Results from simulating the SAN model indicate that under an error rate of 0.1 error per day during a 1-year period in a networked system protected by 20 firewalls, two machines (on the average) will experience security violations. This indicates that error-caused security vulnerabilities can be a non-negligible source of a security threat to a highly secure system.

Next Generation Sequencing (NGS) technologies produce massive amount of low cost data that is very much useful in genomic study and research. However, data produced by NGS is affected by different errors such as substitutions, deletions or insertion. It is essential to differentiate between true biological variants and alterations occurred due to errors for accurate downstream analysis. Many types of methods and tools have been developed for NGS error correction. Some of these methods only correct substitutions errors whereas others correct multi types of data errors. In this article, a comprehensive evaluation of three types of methods (k-spectrum based, Multisequencing alignment and Hybrid based) is presented which are implemented and adopted by different tools. Experiments have been conducted to compare the performance based on runtime and error correction rate. Two different computing platforms have been used for the experiments to evaluate effectiveness of runtime and error correction rate. The mission and aim of this comparative evaluation is to provide recommendations for selection of suitable tools to cope with the specific needs of users and practitioners. It has been noticed that k-mer spectrum based methodology generated superior results as compared to other methods. Amongst all the tools being utilized, Racer has shown eminent performance in terms of error correction rate and execution time for both small as well as large data sets. In multisequence alignment based tools, Karect depicts excellent error correction rate whereas Coral shows better execution time for all data sets. In hybrid based tools, Jabba shows better error correction rate and execution time as compared to brownie. Computing platforms mostly affect execution time but have no general effect on error correction rate.