Error-correcting Properties Research Articles

Barbieri’s Organic Codes Enable Error Correction of Genomes

Barbieri introduced and developed the concept of organic codes. The most basic of them is the genetic code, a set of correspondence rules between otherwise unrelated sequences: strings of nucleotides on the one hand, polypeptidic chains on the other hand. Barbieri noticed that it implies ‘coding by convention’ as arbitrary as the semantic relations a language establishes between words and outer objects. Moreover, the major transitions in life evolution originated in new organic codes similarly involving conventional rules. Independently, dealing with heredity as communication over time and relying on information theory, we asserted that the conservation of genomes over the ages demands that error-correcting codes make them resilient to casual errors. Moreover, the better conservation of very old parts of the genome demands that they result from combining successively established nested codes such that the older an information, the more numerous component codes protect it. Barbieri’s concept of organic code and that of genomic error-correcting code may seem unrelated. We show however that organic codes actually entail error-correcting properties. Error-correcting, in general, results from constraints being imposed on a set of sequences. Mathematical equalities are conveniently used in communication engineering for expressing constraints but error correction only needs that constraints exist. Biological sequences are similarly endowed with error-correcting ability by physical-chemical or linguistic constraints, thus defining ‘soft codes’. These constraints are moreover presumably efficient for correcting errors. Insofar as biological sequences are subjected to constraints, organic codes necessarily involve soft codes, and their successive onset results in the nested structure we hypothesized. Organic codes are generated and maintained by means of molecular ‘semantic feedback loops’. Each of these loops involves genes which code for proteins, the enzymatic action of which controls a function needed for the protein assembly. Taken together, thus, they control the assembly of their own structure as instructed by the genome and, once closed, these loops ensure their own conservation. However, the semantic feedback loops do not prevent the genome lengthening. It increases both the redundancy of the genome (as an error-correcting code) and the information quantity it bears, thus improving the genome reliability and the specificity of the enzymes, which enables further evolution.

Performance and error analysis of Knill's postselection scheme in a two-dimensional architecture

Knill demonstrated a fault-tolerant quantum computation scheme based on concatenated error-detecting codes and postselection with a simulated error threshold of $3\%$ over the depolarizing channel. We show how to use Knill's postselection scheme in a practical two-dimensional quantum architecture that we designed with the goal to optimize the error correction properties, while satisfying important architectural constraints. In our 2D architecture, one logical qubit is embedded in a tile consisting of $5\times 5$ physical qubits. The movement of these qubits is modeled as noisy SWAP gates and the only physical operations that are allowed are local one- and two-qubit gates. We evaluate the practical properties of our design, such as its error threshold, and compare it to the concatenated Bacon-Shor code and the concatenated Steane code. Assuming that all gates have the same error rates, we obtain a threshold of $3.06\times 10^{-4}$ in a local adversarial stochastic noise model, which is the highest known error threshold for concatenated codes in 2D. We also present a Monte Carlo simulation of the 2D architecture with depolarizing noise and we calculate a pseudo-threshold of about $0.1\%$. With memory error rates one-tenth of the worst gate error rates, the threshold for the adversarial noise model, and the pseudo-threshold over depolarizing noise, are $4.06\times 10^{-4}$ and $0.2\%$, respectively. In a hypothetical technology where memory error rates are negligible, these thresholds can be further increased by shrinking the tiles into a $4\times 4$ layout.

