Generalized Viterbi Algorithm Research Articles

Hierarchical Fuzzy Hidden Markov Chain for Web Applications

Fuzzy sets, a scheme for handling nonstatistical vague concepts, provide a natural basis for the theory of possibility space. In this paper, on possibility space, a hierarchical generalization of the fuzzy hidden Markov chain (HFHMC) which is named as FHMC is proposed. For the proposed model, three problems which naturally arise in any kind of hidden Markov models (HMMs) are discussed. To solve these problems, generalized Baum–Welch and generalized Viterbi algorithms are formulated; further it is observed that the generalized Viterbi algorithm itself solves the first two problems namely the likelihood of a given observation sequence and finding the most likelihood state sequence, which exhibits that the time complexity involved in the computation of two problems reduces to a single problem. In order to ensure the ease of models use, the proposed model is applied to our institution website and simulation is performed to analyze the accessibility of the website among the users.

Marginalized Viterbi algorithm for hierarchical hidden Markov models

The generalized Viterbi algorithm, a direct extension of the Viterbi algorithm for hidden Markov models (HMMs), has been used to find the most likely state sequence for hierarchical HMMs. However, the generalized Viterbi algorithm finds the most likely whole level state sequence rather than the most likely upper level state sequence. In this paper, we propose a marginalized Viterbi algorithm, which finds the most likely upper level state sequence by marginalizing lower level state sequences. We show experimentally that the marginalized Viterbi algorithm is more accurate than the generalized Viterbi algorithm in terms of upper level state sequence estimation.

Ordered Statistics Decoding of Linear Block Codes Over Intersymbol Interference Channels

In this paper, we utilize ordered statistics decoding (OSD) techniques for intersymbol interference (ISI) channels. To achieve good efficiency and storage complexity, a combination of a modified generalized Viterbi algorithm (GVA) and Battail's algorithm is proposed to implement OSD for ISI channels. Simulation results showed significant performance improvement for the [128,64,22] eBCH code, and the [255,239,17] Reed-Solomon (RS) binary image, on the (1+D) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> perpendicular recording channel.

HMM-Kalign: a tool for generating sub-optimal HMM alignments

Recent development of strategies using multiple sequence alignments (MSA) or profiles to detect remote homologies between proteins has led to a significant increase in the number of proteins whose structures can be generated by comparative modeling methods. However, prediction of the optimal alignment between these highly divergent homologous proteins remains a difficult issue. We present a tool based on a generalized Viterbi algorithm that generates optimal and sub-optimal alignments between a sequence and a Hidden Markov Model. The tool is implemented as a new function within the HMMER package called hmmkalign.

Exploring the state sequence space for hidden Markov and semi-Markov chains

The knowledge of the state sequences that explain a given observed sequence for a known hidden Markovian model is the basis of various methods that may be divided into three categories: (i) enumeration of state sequences; (ii) summary of the possible state sequences in state profiles; (iii) computation of a global measure of the state sequence uncertainty. Concerning the first category, the generalized Viterbi algorithm for computing the top L most probable state sequences and the forward-backward algorithm for sampling state sequences are derived for hidden semi-Markov chains and hidden hybrid models combining Markovian and semi-Markovian states. Concerning the second category, a new type of state (and state change) profiles is proposed. The Viterbi forward–backward algorithm for computing these state profiles is derived for hidden semi-Markov chains and hidden hybrid models combining Markovian and semi-Markovian states. Concerning the third category, an algorithm for computing the entropy of the state sequence that explains an observed sequence is proposed. The complementarity and properties of these methods for exploring the state sequence space (including the classical state profiles computed by the forward–backward algorithm) are investigated and illustrated with examples.

Traitement itératif conjoint pour les systèmes mobiles sans fil

The classical receiver performs separately three tasks, namely, channel estimation,equalization and decoding. The optimal receiver however would treat them jointly but is often non-tractable due to its tremendous complexity. Throughout this thesis, we identified contexts where this sub-optimality could entail substantial performance loss with the help of the Matched Filter Bound (mfb). Three main contexts were pointed out: wireless LAN with very high data rate and granularity constraints, high data rate cdma with low spreading factor and advanced tdma systems with high order modulation and/or Multiple Input Multiple Output channel. Once these contexts identified, we then tried to alleviate this impairment by suggesting low complexity sub-optimal receivers that perform iteratively/jointly channel estimation,equalization, and decoding (retransmission is seen as a special case of channel coding). In order to tackle the complexity issue while keeping the Maximum A Posteriori criterion, efficient reduced state trellis search techniques mainly based on Per Survivor Processing (psp) are exhaustively described and put into practice for the aforementioned contexts. A generalization of the well known psp technique consisting quite simply in keeping more than one survivor per state was proved to be very robust to error propagation even in the case of non minimum phase channels. This generalization was first introduced for the Generalized Viterbi Algorithm (gva) and the technique itself is refereed as Generalized Per Survivor Processing (gpsp) in this thesis.

