On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.

Strategies for Minimum Distance in Simulated Evacuation of Transport Airplanes

The present paper describes the preliminary stages of the development of a new, comprehensive model conceived to simulate the evacuation of transport airplanes in certification studies. Two previous steps were devoted to implementing an efficient procedure to define the whole geometry of the cabin, and setting up an algorithm for assigning seats to available exits. Now, to clarify the role of the cabin arrangement in the evacuation process, the paper addresses the influence of several restrictions on the seat-to-exit assignment algorithm, maintaining a purely geometrical approach for consistency. Four situations are considered: first, an assignment method without limitations to search the minimum for the total distance run by all passengers along their escaping paths; second, a protocol that restricts the number of evacuees through each exit according to updated FAR 25 capacity; third, a procedure which tends to the best proportional sharing among exits but obliges to each passenger to egress through the nearest fore or rear exits; and fourth, a scenario which includes both restrictions. The four assignment strategies are applied to turboprops, and narrow body and wide body jets. Seat to exit distance and number of evacuees per exit are the main output variables. The results show the influence of airplane size and the impact of non-symmetries and inappropriate matching between size and longitudinal location of exits.

Multi-objective mission flight planning in civil unmanned aerial systems

Unmanned Aerial Vehicles (UAVs) are emerging as an ideal platform for a wide range of civil applications such as disaster monitoring, atmospheric observation and outback delivery. However, the operation of UAVs is currently restricted to specially segregated regions of airspace outside of the National Airspace System (NAS). Mission Flight Planning (MFP) is an integral part of UAV operation that addresses some of the requirements (such as safety and the rules of the air) of integrating UAVs in the NAS. Automated MFP is a key enabler for a number of UAV operating scenarios as it aids in increasing the level of onboard autonomy. For example, onboard MFP is required to ensure continued conformance with the NAS integration requirements when there is an outage in the communications link. MFP is a motion planning task concerned with finding a path between a designated start waypoint and goal waypoint. This path is described with a sequence of 4 Dimensional (4D) waypoints (three spatial and one time dimension) or equivalently with a sequence of trajectory segments (or tracks). It is necessary to consider the time dimension as the UAV operates in a dynamic environment. Existing methods for generic motion planning, UAV motion planning and general vehicle motion planning cannot adequately address the requirements of MFP. The flight plan needs to optimise for multiple decision objectives including mission safety objectives, the rules of the air and mission efficiency objectives. Online (in-flight) replanning capability is needed as the UAV operates in a large, dynamic and uncertain outdoor environment. This thesis derives a multi-objective 4D search algorithm entitled Multi- Step A* (MSA*) based on the seminal A* search algorithm. MSA* is proven to find the optimal (least cost) path given a variable successor operator (which enables arbitrary track angle and track velocity resolution). Furthermore, it is shown to be of comparable complexity to multi-objective, vector neighbourhood based A* (Vector A*, an extension of A*). A variable successor operator enables the imposition of a multi-resolution lattice structure on the search space (which results in fewer search nodes). Unlike cell decomposition based methods, soundness is guaranteed with multi-resolution MSA*. MSA* is demonstrated through Monte Carlo simulations to be computationally efficient. It is shown that multi-resolution, lattice based MSA* finds paths of equivalent cost (less than 0.5% difference) to Vector A* (the benchmark) in a third of the computation time (on average). This is the first contribution of the research. The second contribution is the discovery of the additive consistency property for planning with multiple decision objectives. Additive consistency ensures that the planner is not biased (which results in a suboptimal path) by ensuring that the cost of traversing a track using one step equals that of traversing the same track using multiple steps. MSA* mitigates uncertainty through online replanning, Multi-Criteria Decision Making (MCDM) and tolerance. Each trajectory segment is modeled with a cell sequence that completely encloses the trajectory segment. The tolerance, measured as the minimum distance between the track and cell boundaries, is the third major contribution. Even though MSA* is demonstrated for UAV MFP, it is extensible to other 4D vehicle motion planning applications. Finally, the research proposes a self-scheduling replanning architecture for MFP. This architecture replicates the decision strategies of human experts to meet the time constraints of online replanning. Based on a feedback loop, the proposed architecture switches between fast, near-optimal planning and optimal planning to minimise the need for hold manoeuvres. The derived MFP framework is original and shown, through extensive verification and validation, to satisfy the requirements of UAV MFP. As MFP is an enabling factor for operation of UAVs in the NAS, the presented work is both original and significant.

