Viterbi-like Algorithm Research Articles

Molecular Type Permutation Shift Keying for Molecular Communication

Molecular communication (MC) via diffusion is envisioned to be a new paradigm for information exchange in the future nanonetworks. However, the strong inter-symbol interference (ISI) caused by the diffusion channel significantly deteriorates the performance of MC systems. To this end, we propose a novel modulation technique to reduce the ISI effect, termed as molecular type permutation shift keying (MTPSK), which encodes information on the permutations of multiple types of molecules. We design a Genie-aided maximum-likelihood detector and a conventional maximum-likelihood detector, and analyze their performance in terms of bit error rate (BER). Aiming at lower computational complexity, we further design a low-complexity maximum-likelihood detector using a Viterbi-like algorithm with compromised error performance. BER simulation results corroborate that the proposed MTPSK can outperform the prevailing modulation schemes for MC, including molecular shift keying (MoSK), concentration shift keying, depleted MoSK, and pulse position modulation.

A Leader Improves Things: Reducing Signaling and Complexity in Optimal IoT Storage

This letter characterizes the optimal policy for minimizing the bandwidth use and the number of required connections between nodes for repairing losses in scenarios that use the Internet of Things (IoT) devices for distributed storage. In particular, we consider the problem of a system that will not receive replacement nodes to compensate for node losses and analyze the problem considering a lead node, which coordinates the repair process. We show that the optimal strategy can be computed with a low-complexity, Viterbi-like algorithm. Our numerical results show that the proposed optimal scheme not only achieves the minimum bandwidth use for the problem, but also reduces the number of IoT device-to-device connections from $O(s^{2})$ to $O(s)$ for $s$ remaining nodes, compared to using no leader for coordination.

A Low-Complexity Near-ML Differential Spatial Modulation Detector

Differential spatial modulation (DSM) is a newly-emerging differential scheme tailored to the spatial modulation technique, which selects only one among a group of antennas for transmission at any time instant. DSM, however, gives rise to prohibitive search complexity when the number of transmit antennas is large. In this letter, a low-complexity suboptimal detector is proposed for DSM. It is designed based on the maximum-likelihood criterion but takes more candidates for the antenna activation orders into account. The detection is performed in two steps: the first step is to confine the number of candidates for the modulated symbols to a small portion by exploiting the symmetry of the signal constellation; the second step is to select the most likely modulated symbols from the output of the first step according to the determined antenna activation order via a Viterbi-like algorithm. Analyses and simulations show that the proposed detector achieves near-optimal performance yet largely reduces the search complexity.

Frame Fusion for Video Copy Detection

Content-based video copy detection is very important for copyright protection in view of the growing popularity of video sharing websites, which deals with not only whether a copy occurs in a query video stream but also where the copy is located and where the copy is originated from. While a lot of work has addressed the problem with good performance, less effort has been made to consider the copy detection problem in the case of a continuous query stream, for which precise temporal localization and some complex video transformations like frame insertion and video editing need to be handled. We attempt to attack the problem by presenting a frame fusion based copy detection approach, which converts video copy detection to frame similarity search and frame fusion under a temporal consistency assumption. Our work focuses mainly on the frame fusion stage due to its critical role in copy detection performance. The proposed frame fusion scheme is based on a Viterbi-like algorithm, comprising an online back-tracking strategy with three relaxed constraints. The experimental results show that the proposed approach achieves high localization accuracy in both the query stream and the reference database even when a query video stream undergoes some complex transformations, while achieving comparable performance compared with state-of-the-art copy detection methods.

Heuristic guess-and-determine attacks on stream ciphers

Guess-and-determine (GD) attacks are general attacks on stream ciphers, which have often been implemented in an ad hoc manner. The authors introduce a heuristic approach to the design of GD attacks, that is a dynamic programming method using a Viterbi-like algorithm which is a well-known decoding algorithm for convolutional codes. The authors also show that with this method, the resulting GD attacks, named heuristic GD (HGD) attacks, on TIPSY, SNOW1 and SNOW2 lead to less computational complexity than the previously known GD attacks. The main advantage of HGD attacks, over ad hoc GD attacks, is that while being powerful, they can be designed algorithmically for classes of stream ciphers, holding a certain condition. Using this method, the authors examine the resistance of SOSEMANUK, a word-oriented stream cipher proposed for the Ecrypt Stream Cipher Project. The complexity of the designed GD attack, O(2224), is much less than the complexity of exhaustive search attack on the internal state, O(2384), but larger than the claimed security level, that is O(2128).

