nonlinear state feedback for l 1 optimal control this paper considers l1 optimal control problems with full state feedback in contrast to h optimal control previous work has shown that linear l1 optimal controllers can be dynamic and arbitrarily high order however this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback the derivation which is nonconstructive relies on concepts from viability theory

linear block codes over cyclic groups the main building block for the construction of a geometrically uniform coded modulation scheme is a subgroup of g sup i where g is a group generating a low dimensional signal constellation and i is an index set in this paper we study the properties of these subgroups when g is cyclic we exploit the fact that any cyclic group of q elements is isomorphic to the additive group of z sub q the ring of integers modulo q so that we can make use of concepts related to linearity our attention is focused mainly on indecomposable cyclic groups i e of prime power order since they are the elementary building blocks of any abelian group in analogy with the usual construction of linear codes over fields we define a generator matrix and a parity check matrix trellis construction and bounds on the minimum euclidean distance are also investigated some examples of coded modulation schemes based on this theory are also exhibited and their performance evaluated

spherical codes generated by binary partitions of symmetric pointsets several constructions are presented by which spherical codes are generated from groups of binary codes in the main family of constructions the codes are generated from equally spaced symmetric pointsets on the real line the main ideas are code concatenation and set partitioning extensive tables are presented for spherical codes in dimension n spl les 24

elias bound for general distances and stable sets in edge weighted graphs this paper presents an extension of the elias bound on the minimum distance of codes for discrete alphabets with general possibly infinite valued distances the bound is obtained by combining a previous extension of the elias bound introduced by blahut with an extension of a bound previously introduced by the author which builds upon ideas of gallager lovasz and marton the result can in fact be interpreted as a unification of the elias bound and of lovasz s bound on graph or zero error capacity both being recovered as particular cases of the one presented here previous extensions of the elias bound by berlekamp blahut and piret are shown to be included as particular cases of our bound applications to the reliability function are then discussed

solving the linear matroid parity problem as a sequence of matroid intersection problems in this paper we present an o r4n algorithm for the linear matroid parity problem our solution technique is to introduce a modest generalization the non simple parity problem and identify an important subclass of non simple parity problems called easy parity problems which can be solved as matroid intersection problems we then show how to solve any linear matroid parity problem parametrically as a sequence of easy parity problems

a bounded distance decoding algorithm for the leech lattice with generalizations an algorithm is given that decodes the leech lattice with not much more than twice the complexity of soft decision decoding of the golay code the algorithm has the same effective minimum distance as maximum likelihood decoding and increases the effective error coefficient by less than a factor or two the algorithm can be recognized as a member of the class of multistage algorithms that are applicable to hierarchical constructions it is readily generalized to lattices that can be expressed in terms of binary code formulas and in particular to construction b lattices

symmetry properties of multilevel coded modulation we consider the geometrical uniformity properties of signal space codes generated by multilevel coded modulation first we examine multilevel schemes based on 2 sup l ary psk signal sets and we derive conditions on the binary component codes which lead to geometrically uniform signal space codes next we study the geometrical uniformity of multilevel schemes based on signal sets having a generating group isomorphic to a direct product finally we provide an easy to test criterion for finding if a given signal set or signal space code obtained as the union of two orbits of the same generating group has the uniform distance property

further asymptotic upper bounds on the minimum distance of trellis codes asymptotic upper bounds on the minimum distance of trellis codes are derived a universal bound and bounds specific to phase shift keying psk and quadrature amplitude modulation qam signal sets are obtained

rate gains in block coded modulation systems with interblock memory this paper examines the performance gains achievable by adding interblock memory to and altering the mapping of coded bits to symbols in block coded modulation systems the channel noise considered is additive gaussian and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors in the case of the additive white gaussian noise channel these goals translate into the design of block codes of a given weighted or normalized distance whose rate is as high as possible and whose number of codewords at minimum normalized distance is low the effect of designing codes for normalized distance rather than hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest and many such best codes are given

