a new recursive identification algorithm for singularity free adaptive control reportedly guaranteeing the controllability of the estimated system is a crucial problem in adaptive control in this paper we introduce a least squares based identification algorithm for stochastic siso systems which secures the uniform controllability of the estimated system and presents closed loop identification properties similar to those of the least squares algorithm the proposed algorithm is recursive and therefore easily implementable its use however is confined to cases in which the parameter uncertainly is highly structured

tailbiting codes bounds and search results tailbiting trellis representations of linear block codes with an arbitrary sectionalization of the time axis are studied the notations of regular and irregular tailbiting codes are introduced and their maximal state complexities are lower bounded the asymptotic behavior of the derived bound is investigated furthermore for regular tailbiting codes the product state complexity is lower bounded tables of new tailbiting trellis representations of linear block codes of rates 1 2 1 3 and 1 4 are presented almost all found trellises are optimal in the sense of the new bound on the state complexity and for most codes with nonoptimal trellises there exist time varying trellises which are optimal five of our newly found tailbiting codes are better than the previously known linear codes with the same parameters four of them are also superior to any previously known nonlinear code with the same parameters also more than 40 other quasi cyclic codes have been found that improve the parameter set of previously known quasi cyclic codes

a trellis based recursive maximum likelihood decoding algorithm for binary linear block codes this paper presents an efficient trellis based maximum likelihood decoding algorithm for binary linear block codes this algorithm is recursive in nature and is devised based on the structural properties and optimum sectionalization of a code trellis the complexity of the proposed decoding algorithm is analyzed numerical results show that the proposed decoding algorithm significantly reduces the decoding complexity a recursive method for finding the optimum sectionalization of a trellis in terms of computational complexity is given

integral action in robust adaptive control conditions are studied under which integral action in robust adaptive control is soundly based the method of analysis amounts to verifying that the key conditions needed for convergence are satisfied a simple strategy is described for choosing the integral constant and global convergence is established for the resultant algorithm this illustrates a proof paradigm which could be similarly applied to other problems the principal assumptions used are that the plant when augmented by an integrator has a known degree of controllability and that an overbounding function is known for the unmodeled system response the continuous time case is treated but the corresponding discrete time results follow mutatis mutandis by simply replacing p d dt by delta q 1 delta l sub 2 by l sub 2 integral by sigma and so on

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

three dimensional telegrapher s equation and its fractional generalization we derive the three dimensional telegrapher s equation out of a random walk model the model is a three dimensional version of the multistate random walk where the number of different states form a continuum representing the spatial directions that the walker can take we set the general equations and solve them for isotropic and uniform walks which finally allows us to obtain the telegrapher s equation in three dimensions we generalize the isotropic model and the telegrapher s equation to include fractional anomalous transport in three dimensions

linear tail biting trellises the square root bound and applications for reed muller codes linear tail biting trellises for block codes are considered by introducing the notions of subtrellis merging interval and sub tail biting trellis some structural properties of linear tail biting trellises are proved it is shown that a linear tail biting trellis always has a certain simple structure the parallel merged cosets structure a necessary condition required from a linear code in order to have a linear tail biting trellis representation that achieves the square root bound is presented finally the above condition is used to show that for r spl ges 2 and m spl ges 4r 1 or r spl ges 4 and r 3 spl les m spl les 4r 5 3 the reed muller code rm r m under any bit order cannot be represented by a linear tail biting trellis whose state complexity is half of that of the minimal conventional trellis for the code under the standard bit order

soft decoding techniques for codes and lattices including the golay code and the leech lattice two kinds of algorithms are considered 1 if is a binary code of length n a soft decision decoding algorithm for changes an arbitrary point of r n into a nearest codeword nearest in euclidean distance 2 similarly a decoding algorithm for a lattice lambda in r n changes an arbitrary point of r n into a closest lattice point some general methods are given for constructing such algorithms ami are used to obtain new and faster decoding algorithms for the gosset lattice e 8 the golay code the leech lattice