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Vertical dynamic interaction of trains and rail steel bridges

Rail steel bridges are vulnerable to high impact forces due to the passage of trains; unfortunately the determination of these transient impact forces is not straightforward as these are affected by a large number of parameters, including the wagon design, the wheel-rail contact and the design parameters of the bridge deck and track, as well as the operational parameters – wheel load and speed. To determine these impact forces, a detailed rail train-track/bridge dynamic interaction model has been developed, which includes a comprehensive train model using multi-body dynamics approach and a flexible track/bridge model using Euler– Bernoulli beam theory. Single and multi-span bridges have been modelled to examine their dynamic characteristics. From the single span bridge, the train critical speed is determined; the minimum distance of two peak loadings is found to affect the train critical speed. The impact factor and the dynamic characteristics are discussed.

Equivalent rate 1/2 quasi-cyclic codes

Chen et al. [1] give a list of quasi-cyclic (2m,m) codes which have the largest minimum distance of any quasi-cyclic code, for various values ofm. We present the weight distribution of these codes. It will be seen that many of the codes found by Chen et al. [1] are equivalent in the sense of having identical weight distributions.

Task assignment in a multiprocessor system

One of the key problems in the design of any incompletely connected multiprocessor system is to appropriately assign the set of tasks in a program to the Processing Elements (PEs) in the system. The task assignment problem has proven difficult both in theory and in practice. This paper presents a simple and efficient heuristic algorithm for assigning program tasks with precedence and communication constraints to the PEs in a Message-based Multiple-bus Multiprocessor System, M3, so that the total execution time for the program is minimized. The algorithm uses a cost function: “Minimum Distance and Parallel Transfer” to minimize the completion time. The effectiveness of the algorithm has been demonstrated by comparing the results with (i) the lower bound on the execution time of a program (task) graph and (ii) a random assignment.

Patterns in permuted binary matrices

Reorganizing a dataset so that its hidden structure can be observed is useful in any data analysis task. For example, detecting a regularity in a dataset helps us to interpret the data, compress the data, and explain the processes behind the data. We study datasets that come in the form of binary matrices (tables with 0s and 1s). Our goal is to develop automatic methods that bring out certain patterns by permuting the rows and columns. We concentrate on the following patterns in binary matrices: consecutive-ones (C1P), simultaneous consecutive-ones (SC1P), nestedness, k-nestedness, and bandedness. These patterns reflect specific types of interplay and variation between the rows and columns, such as continuity and hierarchies. Furthermore, their combinatorial properties are interlinked, which helps us to develop the theory of binary matrices and efficient algorithms. Indeed, we can detect all these patterns in a binary matrix efficiently, that is, in polynomial time in the size of the matrix. Since real-world datasets often contain noise and errors, we rarely witness perfect patterns. Therefore we also need to assess how far an input matrix is from a pattern: we count the number of flips (from 0s to 1s or vice versa) needed to bring out the perfect pattern in the matrix. Unfortunately, for most patterns it is an NP-complete problem to find the minimum distance to a matrix that has the perfect pattern, which means that the existence of a polynomial-time algorithm is unlikely. To find patterns in datasets with noise, we need methods that are noise-tolerant and work in practical time with large datasets. The theory of binary matrices gives rise to robust heuristics that have good performance with synthetic data and discover easily interpretable structures in real-world datasets: dialectical variation in the spoken Finnish language, division of European locations by the hierarchies found in mammal occurrences, and co-occuring groups in network data. In addition to determining the distance from a dataset to a pattern, we need to determine whether the pattern is significant or a mere occurrence of a random chance. To this end, we use significance testing: we deem a dataset significant if it appears exceptional when compared to datasets generated from a certain null hypothesis. After detecting a significant pattern in a dataset, it is up to domain experts to interpret the results in the terms of the application.