DNA Codeword Design: Theory and Applications

This is a survey of the origin, current progress and applications of a major roadblock to the development of analytic models for DNA computing (a massively parallel programming methodology) and DNA self-assembly (a nanofabrication methodology), namely the so-called CODEWORD DESIGN problem. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves or to their complements and has been recognized as an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses because of their error correction and prevention properties. Major recent advances include the development of experimental techniques to search for such codes, as well as a theoretical framework to analyze this problem, despite the fact that it has been proven to be NP-complete using any single concrete metric space to model the Gibbs energy. In this framework, codeword design is reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the key to finding such sets would lie in knowledge of the geometry of these spaces. A new general technique has been recently found to embed them in Euclidean spaces in a hybridization-affinity-preserving manner, i.e., in such a way that oligos with high/low hybridization affinity are mapped to neighboring/remote points in a geometric lattice, respectively. This isometric embedding materializes long-held metaphors about codeword design in terms of sphere packing and error-correcting codes and leads to designs that are in some cases known to be provably nearly optimal for some oligo sizes. It also leads to upper and lower bounds on estimates of the size of optimal codes of size up to 32–mers, as well as to infinite families of solutions to CODEWORD DESIGN, based on estimates of the kissing (or contact) number for sphere packings in Euclidean spaces. Conversely, this reduction suggests interesting new algorithms to find dense sphere packing solutions in high dimensional spheres using results for CODEWORD DESIGN previously obtained by experimental or theoretical molecular means, as well as a proof that finding these bounds exactly is NP-complete in general. Finally, some research problems and applications arising from these results are described that might be of interest for further research.

Speed, Noise Immunity, Power Consumption and Area Comparison between Different Approaches of Low-Power Viterbi Decoder for Digital Wireless Communication Applications

Noise immunity and speed are two vital issues for designing encoding-decoding system for wireless communication. Convolutional coding is widely used in wireless communication system for its error correction property. For the decoding purpose of Convolutional coding Viterbi decoder is used. Core module of Viterbi decoder is Adder-Comparator-Selector (ACS) which takes approximately 70% of total power consumption. So, Adder-Comparator-Selector (ACS) module is transformed into Comparator-Selector-Adder CSA) module for power saving. Reduction of Hamming Distance Logic Circuitry for branch metric calculation also saving power but enhances the packing density of the circuit. In this paper the comparison between ACS and CSA is not only described in terms of power reduction and area but also speed and noise immunity are compared. Basically there are three types of Viterbi decoders: namely Register Exchange, Shift Update and Selective Update. These decoders do not follows the parallelism and pipelining concept but folding cascaded designing of Viterbi Decoder supports parallelism which enhance the speed of the system. This paper gives a new idea of logic reduction of Viterbi Decoder as well as comparison of different Viterbi decoders in different aspects.

Robust Prefix Encoding Using Lower (2,3) Number Representation

Binary error-correction encoding using the two-base numeration system with the radices 2 and 3 is proposed. Properties and error-correcting capabilities of such codes for one and two errors are analyzed. A special kind of the (2, 3) code, namely, the lower (2, 3) code is introduced to provide error-correcting properties.

Detecting Hardware Trojan through Time Domain Constrained Estimator Based Unified Subspace Technique

SUMMARY Hardware Trojan (HT) has emerged as an impending security threat to hardware systems. However, conventional functional tests fail to detect HT since Trojans are triggered by rare events. Most of the existing side-channel based HT detection techniques just simply compare and analyze circuit’s parameters and offer no signal calibration or error correction properties, so they suffer from the challenge and interference of large process variations (PV) and noises in modern nanotechnology which can completely mask Trojan’s contribution to the circuit. This paper presents a novel HT detection method based on subspace technique which can detect tiny HT characteristics under large PV and noises. First, we formulate the HT detection problem as a weak signal detection problem, and then we model it as a feature extraction model. After that, we propose a novel subspace HT detection technique based on time domain constrained estimator. It is proved that we can distinguish the weak HT from variations and noises through particular subspace projections and reconstructed clean signal analysis. The reconstructed clean signal of the proposed algorithm can also be used for accurate parameter estimation of circuits, e.g. power estimation. The proposed technique is a general method for related HT detection schemes to eliminate noises and PV. Both simulations on benchmarks and hardware implementation validations on FPGA boards show the effectiveness and high sensitivity of the new HT detection technique.

Short Barcodes for Next Generation Sequencing

We consider the design and evaluation of short barcodes, with a length between six and eight nucleotides, used for parallel sequencing on platforms where substitution errors dominate. Such codes should have not only good error correction properties but also the code words should fulfil certain biological constraints (experimental parameters). We compare published barcodes with codes obtained by two new constructions methods, one based on the currently best known linear codes and a simple randomized construction method. The evaluation done is with respect to the error correction capabilities, barcode size and their experimental parameters and fundamental bounds on the code size and their distance properties. We provide a list of codes for lengths between six and eight nucleotides, where for length eight, two substitution errors can be corrected. In fact, no code with larger minimum distance can exist.