new constructions of high performance low complexity convolutional codes in this paper new constructions of low trellis complexity convolutional codes are presented new codes are found by searching into a specific class of time varying convolutional codes which is shaped by some basic properties and search restrictions an efficient technique for obtaining minimal trellis modules for the proposed codes is provided finally new low complexity convolutional codes of various code rates and memory sizes are tabulated

a robust indirect adaptive control approach this paper considers the robust design of an indirect adaptive control approach which is applicable when the unknown parameters of a linear time invariant plant lie in a known convex set throughout which no unstable pole zero cancellation occurs in order to achieve the robustness the use of a relative dead zone in the adaptive law is proposed it is shown that with a suitably designed relative dead zone the adaptive control system is globally stable even in the presence of small unmodeled plant uncertainties

generalized cattaneo telegrapher s equations in modeling anomalous diffusion phenomena we study generalized cattaneo telegrapher s equations involving memory effects introduced by smearing the time derivatives consistency conditions where the smearing functions obey restrict freedom in their choice but the proposed scheme goes beyond the approach based on using fractional derivatives we find conditions under which solutions of the equations considered so far can be recognized as probability distributions i e are normalizable and nonnegative on their domains nonnegativity of solutions is demonstrated by methods of positive definite and completely monotonic functions with the bernstein theorem being the cornerstone of the ongoing proofs analysis of exactly solvable examples and relevant mean squared displacements enables us to classify diffusion processes described by such got solutions and to identify them with either ordinary or anomalous diffusion which character may change over time to complete the present research we compare our results with those obtained using the continuous time random walk and the continuous time persistent random walk approaches

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

robust adaptive lq control schemes the certainty equivalence principle is used to combine a robust adaptive law with a control structure derived from the linear quadratic lq control problem the resulting adaptive control scheme is applicable to minimum and nonminimum phase continuous time plants and is robust with respect to unmodeled dynamics and bounded disturbances the computational complexity of the continuous time adaptive lq control scheme is improved by using a hybrid adaptive law which requires the solution of an algebraic riccati equation at each interval of time rather than at each time t

robustness of model reference adaptive controllers an input output approach a general input output approach is employed to study the direct model reference adaptive control problem in the presence of parametric and unstructured uncertainty a sufficient condition for the boundedness of the closed loop signals is developed relating an appropriately defined size of the unstructured uncertainty to the size of the parametric uncertainty this condition involves the intuitively appealing gains of various sensitivity operators and allows for the study of the effect of the design parameters on the boundedness properties of the closed loop system the results of this work indicate a direction towards a unified and systematic theory in adaptive control

the leech lattice and the golay code bounded distance decoding and multilevel constructions multilevel constructions of the binary golay code and the leech lattice are described both constructions are based upon the projection of the golay code and the leech lattice onto the 6 3 4 hexacode over gf 4 however unlike the previously reported constructions the new multilevel constructions make the three levels independent by way of using a different set of coset representatives for one of the quaternary coordinates based upon the multilevel structure of the golay code and the leech lattice efficient bounded distance decoding algorithms are devised the bounded distance decoder for the binary golay code requires at most 431 operations as compared to 651 operations for the best known maximum likelihood decoder efficient bounded distance decoding of the leech lattice is achieved by means of partitioning it into four cosets of q sub 24 beyond the conventional partition into two h sub 24 cosets the complexity of the resulting decoder is only 953 real operations on the average and 1007 operations in the worst case as compared to about 3600 operations for the best known in maximum likelihood decoder it is shown that the proposed algorithms decode correctly at least up to the guaranteed error correction radius of the maximum likelihood decoder thus the loss in coding gain is due primarily to an increase in the effective error coefficient which is calculated exactly for both algorithms furthermore the performance of the leech lattice decoder on the awgn channel is evaluated experimentally by means of a comprehensive computer simulation the results show a loss in coding gain of less than 0 1 db relative to the maximum likelihood decoder for ber ranging from 10 sup 1 to 10 sup 7