Adaptive equalization and interference cancellation for wireless communication systems

An adaptive equalization and interference cancellation method is proposed. The proposed scheme can cancel both intersymbol interference and cochannel interference, and is blind in the sense that no knowledge of the training sequences of the interfering users is required. In particular, it is a maximum likelihood sequence estimation (MLSE) equalizer that is implemented by the generalized Viterbi algorithm (GVA) with an RLS-based channel estimator. To demonstrate the potential of the proposed method, various simulation results over a frequency selective Rayleigh fading environment in the presence of cochannel interference are presented. In addition, a sequential algorithm is introduced to reduce the computational complexity of GVA.

Study of an extended partial-response, class IV, channel for digital magnetic recording

In this work, we study an EPR-IV system for high density digital recording and compare it to the PRML recording system. A combinatorial optimization technique that uses the simulated annealing algorithm in conjunction with a descent method is employed for optimization of partial response (PR) equalizers. The gradient algorithm to track variations of timing phase for the EPR-IV channel is investigated. Also, a generalized Viterbi algorithm is used for detecting the EPR-IV system. Simulation results demonstrate that at high recording density, a coding gain over the PRML system can be obtained for the EPR-IV system with a comparable complexity.

A generalized Viterbi algorithm for detection of partial response recording systems

In this work, we study a receiver for a high density recording system and compare it with the PRML recording system. In the receiver, the playback signal of a high density recording system is equalized to a higher-order partial response (PR) target. Also, a reduced-state Viterbi algorithm, called the generalized Viterbi algorithm (GVA), is used for detecting the PR system. In the GVA, the states are grouped into L subsets or lists and the best S paths in each list are selected for extension. Simulation results demonstrate that coding gain over the PRML system can be obtained even for the receiver with less complexity than that of the PRML system.

Codes and iterative decoding on general graphs

AbstractA general framework, based on ideas of Tanner, for the description of codes and iterative decoding (“turbo coding”) is developed. Just like trellis‐based code descriptions are naturally matched to Viterbi decoding, code descriptions based on Tanner graphs (which may be viewed as generalized trellises) are naturally matched to iterative decoding. Two basic iterative decoding algorithms (which are versions of the algorithms of Berrou et al. and of Hagenauer, respectively) are shown to be natural generalizations of the forward‐backward algorithm (Bahl et al.) and the Viterbi algorithm, respectively, to arbitrary Tanner graphs. The careful derivation of these algorithms clarifies, in particular, which a priori probabilities are admissible and how they are properly dealt with. For cycle codes (a class of binary linear block codes), a complete characterization is given of the error patterns that are corrected by the generalized Viterbi algorithm after infinitely many iterations.

A coded ARQ scheme with the generalized Viterbi algorithm

A coded automatic repeat request (ARQ) scheme based on a generalized Viterbi decoding algorithm is proposed. The scheme utilizes the error propagation, which is commonly observed in reduced-complexity decoding, as a means of error detection. It is shown that a small undetectable error probability is obtained with a small retransmission probability for a discrete memoryless channel, contrary to the conventional convolutionally coded ARQ schemes with Viterbi decoding where a compromise between the retransmission probability and the undetectable error probability must be reached. >

A list-type reduced-constraint generalization of the Viterbi algorithm

The Viterbi algorithm (VA), an optimum decoding rule for a Q -ary trellis code of constraint length K , operates by taking the best survivor from each of Q^{K-1} lists of candidates at each decoding step. A generalized VA (GVA) is proposed that makes comparisons on the basis of a label of length L(L\leq K) . It selects, incorporating the notion of list decoding, the S best survivors from each of Q^{L-1} lists of candidates at each decoding step. Coding theorems for a discrete memoryless channel are proved for GVA decoding and shown to be natural generalizations of those for VA decoding. An example of intersymbol interference removal is given to illustrate the practical benefits that the GVA can provide.