Neural Network Based Real-time Correction of Transducer Dynamic Errors

Abstract In order to carry out real-time dynamic error correction of transducers described by a linear differential equation, a novel recurrent neural network was developed. The network structure is based on solving this equation with respect to the input quantity when using the state variables. It is shown that such a real-time correction can be carried out using simple linear perceptrons. Due to the use of a neural technique, knowledge of the dynamic parameters of the transducer is not necessary. Theoretical considerations are illustrated by the results of simulation studies performed for the modeled second order transducer. The most important properties of the neural dynamic error correction, when emphasizing the fundamental advantages and disadvantages, are discussed.

Formation and Regulation of Dynamic Patterns in Two-Dimensional Spiking Neural Circuits with Spike-Timing-Dependent Plasticity

Spike-timing-dependent plasticity (STDP) is an important synaptic dynamics that is capable of shaping the complex spatiotemporal activity of neural circuits. In this study, we examine the effects of STDP on the spatiotemporal patterns of a spatially extended, two-dimensional spiking neural circuit. We show that STDP can promote the formation of multiple, localized spiking wave patterns or multiple spike timing sequences in a broad parameter space of the neural circuit. Furthermore, we illustrate that the formation of these dynamic patterns is due to the interaction between the dynamics of ongoing patterns in the neural circuit and STDP. This interaction is analyzed by developing a simple model able to capture its essential dynamics, which give rise to symmetry breaking. This occurs in a fundamentally self-organizing manner, without fine-tuning of the system parameters. Moreover, we find that STDP provides a synaptic mechanism to learn the paths taken by spiking waves and modulate the dynamics of their interactions, enabling them to be regulated. This regulation mechanism has error-correcting properties. Our results therefore highlight the important roles played by STDP in facilitating the formation and regulation of spiking wave patterns that may have crucial functional roles in brain information processing.

Oil price shocks and producer prices in Taiwan: an application of non-linear error-correction models

This study estimated the short-term and long-term pass-through effects of oil prices on inflation in Taiwan from 1981M1-2011M5, employing the producer price general index and various basic sub-indices for evaluation. The empirical results show that oil prices have long-term and short-term pass-through effects on Taiwan’s producer price indices. Moreover, producer prices have significant non-linear error-correction relationships with the oil price, output and wages, suggesting asymmetric and time-variant properties of error correction. When the deviation of price in the equilibrium is greater, the error-correction adjustment will be faster. Our findings could therefore enable the monetary authorities and manufacturers to formulate a more effective policy from the oil price shocks.

Generalized DNA barcode design based on Hamming codes.

The diversity and scope of multiplex parallel sequencing applications is steadily increasing. Critically, multiplex parallel sequencing applications methods rely on the use of barcoded primers for sample identification, and the quality of the barcodes directly impacts the quality of the resulting sequence data. Inspection of the recent publications reveals a surprisingly variable quality of the barcodes employed. Some barcodes are made in a semi empirical fashion, without quantitative consideration of error correction or minimal distance properties. After systematic comparison of published barcode sets, including commercially distributed barcoded primers from Illumina and Epicentre, methods for improved, Hamming code-based sequences are suggested and illustrated. Hamming barcodes can be employed for DNA tag designs in many different ways while preserving minimal distance and error-correcting properties. In addition, Hamming barcodes remain flexible with regard to essential biological parameters such as sequence redundancy and GC content. Wider adoption of improved Hamming barcodes is encouraged in multiplex parallel sequencing applications.

