Large Number Of Codewords Research Articles

Fast high-precision 3D shape measurement using linear phase encoding with geometry constraints

A three-dimensional (3D) profile measurement method based on geometric constraints combined with linear phase encoding (GCPE) is proposed. This method encodes the wrapped phase and the linear signal in the same phase domain, achieves the elimination of the phase ambiguity within the local fringe period, and obtains an unambiguous absolute phase within the entire period through geometric constraints. Compared with the traditional phase encoding method, this method solves the problem of period sequence errors caused by a large number of codewords by encoding linear signals in the phase domain and using a period order correction method to deal with the period jump phenomenon caused by noise. At the same time, the measurement range of the fringe projection system under geometric constraints is significantly improved. Experimentally, 3D profiles of standard planes, complex statues, and separated objects were measured by the use of the GCPE. The results show that the GCPE has the advantage of fast speed and high accuracy in measuring the 3D profile of objects.

Absolute phase measurement method based onbidirectional coding patterns.

The stair-phase-coding patterns have been widely used to determine the fringe order for phase unwrapping of the wrapped phase in three-dimensional shape measurement. Although the special coding sequence algorithm can achieve with a large number of codewords, it needs the current codeword and its adjacent codewords to jointly determine the fringe order. If any codeword of the grouped adjacent codewords is incorrectly recognized, it will result in many false fringe orders. It increases the probability of fringe order error in the decoding process. And it is challenging to significantly increase the number of codewords. To solve this problem, we propose an absolute phase measurement method based on bidirectional coding patterns. The wrapped phase of the object is obtained by four-step phase-shifting patterns, and the fringe order is obtained by bidirectional coding patterns. When generating the bidirectional coding patterns, we code two groups of stair phase with different frequencies along the horizontal direction, which respectively represent local fringe order and partition information. Then, we alternately repeat the two groups of stair phase along the vertical direction in the whole pattern to obtain the bidirectional coding patterns. Each local fringe order information and the corresponding partition information in a small region jointly determine the fringe order of pixels in this small region. Fringe order errors in a small region do not affect other regions. To verify the effectiveness of our method, we performed simulations and experiments. Simulation and experimental results show that our method is effective for objects with different sizes and isolated objects.

Absolute phase measurement with four patterns based on variant shifting phases.

Fringe projection profilometry has been proverbially utilized for measuring the shapes of objects. A common challenge in those systems is to accurately obtain a smooth absolute phase. Many new methods have been proposed to address this challenge. In this paper, we discuss a technique based on variant shifting phases. This approach embeds codewords into the shifting phase and only needs four patterns. However, reliable measurement results are difficult to achieve with a large number of codewords because of the phase errors. To address this shortcoming, we present a robust coding method that embeds a specific code sequence into the shifting phase and can generate more than 36 periods. The fringe order is determined using unique three-adjacent-codes combining the current period and its neighbors. An error correction algorithm is also proposed to optimize the codewords. The proposed method is experimentally verified using an established measurement system. The result shows that the proposed method is robust and efficient.

Absolute phase retrieval via color phase-coding

Phase-coding method that embeds codewords into phase rather than intensity performs well for absolute phase retrieval. However, this method becomes instable when dealing with a large number of codewords. This paper designs three color phase-coding fringes to determine the fringe order pixel by pixel. Specifically, six groups of N-stairs are encoded into three coding fringes, and each group is endowed with a different color to eliminate ambiguity between groups. Such that three additional fringes can generate more than 6N codewords by combining the color and phase information. Experiment results confirmed the validity of the proposed method.

Construction of DNA codes by using algebraic number theory

The canonical structure of DNA has four bases – Thymine (T), Adenine (A), Cytosine (C), and Guanine (G) – and DNA codes are regarded as words over the alphabet set Σ={A,C,G,T}, satisfying certain combinatorial conditions. Good DNA codes are desirable for DNA computation, DNA microarray technologies and molecular barcodes, etc. One of the main tasks in DNA code designing is to build more codewords and better GC-content for given fixed word length n. Existing heuristic methods work well for small n. In this paper, we present a systematic method for constructing good DNA codes for large n by using irreducible cyclic codes. Being different from traditional DNA constructions, our method is based on algebraic number theory rather than classical heuristic algorithms and the conventional coding theory. Furthermore, comparing with the traditional DNA codes, our codes have larger number of codewords and better GC-content. As far as we know, it is the very first time to utilize irreducible cyclic codes for constructing a type of DNA codes.

Insertion and deletion correcting DNA barcodes based on watermarks.