maximum likelihood soft decoding of binary block codes and decoders for the golay codes maximum likelihood soft decision decoding of linear block codes is addressed a binary multiple check generalization of the wagner rule is presented and two methods for its implementation one of which resembles the suboptimal forney chase algorithms are described besides efficient soft decoding of small codes the generalized rule enables utilization of subspaces of a wide variety thereby yielding maximum likelihood decoders with substantially reduced computational complexity for some larger binary codes more sophisticated choice and exploitation of the structure of both a subspace and the coset representatives are demonstrated for the 24 12 golay code yielding a computational gain factor of about 2 with respect to previous methods a ternary single check version of the wagner rule is applied for efficient soft decoding of the 12 6 ternary golay code

minimal trellises for block codes basic concepts in the study of trellises of block codes are defined it is shown that minimal proper trellises exists for all block codes bounds on the size of such trellises are established these bounds are shown to be exact for maximum distance separable codes and nearly so for perfect codes

ordered binary decision diagrams and minimal trellises ordered binary decision diagrams obdds are graph based data structures for representing boolean functions they have found widespread use in computer aided design and in formal verification of digital circuits minimal trellises are graphical representations of error correcting codes that play a prominent role in coding theory this paper establishes a close connection between these two graphical models as follows let spl cscr be a binary code of length n and let f sub c x sub 1 x sub n be the boolean function that takes the value 0 at x sub 1 x sub n if and only if x sub 1 x sub n spl isin spl cscr given this natural one to one correspondence between boolean functions and binary codes we prove that the minimal proper trellis for a code spl cscr with minimum distance d 1 is isomorphic to the single terminal obdd for its boolean indicator function f sub c x sub 1 x sub n prior to this result the extensive research during the past decade on binary decision diagrams in computer engineering and on minimal trellises in coding theory has been carried out independently as outlined in this work the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines

bifurcation in model reference adaptive control systems abstract we study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism exact stability boundaries are computed and different routes to chaotic behavior and global instability are described typically we observed a region of period doubling and hopf bifurcations similar to those observed in the ziegler nichols approach to pid control design the analysis applies to higher order and certain nonlinear systems as well

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

robust pole placement direct adaptive control a pole placement direct adaptive control for not necessarily minimum phase plants is presented which is robust with respect to unmodeled dynamics and bounded disturbances the robustness is achieved by using both a normalized least squares algorithm with dead zone and appropriate nonlinear feedback the resulting closed loop system is shown to be globally stable subject to standard assumptions

two dimensional telegraphic processes and their fractional generalizations we study the planar motion of telegraphic processes we derive the two dimensional telegrapher s equation for isotropic and uniform motions starting from a random walk model which is the two dimensional version of the multistate random walk with a continuum number of states representing the spatial directions we generalize the isotropic model and the telegrapher s equation to include planar fractional motions earlier we worked with the one dimensional version masoliver phys rev e 93 052107 2016 prehbm2470 004510 1103 physreve 93 052107 and derived the three dimensional version masoliver phys rev e 96 022101 2017 prehbm2470 004510 1103 physreve 96 022101 an important lesson is that we cannot obtain the two dimensional version from the three dimensional or the one dimensional one from the two dimensional result each dimension must be approached starting from an appropriate random walk model for that dimension

optimal soft decision block decoders based on fast hadamard transform an approach for efficient utilization of fast hadamard transform in decoding binary linear block codes is presented computational gain is obtained by employing various types of concurring codewords and memory reduction is also achieved by appropriately selecting rows for the generator matrix the availability of these codewords in general and particularly in some of the most frequently encountered codes is discussed

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

the nordstrom robinson code representation over gf 4 and efficient decoding we show that the nordstrom robinson 1968 code may be represented as the union of binary images of two isomorphic linear 4 2 3 codes over gf 4 certain symmetries of the unique quaternary 4 2 3 quadracode are discussed it is shown how the properties of the nordstrom robinson code itself such as weight distribution distance invariance and the well known representation as the union of eight cosets of the 16 5 8 reed muller code may be easily rederived from these symmetries in addition we introduce a decoding algorithm for the nordstrom robinson code which involves projecting its codewords onto the codewords of the quadracode the algorithm is simple enough to enable hard decision decoding of the nordstrom robinson code by hand furthermore we present an algorithm for maximum likelihood soft decision decoding of the nordstrom robinson code based on its representation over gf 4 the complexity of the proposed algorithm is at most 205 real operations this is to the best of our knowledge less than the complexity of any existing decoder and twice as efficient as the fast maximum likelihood decoder of adoul 1987 we also investigate several related topics such as bounded distance decoding sphere packings and the 20 2048 6 code