Geometric Approaches to Gibbs Energy Landscapes and DNA Oligonucleotide Design

DNA codeword design has been a fundamental problem since the early days of DNA computing. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves, to each other or to others' complements. Such strands represent so-called domains, particularly in the language of chemical reaction networks (CRNs). The problem has shown to be of interest in other areas as well, including DNA memories and phylogenetic analyses because of their error correction and prevention properties. In prior work, a theoretical framework to analyze this problem has been developed and natural and simple versions of Codeword Design have been shown to be NP-complete using any single reasonable metric that approximates the Gibbs energy, thus practically making it very difficult to find any general procedure for finding such maximal sets exactly and efficiently. In this framework, codeword design is partially reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the size of such sets depends on the geometry of these spaces. Here, the authors describe in detail a new general technique to embed them in Euclidean spaces in such a way that oligonucleotides with high (low, respectively) hybridization affinity are mapped to neighboring (remote, respectively) points in a geometric lattice. This embedding materializes long-held metaphors about codeword design in analogies with error-correcting code design in information theory in terms of sphere packing and leads to designs that are in some cases known to be provably nearly optimal for small oligonucleotide sizes, whenever the corresponding spherical codes in Euclidean spaces are known to be so. It also leads to upper and lower bounds on estimates of the size of optimal codes of size under 20-mers, as well as to a few infinite families of DNA strand lengths, based on estimates of the kissing (or contact) number for sphere codes in high-dimensional Euclidean spaces. Conversely, the authors show how solutions to DNA codeword design obtained by experimental or other means can also provide solutions to difficult spherical packing geometric problems via these approaches. Finally, the reduction suggests a tool to provide some insight into the approximate structure of the Gibbs energy landscapes, which play a primary role in the design and implementation of biomolecular programs.

Short-Term Effects of Muscular Denervation and Fasciotomy on Global Limb Variables during Locomotion in the Decerebrate Cat

The motor system is capable of preserving the trajectories during locomotion of task level variables such as limb length and limb orientation in the face of paralysis of major muscle groups. This compensation is accomplished by the adjustment of the kinematics of joints other than the one most affected by the paralysis. The conservation of these task level variables could be accomplished quickly by feedback regulation or intrinsic mechanics, or by a longer-term adaptive process. We investigated the immediate effects of denervation of the triceps surae muscles in one limb of stepping, decerebrate cats to determine whether task level variables were preserved by short-term regulatory or intrinsic mechanisms. We further investigated the effects of disruption of the crural fascia in conjunction with denervation of the triceps surae muscles to determine whether the system consisting of multi-articular muscles of the thigh and crural fascia provided some contribution toward the preservation of limb length and orientation. Denervation led to substantial increases in ankle yield during stance, as previously observed, but also to significant decreases in limb length during early stance. Disruption of the crural fascia did not lead to increased ankle yield but, instead, to evidence for decreased propulsion. The results suggest that the preservation of task level variables observed in other studies does not result from online error correction or intrinsic properties of the musculoskeletal system but, by inference, from longer-term neural adaptation.

Error decodable secret sharing and one-round perfectly secure message transmission for general adversary structures

An error decodable secret-sharing scheme is a secret-sharing scheme with the additional property that the secret can be recovered from the set of all shares, even after a coalition of participants corrupts the shares they possess. In this paper, schemes that can tolerate corruption by sets of participants belonging to a monotone coalition structure are considered. This coalition structure may be unrelated to the authorised sets of the secret-sharing scheme. This is generalisation of both a related notion studied in the context of multiparty computation, and the well-known error-correction properties of threshold schemes based on Reed-Solomon codes. Necessary and sufficient conditions for the existence of such schemes are deduced, and methods for reducing the storage requirements of a technique of Kurosawa for constructing error-decodable secret-sharing schemes with efficient decoding algorithms are demonstrated. In addition, the connection between one-round perfectly secure message transmission (PSMT) schemes with general adversary structures and secret-sharing schemes is explored. We prove a theorem that explicitly shows the relation between these structures. In particular, an error decodable secret-sharing scheme yields a one-round PSMT, but the converse does not hold. Furthermore, we are able to show that some well-known results concerning one-round PSMT follow from known results on secret-sharing schemes. These connections are exploited to investigate factors affecting the performance of one-round PSMT schemes such as the number of channels required, the communication overhead, and the efficiency of message recovery.

Author Disambiguation using an Hybrid Approach of Queries and String Matching Techniques

Common problems when searching for publications by author names are misspellings, name abbreviations, and format differences. This paper attempted to solve this problem by combining database SQL queries with the error detection and correction properties of string comparisons. The use of these combination of methods increased the amount of relevant records retrieved while reducing the number of irrelevant records compared to other well know string matching techniques.