Memory Efficient Hierarchical Lookup Tables for Mass Arbitrary-Side Growing Huffman Trees Decoding

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper addresses the optimization problem of minimizing the number of memory access subject to a rate constraint for any Huffman decoding of various standard codecs. We propose a Lagrangian multiplier based penalty-resource metric to be the targeting cost function. To the best of our knowledge, there is few related discussion, in the literature, on providing a criterion to judge the approaches of entropy decoding under resource constraint. The existing approaches which dealt with the decoding of the single-side growing Huffman tree may not be memory-efficient for arbitrary-side growing Huffman trees adopted in current codecs. By grouping the common prefix part of a Huffman tree, in stead of the commonly used single-side growing Huffman tree, we provide a memory efficient hierarchical lookup table to speed up the Huffman decoding. Simulation results show that the proposed hierarchical table outperforms previous methods. A Viterbi-like algorithm is also proposed to efficiently find the optimal hierarchical table. More importantly, the Viterbi-like algorithm obtains the same results as that of the brute-force search algorithm. </para>

A distortion optimal rate allocation algorithm for transmission of embedded bitstreams over noisy channels

We propose a distortion optimal rate allocation algorithm for robust transmission of embedded bitstreams over noisy channels. The algorithm is based on the backward application of a Viterbi-like algorithm to a search trellis, and can be applied to both scenarios of fixed and variable channel packet length problems, referred to as FPP and VPP, respectively. For the VPP, the complexity of the algorithm is comparable to the well-known dynamic programming approach of Chande and Farvardin. For the FPP, where no low-complexity algorithm is known, the complexity of the proposed algorithm is O(N/sup 2/), where N is the number of transmitted packets.

On the complexity of joint source-channel decoding of Markov sequences over memoryless channels

We investigate the complexity of joint source- channel maximum a posteriori (MAP) decoding of a Markov sequence which is first encoded by a source code, then encoded by a convolutional code, and sent through a noisy memoryless channel. As established previously the MAP decoding can be performed by a Viterbi-like algorithm on a trellis whose states are triples of the states of the Markov source, source coder and convolutional coder. The large size of the product space (in the order of K2N, where K is the number of source symbols and N is the number of states of the convolutional coder) appears to prohibit such a scheme. We show that for finite impulse response convolutional codes, the state space size of joint source-channel decoding can be reduced to O(K2+N log N), hence the decoding time becomes O(TK2 +TN log N), where T is the length in bits of the decoded bitstream. We further prove that an additional complexity reduction can be achieved when K > N, if the logarithm of the source transition probabilities satisfy the so- called Monge property. This decrease becomes more significant as the tree structure of the source code is more unbalanced. The reduction factor ranges between O(K/N) (for a fixed-length source code) and O(K / log N) (for Golomb-Rice code).

Track-before-detect procedures for early detection of moving target from airborne radars

In this paper we present a family of track-before-detect (TBD) procedures for early detection of moving targets from airborne radars. Upon a sectorization of the coverage area, the received echoes are jointly processed in the azimuth-range-Doppler domain and in the time domain through a Viterbi-like algorithm that exploits the physically admissible target transitions between successive illuminations, in order to collect all of the energy back-scattered during the time on target (TOT). A reduced-complexity implementation is derived assuming, at the design stage, that the target does not change resolution cell during the TOT in each scan. The constant false alarm rate (CFAR) constraint is also englobed in the proposed procedures as well as the possibility of working with quantized data. Simulation results show that the proposed algorithms have good detection and tracking capabilities even for high target velocities and low quantization rates.

Computational Methods for Hidden Markov Tree Models—An Application to Wavelet Trees

The hidden Markov tree models were introduced by Crouse et al. in 1998 for modeling nonindependent, non-Gaussian wavelet transform coefficients. In their paper, they developed the equivalent of the forward-backward algorithm for hidden Markov tree models and called it the algorithm. This algorithm is subject to the same numerical limitations as the forward-backward algorithm for hidden Markov chains (HMCs). In this paper, adapting the ideas of Devijver from 1985, we propose a new upward-downward algorithm, which is a true smoothing algorithm and is immune to numerical underflow. Furthermore, we propose a Viterbi-like algorithm for global restoration of the hidden state tree. The contribution of those algorithms as diagnosis tools is illustrated through the modeling of statistical dependencies between wavelet coefficients with a special emphasis on local regularity changes.