stability analysis of input constrained continuous time indirect adaptive control abstract stability analysis of continuous time indirect pole placement adaptive control with input constraint is presented in this paper it is shown that the closed loop system for a class of stable type 1 plants is globally stable in the sense that all the signals in the loop remain bounded and that certain degree of robustness with respect to modelling uncertainties and disturbances can be achieved by implementing a simple fixed dead zone in the parameter estimator it is also shown that if the plant is free from modelling uncertainties and disturbances and the control input is not saturated for a finite period of time then the closed loop system will asymptotically be characterized by the desired closed loop poles within this time period

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

map algorithms for decoding linear block codes based on sectionalized trellis diagrams the maximum a posterioriprobability map algorithm is a trellis based map decoding algorithm it is the heart of turbo or iterative decoding that achieves an error performance near the shannon limit unfortunately the implementation of this algorithm requires large computation and storage furthermore its forward and backward recursions result in a long decoding delay for practical applications this decoding algorithm must be simplifled and its decoding complexity and delay must be reduced in this paper the map algorithm and its variation s such as log map and max log map algorithms are first applied to sectionalized trellises for linear block codes and carried out as two stage decodings using the structural properties of properly sectionalized trellises the decoding complexity and delay of the map algorithms can be reduced computation wise optimum sectionalizations of a trellis for map algorithms are investigated also presented in this paper are bidirectional and parallel map decodings

optimal sectionalization of a trellis while the complexity of trellis decoding for a given block code is essentially a function of the number of states and branches in its trellis the decoding complexity may be often reduced by means of an appropriate sectionalization of the trellis notwithstanding the many examples of such sectionalizations for particular codes that appeared in the literature no systematic method for finding the best sectionalization of a given trellis is presently known we present a polynomial time algorithm which produces the optimal sectionalization of a given trellis t in time o n sup 2 where n is the length of the code generated by t the algorithm is developed in a general setting of certain operations and functions defined on the set of trellises it therefore applies to both linear and nonlinear codes and easily accommodates a broad range of optimality criteria the particular optimality criterion based on minimizing the total number of additions and comparisons required for maximum likelihood trellis decoding is investigated in detail several different methods for decoding a given trellis are discussed and compared in a number of examples finally analysis of the dynamical properties of certain optimal sectionalizations is presented

even more efficient bounded distance decoding of the hexacode the golay code and the leech lattice we present a new bounded distance decoding algorithm for the hexacode which requires at most 34 real operations in the worst case as compared to 57 such operations in the best previously known decoder the new algorithm is then employed for bounded distance decoding of the leech lattice and the golay code the error correction radius of the resulting decoders is equal to that of a maximum likelihood decoder the resulting decoding complexity is at most 331 real operations for the leech lattice and at most 121 operations for the golay code for all the three codes the hexacode the golay code and the leech lattice the proposed decoders are considerably more efficient than any decoder presently known

robust adaptive regulation without persistent excitation a globally convergent adaptive regulator for minimum or nonminimum phase systems subject to bounded disturbances is presented the control strategy is designed for a particular input output representation obtained from the state space representation of the system the leading coefficient of the novel representation is the product of the observability and controllability matrices of the system the controller scheme uses a least squares identification algorithm with a dead zone the dead zone is chosen to obtain convergence properties on the estimates and on the covariance matrix as well this allows the definition of modified estimates which secure well conditioned matrices in the adaptive control law explicit bounds on the plant output are given