Quantum convolutional coding with shared entanglement: general structure

We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the Calderbank–Shor–Steane structure as in previous work. We provide two significant advances for quantum convolutional coding theory. We first show how to “expand” a given set of quantum convolutional generators. This expansion step acts as a preprocessor for a polynomial symplectic Gram–Schmidt orthogonalization procedure that simplifies the commutation relations of the expanded generators to be the same as those of entangled Bell states (ebits) and ancilla qubits. The above two steps produce a set of generators with equivalent error-correcting properties to those of the original generators. We then demonstrate how to perform online encoding and decoding for a stream of information qubits, halves of ebits, and ancilla qubits. The upshot of our theory is that the quantum code designer can engineer quantum convolutional codes with desirable error-correcting properties without having to worry about the commutation relations of these generators.

Secure Key Generation in Sensor Networks Based on Frequency-Selective Channels

Key management in wireless sensor networks faces several new challenges. The scale, resource limitations, and new threats such as node capture necessitate the use of an on-line key generation by the nodes themselves. However, the cost of such schemes is high since their secrecy is based on computational complexity. Recently, several research contributions justified that the wireless channel itself can be used to generate information-theoretic secure keys. By exchanging sampling messages during movement, a bit string can be derived that is only known to the involved entities. Yet, movement is not the only possibility to generate randomness. The channel response is also strongly dependent on the frequency of the transmitted signal. In our work, we introduce a protocol for key generation based on the frequency-selectivity of channel fading. The practical advantage of this approach is that we do not require node movement. Thus, the frequent case of a sensor network with static motes is supported. Furthermore, the error correction property of the protocol mitigates the effects of measurement errors and other temporal effects, giving rise to an agreement rate of over 97%. We show the applicability of our protocol by implementing it on MICAz motes, and evaluate its robustness and secrecy through experiments and analysis.

Entanglement-assisted quantum convolutional coding

We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary classical binary convolutional codes. The rate and error-correcting properties of the classical convolutional codes directly determine the corresponding properties of the resulting entanglement-assisted quantum convolutional code. We explain how to encode our CSS entanglement-assisted quantum convolutional codes starting from a stream of information qubits, ancilla qubits, and shared entangled bits.

Extra shared entanglement reduces memory demand in quantum convolutional coding

We show how extra entanglement shared between sender and receiver reduces the memory requirements for a general entanglement-assisted quantum convolutional code. We construct quantum convolutional codes with good error-correcting properties by exploiting the error-correcting properties of an arbitrary basic set of Pauli generators. The main benefit of this particular construction is that there is no need to increase the frame size of the code when extra shared entanglement is available. Then there is no need to increase the memory requirements or circuit complexity of the code because the frame size of the code is directly related to these two code properties. Another benefit, similar to results of previous work in entanglement-assisted convolutional coding, is that we can import an arbitrary classical quaternary code for use as an entanglement-assisted quantum convolutional code. The rate and error-correcting properties of the imported classical code translate to the quantum code. We provide an example that illustrates how to import a classical quaternary code for use as an entanglement-assisted quantum convolutional code. We finally show how to ``piggyback'' classical information to make use of the extra shared entanglement in the code.

Enabling Cognitive Load‐Aware AR with Rateless Coding on a Wearable Network

Augmented reality (AR) on a head‐mounted display is conveniently supported by a wearable wireless network. If, in addition, the AR display is moderated to take account of the cognitive load of the wearer, then additional biosensors form part of the network. In this paper, the impact of these additional traffic sources is assessed. Rateless coding is proposed to not only protect the fragile encoded video stream from wireless noise and interference but also to reduce coding overhead. The paper proposes a block‐based form of rateless channel coding in which the unit of coding is a block within a packet. The contribution of this paper is that it minimizes energy consumption by reducing the overhead from forward error correction (FEC), while error correction properties are conserved. Compared to simple packet‐based rateless coding, with this form of block‐based coding, data loss is reduced and energy efficiency is improved. Cross‐layer organization of piggy‐backed response blocks must take place in response to feedback, as detailed in the paper. Compared also to variants of its default FEC scheme, results from a Bluetooth (IEEE 802.15.1) wireless network show a consistent improvement in energy consumption, packet arrival latency, and video quality at the AR display.