BackgroundBarcode multiplexing is a key strategy for sharing the rising capacity of next-generation sequencing devices: Synthetic DNA tags, called barcodes, are attached to natural DNA fragments within the library preparation procedure. Different libraries, can individually be labeled with barcodes for a joint sequencing procedure. A post-processing step is needed to sort the sequencing data according to their origin, utilizing these DNA labels. The final separation step is called demultiplexing and is mainly determined by the characteristics of the DNA code words used as labels.Currently, we are facing two different strategies for barcoding: One is based on the Hamming distance, the other uses the edit metric to measure distances of code words. The theory of channel coding provides well-known code constructions for Hamming metric. They provide a large number of code words with variable lengths and maximal correction capability regarding substitution errors. However, some sequencing platforms are known to have exceptional high numbers of insertion or deletion errors. Barcodes based on the edit distance can take insertion and deletion errors into account in the decoding process. Unfortunately, there is no explicit code-construction known that gives optimal codes for edit metric.ResultsIn the present work we focus on an entirely different perspective to obtain DNA barcodes. We consider a concatenated code construction, producing so-called watermark codes, which were first proposed by Davey and Mackay, to communicate via binary channels with synchronization errors. We adapt and extend the concepts of watermark codes to use them for DNA sequencing. Moreover, we provide an exemplary set of barcodes that are experimentally compatible with common next-generation sequencing platforms. Finally, a realistic simulation scenario is use to evaluate the proposed codes to show that the watermark concept is suitable for DNA sequencing applications.ConclusionOur adaption of watermark codes enables the construction of barcodes that are capable of correcting substitutions, insertion and deletion errors. The presented approach has the advantage of not needing any markers or technical sequences to recover the position of the barcode in the sequencing reads, which poses a significant restriction with other approaches.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0482-7) contains supplementary material, which is available to authorized users.

Phase coding method for absolute phase retrieval with a large number of codewords

A recently proposed phase coding method for absolute phase retrieval performs well because its codeword is embedded into phase domain rather than intensity. Then, the codeword can determine the fringe order for the phase unwrapping. However, for absolute phase retrieval with a large number of codewords, the traditional phase coding method becomes not so reliable. In this paper, we present a novel phase coding method to tackle this problem. Six additional fringe images can generate more than 64(2(6)) unique codewords for correct absolute phase retrieval. The novel phase coding method can be used for absolute phase retrieval with high frequency. Experiment results demonstrate the proposed method is effective.

M-Ary Substitution/Deletion/Insertion/Adjacent-Symbol-Transposition Error Correcting Codes for Data Entry Systems

Nonbinary M-ary data processed by data entry systems, such as keyboard devices and character recognition systems, often have various types of error, such as symbol-substitution errors, deletion errors, insertion errors, and adjacent-symbol-transposition errors. This paper proposes nonsystematic M-ary codes capable of correcting these errors. The code is defined as a set of codewords that satisfy three conditions required to correct substitution, deletion/insertion, and adjacent-symbol-transposition errors. Since symbol-substitution errors in data entry systems are usually asymmetric, this paper also presents asymmetric-symbol-substitution error correcting codes capable of correcting deletion, insertion, and adjacent-symbol-transposition errors. For asymmetric-symbol-substitution error correction, we employ a mapping derived from the vertex coloring in an error directionality graph. The evaluation shows that the asymmetric codes have three to five times larger number of codewords than the symmetric codes.

Novel accelerated simulation techniques for low bit error rate communication systems

Conventional simulation techniques are not suitable for modern low bit error rate communication systems, since significant computational power is required to achieve statistically significant results. Two novel simulation techniques are presented, which reduce the time required without affecting the performance. These are based on channel noise statistics, and generate error events without simulating a prohibitively large number of code words. This reduces the total number of code words that must be simulated, depending on the error correcting power of the code. The reduction in the simulation time required is two orders of magnitude, compared with conventional simulation techniques.

Codeword distribution for frequency sensitive competitive learning with one-dimensional input data

We study the codeword distribution for a conscience-type competitive learning algorithm, frequency sensitive competitive learning (FSCL), using one-dimensional input data. We prove that the asymptotic codeword density in the limit of large number of codewords is given by a power law of the form Q(x)=C.P(x)(alpha), where P(x) is the input data density and alpha depends on the algorithm and the form of the distortion measure to be minimized. We further show that the algorithm can be adjusted to minimize any L(p) distortion measure with p ranging in (0,2].

An improvement of the minimum distortion encoding algorithm for vector quantization

In this note we present a very simple method for improving the efficiency of minimum distortion encoding for vector quantization. Simulations indicates a reduction of up to 70 percent in the number of multiplications for a full search vector quantizer with a large number of codewords, and about 25-40 percent for a tree search vector quantizer. Similar improvement can be achieved in other vector quantization systems.