on the bcjr trellis for linear block codes in this semi tutorial paper we will investigate the computational complexity of an abstract version of the viterbi algorithm on a trellis and show that if the trellis has e edges the complexity of the viterbi algorithm is spl theta e this result suggests that the best trellis representation for a given linear block code is the one with the fewest edges we will then show that among all trellises that represent a given code the original trellis introduced by bahl cocke jelinek and raviv in 1974 and later rediscovered by wolf 1978 massey 1978 and forney 1988 uniquely minimizes the edge count as well as several other figures of merit following forney and kschischang and sorokine 1995 we will also discuss trellis oriented or minimal span generator matrices which facilitate the calculation of the size of the bcjr trellis as well as the actual construction of it

lower bounds on trellis complexity of block codes the trellis state complexity s of a linear block code is defined as the logarithm of the maximum number of states in its minimal trellis we present a new lower bound on the state complexity of linear codes which includes most of the existing bounds as special cases the new bound is obtained by dividing the time axis for the code into several sections of varying lengths as opposed to the division into two sections the past and the future employed in the well known dlp bounds for a large number of codes this results in a considerable improvement upon the dlp bound moreover we generalize the new bound to nonlinear codes and introduce several alternative techniques for lower bounding the trellis complexity based on the distance spectrum and other combinatorial properties of the code we also show how the general ideas developed in this paper may be employed to lower bound the maximum and the total number of branches in the trellis leading to considerably tighter bounds on these quantities furthermore the asymptotic behavior of the new bounds is investigated and shown to improve upon the previously known asymptotic estimates of trellis state complexity

codes on graphs constraint complexity of cycle free realizations of linear codes cycle free graphical realizations of linear codes generalize trellis realizations given a linear code c and a cycle free graph topology there exists a well defined minimal realization for c on that graph in which each constraint is a linear code with a well defined length and dimension the constraint complexity of the realization is defined as maximum dimension of any constraint code there exists a graph that minimizes constraint complexity in which all internal nodes have degree 3 and all interface nodes have degree 2 and which moreover can be put in the form of a tree structured trellis realization the constraint complexity of a general cycle free graph realization can be less than that of any conventional trellis realization but not by very much such realizations can yield reductions in decoding complexity even when they do not reduce constraint complexity

on the time fractional cattaneo equation of distributed order abstract the present work revisits the time fractional cattaneo equation tfce by considering a generic class of time fractional derivatives of distributed order 0 1 at first we shed light on two main forms of tfce one natural generalization uses the caputo fractional derivative and the other compte metzler generalization is defined in the riemann liouville sense and the equivalence condition between their solutions is provided some special cases of these two forms are addressed hence different versions of distributed order tfce are proposed the fundamental solution of the two general forms of distributed order tfce are derived using integral transform technique the non negativity of solutions of tfce and its distributed order versions is examined using the special type functions technique gorenflo luchko and stojanovic 2013 two classes of order distribution are considered discrete order and continuous order distributions and some random choices of non negative order densities affirm graphically the non negativity of the general forms of distributed order tfce the double order as an example on the discrete order and exponentially exp and sinusoidally sin distributed order as an example on the continuous order are chosen finally connections between some models of distributed order tfce and continuous time random walk theory are established and the corresponding mean squared displacements are discussed

trellis decoding complexity of linear block codes in this partially tutorial paper we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity maximum state and edge dimensions total span length and total vertices edges and mergers we obtain bounds on these complexities as extensions of well known dimension length profile dlp bounds codes meeting these bounds minimize all the complexity measures simultaneously conversely a code attaining the bound for total span length vertices or edges must likewise attain it for all the others we define a notion of uniform optimality that embraces different domains of optimization such as different permutations of a code or different codes with the same parameters and we give examples of uniformly optimal codes and permutations we also give some conditions that identify certain cases when no code or permutation can meet the bounds in addition to dlp based bounds we derive new inequalities relating one complexity measure to another which can be used in conjunction with known bounds on one measure to imply bounds on the others as an application we infer new bounds on maximum state and edge complexity and on total vertices and edges from bounds on span lengths

on the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes it was shown earlier that for a punctured reed muller rm code or a primitive bch code which contains a punctured rm code of the same minimum distance as a large subcode the state complexity of the minimal trellis diagrams is much greater than that for an equivalent code obtained by a proper permutation of the bit positions the problem of finding a permutation of the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is related to the generalized hamming weight hierarchy of a code and it is shown that for rm codes the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to v k wei 1991 the state complexity of the trellis diagram for the extended and permuted 64 24 bch code is discussed