Modulation Diversity in Fading Channels with a Quantized Receiver

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at the receiver. With an unquantized receiver, coding based on algebraic rotations is known to achieve maximum modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee gains in diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder and perfect channel knowledge. Relaxing the perfect channel knowledge assumption we propose a novel channel training/estimation technique to estimate the channel. We show that our coding/training/estimation scheme and minimum distance decoding achieves an error probability performance similar to that achieved with perfect channel knowledge.

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.

Codes with local regeneration

Regenerating codes and codes with locality are schemes recently proposed for a distributed storage network. While regenerating codes minimize the data downloaded for node repair, codes with locality minimize the number of nodes accessed during repair. In this paper, we provide some constructions of codes with locality, in which the local codes are regenerating codes, thereby combining the advantages of both classes of codes. The proposed constructions achieve an upper bound on minimum distance and are hence optimal. The constructions include both the cases when the local regenerating codes correspond to the MSR point as well as the MBR point on the storage repair-bandwidth tradeoff curve.

Wireless Network Coding for MIMO Two-Way Relaying

The design of modulation schemes for the physical layer network-coded two-way MIMO relaying scenario is considered, with the denoise-and-forward protocol which employs two phases: Multiple Access phase and Broadcast phase. It is shown that for MIMO two-way relaying, the minimum distance of the effective constellation at the relay becomes zero when all the rows of the channel fade coefficient matrix belong to a finite number of vector subspaces referred to as the singular fade subspaces. The singular fade subspaces can be classified into two kinds based on whether their harmful effects can be removed or not: (i) the removable and (ii) the non-removable singular fade subspaces. It is shown that network coding maps obtained by the completion of appropriate partially filled Latin Rectangles can remove the harmful effects of all the removable singular fade subspaces. For 2(lambda)-PSK signal set, the removable and non-removable singular fade subspaces are characterized and, it is shown that the number of non-removable singular fade subspaces is a small fraction of the total number of singular fade subspaces and this fraction tends to zero as the constellation size tends to infinity. The Latin Rectangles for the case when the end nodes use different number of antennas are shown to be obtainable from the Latin Squares for the case when they use the same number of antennas. Also, the network coding maps which remove all the removable singular singular fade subspaces are shown to be obtainable from a small set of Latin Squares. The removal of all the singular fade subspaces by properly choosing the network coding map, provides a gain of 5.5 dB over the conventional Exclusive-OR network coding, in a Rayleigh fading scenario with 2 antennas at the end nodes and one antenna at the relay node, for 4-PSK signal set.

Wireless Network-Coded Bidirectional Relaying Using Latin Squares for M-PSK Modulation

The design of modulation schemes for the physical layer network-coded two-way relaying scenario is considered with a protocol which employs two phases: multiple access (MA) phase and broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of MA interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, that this relationship can be used to get the network coding maps satisfying the exclusive law. The channel fade states for which the minimum distance of the effective constellation at the relay become zero are referred to as the singular fade states. For M - PSK modulation (M any power of 2), it is shown that there are (M-2/4 - M/2 + 1) M singular fade states. Also, it is shown that the constraints which the network coding maps should satisfy so that the harmful effects of the singular fade states are removed, can be viewed equivalently as partially filled Latin Squares (PFLS). The problem of finding all the required maps is reduced to finding a small set of maps for M - PSK constellations (any power of 2), obtained by the completion of PFLS. Even though the completability of M x M PFLS using M symbols is an open problem, specific cases where such a completion is always possible are identified and explicit construction procedures are provided. Having obtained the network coding maps, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map chosen in a particular region. It is shown that the complex plane can be partitioned into two regions: a region in which any network coding map which satisfies the exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for M = 4-PSK signal set by Koike-Akino et al., when specialized for Simulation results show that the proposed scheme performs better than the conventional exclusive-OR (XOR) network coding and in some cases outperforms the scheme proposed by Koike-Akino et al.