Selective Avoidance of Cycles in Irregular LDPC Code Construction

This letter explains the effect of graph connectivity on error-floor performance of low-density parity-check (LDPC) codes under message-passing decoding. A new metric, called extrinsic message degree (EMD), measures cycle connectivity in bipartite graphs of LDPC codes. Using an easily computed estimate of EMD, we propose a Viterbi-like algorithm that selectively avoids small cycle clusters that are isolated from the rest of the graph. This algorithm is different from conventional girth conditioning by emphasizing the connectivity as well as the length of cycles. The algorithm yields codes with error floors that are orders of magnitude below those of random codes with very small degradation in capacity-approaching capability.

On Viterbi-like algorithms and their application to Reed–Muller codes

For a Viterbi-like algorithm over a sectionalized trellis of a linear block code, the decoding procedure consists of three parts: computing the metrics of the edges, selecting the survivor edge between each pair of adjacent vertices and determining the survivor path from the origin to each vertex. In this paper, some new methods for computing the metrics of the edges are proposed. Our method of “partition of index set” for computing the metrics is shown to be near-optimal. The proposed methods are then applied to Reed–Muller (RM) codes. For some RM codes, the computational complexity of decoding is significantly reduced in comparison to the best-known ones. For the RM codes, a direct method for constructing their trellis-oriented-generator-matrices is proposed and some shift invariances are deduced.

A Viterbi-like algorithm with adaptive clustering for channel assignment in cellular radio networks

A new channel assignment algorithm, called the Viterbi (1967) -like algorithm (VLA), is proposed to solve the channel assignment problem in cellular radio networks. The basic idea of the proposed algorithm is step-by-step (sequential) channel assignment with the objectives of minimum bandwidth required at every step, subject to adjacent channel and cochannel separation constraints. The VLA provides the benefits of minimum required bandwidth, stability of solution, and fast execution time. The performance of the VLA is evaluated by computer simulation, applied first to 19 benchmark problems on channel assignment and then applied to study cellular radio network performance. Results from computer simulation studies show that bandwidth requirements by VLA closely match or are sometimes better than those of the existing channel assignment algorithms. Furthermore, it is found that execution of VLA is approximately two times faster than the local search algorithm-the existing channel assignment algorithm with the least bandwidth requirements. The combined advantages of minimum required bandwidth, stability of solution, and fast execution time make the VLA a useful candidate for cellular radio network planning.

The trellis complexity of convolutional codes

Convolutional codes have a natural, regular, trellis structure that facilitates the implementation of Viterbi's algorithm. Linear block codes also have a natural, though not in general a regular, "minimal" trellis structure, which allows them to be decoded with a Viterbi-like algorithm. In both cases, the complexity of an unenhanced Viterbi decoding algorithm can be accurately estimated by the number of trellis edge symbols per encoded bit. It would therefore appear that we are in a good position to make a fair comparison of the Viterbi decoding complexity of block and convolutional codes. Unfortunately, however, this comparison is somewhat muddled by the fact that some convolutional codes, the punctured convolutional codes, are known to have trellis representations which are significantly less complex than the conventional trellis. In other words, the conventional trellis representation for a convolutional code may not be the "minimal" trellis representation. Thus ironically, we seem to know more about the minimal trellis representation for block than for convolutional codes. We provide a remedy, by developing a theory of minimal trellises for convolutional codes. This allows us to make a direct performance-complexity comparison for block and convolutional codes. A by-product of our work is an algorithm for choosing, from among all generator matrices for a given convolutional code, what we call a trellis-canonical generator matrix, from which the minimal trellis for the code can be directly constructed. Another by-product is that in the new theory, punctured convolutional codes no longer appear as a special class, but simply as high-rate convolutional codes whose trellis complexity is unexpectedly small.

New syndrome decoding techniques for the (n,k) convolutional codes

This paper presents a new syndrome decoding algorithm for the (n,k) convolutional codes (CC) which differs completely from an earlier syndrome decoding algorithm of Schalkwijk and Vinck. The new algorithm is based on the general solution of the syndrome equation, a linear Diophantine equation for the error polynomial vector E(D). The set of Diophantine solutions is a coset of the CC. In this error coset a recursive, Viterbi-like algorithm is developed to find the minimum weight error vector (circumflex)E(D). An example, illustrating the new decoding algorithm, is given for the binary nonsystemmatic (3,1)CC.