the dynamics of group codes state spaces trellis diagrams and canonical encoders a group code c over a group g is a set of sequences of group elements that itself forms a group under a component wise group operation a group code has a well defined state space sigma sub k at each time k each code sequence passes through a well defined state sequence the set of all state sequences is also a group code the state code of c the state code defines an essentially unique minimal realization of c the trellis diagram of c is defined by the state code of c and by labels associated with each state transition the set of all label sequences forms a group code the label code of c which is isomorphic to the state code of c if c is complete and strongly controllable then a minimal encoder in controller canonical feedbackfree form may be constructed from certain sets of shortest possible code sequences called granules the size of the state space sigma sub k is equal to the size of the state space of this canonical encoder which is given by a decomposition of the input groups of c at each time k if c is time invariant and nu controllable then mod sigma sub k mod pi sub 1

bit level soft decision decoding of reed solomon codes a reed solomon decoder that makes use of bit level soft decision information is presented a reed solomon generator matrix that possesses a certain inherent structure in gf 2 is derived this structure allows the code to be represented as a union of cosets each coset being an interleaver of several binary bch codes such partition into cosets provides a clue for efficient bit level soft decision decoding two decoding algorithms are derived in the development of the first algorithm a memoryless channel is assumed making the value of this algorithm more conceptual than practical the second algorithm which is obtained as a modification of the first does account for channel memory and thus accommodates a bursty channel both decoding algorithms are in many cases orders of magnitude more efficient than conventional techniques

on construction of the 24 12 8 golay codes two product array codes are used to construct the 24 12 8 binary golay code through the direct sum operation this construction provides a systematic way to find proper 8 4 4 linear block component codes for generating the golay code and it generates and extends previously existing methods that use a similar construction framework the code constructed is simple to decode

robustness of discrete time adaptive controllers an input output approach a general input output approach that can be used for the design and analysis of robust discrete time adaptive control schemes is presented in particular a model reference adaptive controller is considered the design approach involves the use of the certainty equivalence principle to combine a robust control structure with a robust adaptive law using exponentially weighted i sub 2 norms and exploiting the properties of the adaptive law and the control structure robust stability is established for the closed loop adaptive control scheme

fractional telegrapher s equation from fractional persistent random walks we generalize the telegrapher s equation to allow for anomalous transport we derive the space time fractional telegrapher s equation using the formalism of the persistent random walk in continuous time we also obtain the characteristic function of the space time fractional process and study some particular cases and asymptotic approximations similarly to the ordinary telegrapher s equation the time fractional equation also presents distinct behaviors for different time scales specifically transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses

conditionally cycle free graphical models for coset codes conditionally cycle free graphical models i e cyclic graphical models which become cycle free after conditioning on a subset of the hidden variables are constructed for coset codes following the description of a general construction procedure examples of a number of families of codes including first order reed muller rm and the delsarte goethals codes are provided for which the proposed procedure yields optimal soft in soft out siso decoding algorithms that are less complex than the best known trellis based algorithms in the case of the first order rm codes which have a recursive coset construction the optimal siso decoding algorithm that results when the proposed construction is applied repeatedly is denoted recursive coset representation rcr decoding connections are made between rcr decoding and existing algorithms that exploit fast hadamard transforms finally the utility of the proposed decoding algorithms are supported by a practically motivated application the construction of serially concatenated codes that have high rates and low error floors extended hamming codes are proposed as outer codes in such constructions with efficient decoding employing the siso algorithms developed herein

anomalous diffusion under stochastic resettings a general approach we present a general formulation of the resetting problem which is valid for any distribution of resetting intervals and arbitrary underlying processes we show that in such a general case a stationary distribution may exist even if the reset free process is not stationary as well as a significant decreasing in the mean first passage time we apply the general formalism to anomalous diffusion processes which allow simple and explicit expressions for poissonian resetting events

