Explore chapters and articles related to this topic
An Introduction to Error-Correcting Codes
Published in Erozan M. Kurtas, Bane Vasic, Advanced Error Control Techniques for Data Storage Systems, 2018
Pn(D) channel as a finite state machine, as is usually done for convolutional encoders. Assuming binary channel inputs, the trellis associated with the channel has 2n+1 states. This channel trellis is then combined with the trellis describing the convolutional code, resulting in a trellis for the overall system that describes all possible coded sequences. Decoding is provided by the Viterbi algorithm operating on this trellis. The properties of this trellis are discussed in detail in this chapter. The combination of a precoder and a convolutional encoder drawn from a restricted set of generator matrices plays a key role in reducing the number of required decoder states. Other issues taken into consideration are the limitation of the length of equal symbol runs, which is addressed through the use of cosets of convolutional codes, and a code search for good codes based upon the (squared Euclidean) distance spectrum criterion.
Introduction
Published in Le Nguyen Binh, Advanced Digital, 2017
Chapter 12 introduces the processes in the electronic domain that equalize the transmitted pulse sequence degraded by impairments of the transmission media, the quadratic phase optical fibers. Both linear and nonlinear equalization processes are described. Noise contributions in the equalization processes are stated and derived for the BER. Transmission examples are given for duobinary modulation and MSE with Viterbi trellis tracing. The chapter briefly reviews the principles of the MLSE equalization technique, Viterbi algorithm, and state trellis structure. Detailed explanations of state-based Viterbi-MLSE equalizers for optical communications are given. The chapter then investigates the performance of MLSE equalizers for 40 Gbps OFDR-based optical MSK systems. In this receiver scheme, OFDR serves as the optical front end and is integrated with a postdetection MLSE equalizer. The CD tolerance performance of both Viterbi–MLSE and template-matching MLSE equalizers is studied. The performance limit of Viterbi–MLSE equalizers with 24–210 states is then investigated based on maximum uncompensated transmission distances. The performance of 16-state Viterbi–MLSE equalizers for PMD equalization is also investigated. This number of states reflects the feasibility of high-speed electronic signal processing in the near future. The significance of multisample sampling schemes (two and four samples per one-bit period) over the conventional single-sample sampling technique is also highlighted in this chapter [62,63].
Advanced Coding for Fiber-Optics Communications Systems
Published in Andrew Ellis, Mariia Sorokina, Optical Communication Systems, 2019
Each component code can be represented using the trellis diagram description of the code. By taking the Cartesian product of individual trellises and then perform mapping based on set partitioning we obtain a trellis description of this MCM scheme. Now we can apply either Viterbi algorithm or BCJR algorithm to perform decoding on such a trellis. Unfortunately, the complexity of such decoding is too high to be of practical importance. Instead, the decoding is typically based on so-called multistage decoding (MSD) algorithm [64] in which the decisions from prior (lower) decoding stage are passed to next (higher) stages, which is illustrated in Fig. 6.17.
Review of Feature Extraction Techniques for Character Recognition
Published in IETE Journal of Research, 2018
Narasimha Reddy Soora, Parag S. Deshpande
Pati and Ramakrishnan in the paper [72] categorized methodologies of Indian OCRs existing in the literature. In this paper, Indian OCR feature extraction methods were categorized into correlation-based features, transform-based features, statistical features, and geometric features. Rammohan and Chatterji in the paper [73] proposed an OCR system to recognize distorted Kannada characters using modified trellis diagram, Hamming distance, and Viterbi algorithm. The proposed procedure eliminates pattern classes using fractional pattern of the input sequences which are irrelevant to the input data which results in few input patterns to be classified. The proposed procedure was tested using 500 hand-printed Kannada characters and reported a success rate of 85% using Viterbi algorithm and 65% by Hamming distance. Chaudhuri et al. [74] proposed a directed curve tracing method coupled with T-tuple for shape matching to recognize the Telugu script characters and this paper have not reported any recognition accuracy. Srikantan et al. in the paper [75] proposed a feature extraction method to extract low-level, structural and stroke-type features such as object contour and structure encoded from a gradient representation of the input character and reported 99.4% success rate for machine printed images.
Refinement of HMM Model Parameters for Punjabi Automatic Speech Recognition (PASR) System
Published in IETE Journal of Research, 2018
Virender Kadyan, Archana Mantri, R. K. Aggarwal
The pattern matching of the input signal is performed by acquiring the knowledge of the trained HMM model and language model. A set of untrained phones of HMM requires pronunciation lexicon and a well-defined phone set. Now, with the help of such mentioned files, system is ready to train the transition matrix A (with aij entries) and output likelihood estimator B (with bj(ot) entries) for the HMMs. The Viterbi algorithm is used to determine the most suitable sequence of hidden states of an HMM model that contains hidden variables using the following equation:where i = 1, 2, 3,…, n. The algorithm initializes the probability using Equation (22) by taking the product of initial hidden state probabilities with the associated observation probabilities using Equation (23). It is used to find the most probable way for the next state. This can be achieved by the product of maximal probabilities derived in Equation (24) from the earlier step with transition probabilities [14]. To follow the most probable route, backtracking Equation (25) has been used. The sequence i1…iT will hold the most probable sequence of hidden states for the analysis of sequence. The Viterbi algorithm gets its efficiency via concentrating on survival paths of the trellis. It can be achieved by passing parameters value to the Viterbi function in pattern matching process as follows:where SEQ = sequence, A = calculates the most likely path through the HMM specified by transition probability matrix, and B = emission probability matrix.
Implementation of Novel Block and Convolutional Encoding Circuit Using FS-GDI
Published in IETE Journal of Research, 2023
Mohsen A. M. El-Bendary, O. Al-Badry, A. E. Abou-El. Azm
Viterbi algorithm uses a trellis diagram for decoding the encoded words of the convolutional codes, and its operation is described as shown in Figure 3. This figure gives the state transition of ( = 2) encoder, and it is considered trellis diagram unit. Trellis diagram is used in executing the Viterbi algorithm for decoding the encoded data of the convolutional codes as shown in Figure 3; it uses Hamming distance to compare different paths in the diagram and accumulate error metrics at every state and select the lower error path through the tracing back process.