a low weight trellis based iterative soft decision decoding algorithm for binary linear block codes this paper presents a new low weight trellis based soft decision iterative decoding algorithm for binary linear block codes the algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test the initial candidate codeword is generated by a simple decoding method the subsequent candidate codewords if needed are generated by a chain of low weight trellis searches one at a time each search is conducted through a low weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested this improvement is then used as the next candidate codeword for a test of optimality the decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low weight trellis search results in a repetition of a previously generated candidate codeword a divide and conquer technique is also presented for codes that are not spanned by their minimum weight codewords the proposed decoding algorithm has been applied to some well known codes of lengths 48 64 and 128 simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the 128 29 32 rm code with a significant reduction in computational decoding complexity

suboptimal decoding of linear codes partition technique general symmetric channels are introduced and near maximum likelihood decoding in these channels is studied first we define a class of suboptimal decoding algorithms based on an incomplete search through the code trellis it is proved that the decoding error probability of suboptimal decoding is bounded above for any q ary code of length n and code rate r by twice the error probability of its maximum likelihood decoding and tends to the latter as n grows second we design a suboptimal trellis like algorithm which reduces the known decoding complexity of the order of q sup n min r 1 r operations to that of q sup nr i r operations for all cyclic codes and virtually all long linear codes we also consider the corresponding bounds for concatenated codes an important corollary is that this suboptimal decoding can provide complexity below the lower bounds on trellis complexity at a negligible expense in terms of decoding error probability

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

robust adaptive control of discrete time systems using persistent excitation abstract an important result in the robust adaptive control of continuous time systems using the persistent excitation of the reference input was recently given by narendra and annaswamy 1986 ieee trans aut control ac 31 306 315 according to this result the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance the main theorem in narendra and annaswamy 1986 is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real a condition which involves constraints on the relative degree of the plant this paper presents a generalization of the above result to plants of arbitrary relative degree together with the work reported in the earlier paper it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input

proof of a conjecture of mceliece regarding the expansion index of the minimal trellis we prove a conjecture of mceliece establishing that for each fixed order of positions of a linear code c the minimal trellis minimizes the quantity e v 1 where e and v stand for the number of edges and vertices in the trellis respectively as a consequence it follows that the minimal trellis uniquely minimizes the total number of operations required for viterbi decoding of a given code moreover we show that these results extend to the general class of rectangular codes namely the class of codes that admit a biproper trellis presentation which includes all group codes and many other useful nonlinear codes

maximum likelihood decoding of the leech lattice an algorithm for maximum likelihood decoding of the leech lattice is presented the algorithm involves projecting the points of the leech lattice directly onto the codewords of the 6 3 4 quaternary code the hexacode projection on the hexacode induces a partition of the leech lattice into four cosets of a certain sublattice 24 such a partition into cosets enables maximum likelihood decoding of the leech lattice with 3595 real operations in the worst case and only 2955 operations on the average this is about half the worst case and the average complexity of the best previously known algorithm

on the pless construction and ml decoding of the 48 24 12 quadratic residue code we present a method for maximum likelihood decoding of the 48 24 12 quadratic residue code this method is based on projecting the code onto a subcode with an acyclic tanner graph and representing the set of coset leaders by a trellis diagram this results in a two level coset decoding which can be considered a systematic generalization of the wagner rule we show that unlike the 24 12 8 golay code the 48 24 12 code does not have a pless construction which has been an open question in the literature it is determined that the highest minimum distance of a 48 24 binary code having a pless 1986 construction is 10 and up to equivalence there are three such codes

nonstationary markovian replication process causing diverse diffusions we introduce a single generative mechanism that can be used to describe diverse nonstationary diffusions a nonstationary markovian replication process for steps is considered for which we derive analytically the time evolution of the probability distribution of the walker s displacement and the generalized telegrapher equation with time varying coefficients and we find that diffusivity can be determined by temporal changes of replication of an immediate step by controlling the replications we realize diverse diffusions such as alternating diffusion superdiffusion subdiffusion and marginal diffusion which originate from oscillating increasing decreasing and slowly increasing or decreasing replications with time respectively