on linear structure and phase rotation invariant properties of block m psk modulation codes two important structural properties of block m 2 sup ary psk modulation codes linear structure and phase symmetry are investigated an m ary modulation code is first represented as a code with symbols from the integer group s sub m psk 0 1 2 m 1 under modulo m addition then the linear structure of block m psk modulation codes over s sub m psk with respect to modulo m vector addition is defined and conditions are derived under which a block m psk modulation code is linear once the linear structure is developed the phase symmetry of block m psk modulation codes is studied in particular a necessary and sufficient condition for a block m psk modulation code that is linear as a binary code to be invariant under 2 sup h 180 degrees m phase rotation for 1

bounds for codes over the unit circle let c be a code of length n and rate r over the alphabet a q exp 2 pi ir q r o 1 cdots q 1 and let d c be the minimum euclidean distance of c for large n the lower and upper bounds are obtained in parametric form on the achievable pairs r delta where delta d 2 c n holds to obtain these bounds the arguments leading to the gilbert bound and the elias bound respectively are applied to the alphabet a q for q rightarrow infty they are shown to be expressible in terms of the modified bessel function of the first kind the elias type bound is compared with the kabatyanskii levenshtein k l bound that holds for less restrictive alphabets it turns out that our upper bound improves the k l bound for delta leq 0 93

block coded m psk modulation over gf m channel codes where the redundancy is obtained not from parity symbols but from expanding the channel signal set are addressed they were initially proposed by g ungerboeck 1982 using a convolutional code here a block coding approach is given rate m m 1 coded 2 sup m 1 ary phase shift keying psk is considered the expanded signal set is given the structure of a finite field the code is defined by a square nonsingular circulant generator matrix over the field binary data are mapped on a dataword of the same length as the codewords over an additive subgroup of the field the codes using trellises are described and then the viterbi algorithm for decoding is applied the asymptotic coding gain ranges from 1 8 to 6 0 db for qpsk going from blocklength 3 to 12 for 8 psk the gain is from 0 7 to 3 0 db with blocklength 4 to 8 with only four states in the trellis codes of any length for qpsk and 8 psk are constructed each having an asymptotic coding gain of 3 0 db simulation results are presented it is found that the bit error rate performance at moderate signal to noise ratios is sensitive to the number of nearest and next nearest neighbors

optimum matching forests i special weights we introduce the concept of matching forests as a generalization of branchings in a directed graph and matchings in an undirected graph given special weights on the edges of a mixed graph we present an efficient algorithm for finding an optimum weight sum matching forest the algorithm is a careful application of known branching and matching algorithms the maximum cardinality matching forest problem is solved as a special case

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

construction of linear ring codes for 6 psk the algebraic construction of linear codes over zm for m psk is considered for the case that m is the product of two distinct primes by means of the chinese remainder theorem crt such codes can be constructed from linear codes over the corresponding prime fields it is shown that for given component codes the crt composition yields psk codes that are at least as good and often much better than the codes obtained from the standard coset coding technique a lower bound on the minimum euclidean distance of 6 psk codes is derived that is based on the hamming weight distribution of the component codes

noncoherent block coded tapsk for coherent detection block coded modulation is a bandwidth efficient scheme in this paper we propose theorems about the error performance of block coded modulation using m ary phase shift keying mpsk for noncoherent detection based on these theorems we propose a novel block coded modulation scheme for noncoherent detection called noncoherent block coded mpsk the proposed scheme provides flexible designs of noncoherent block codes with different code rate block length and error performance good noncoherent block codes can be easily obtained by properly choosing binary linear block codes as the component codes moreover noncoherent block codes of this new scheme can be decoded by multistage decoding which has the advantage of low complexity and satisfactory error performance in this paper two algorithms of multistage decoding for noncoherent detection are proposed as well the error performance of some designed codes and decoding algorithms is verified by computer simulation

multilevel trellis coded modulations for the rayleigh fading channel the authors present coded 8 phase shift keyed 8 psk modulations for the rayleigh fading channel the schemes are based on multilevel trellis coded modulation constructions and utilize maximum free hamming distance binary convolutional codes as building blocks a suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated examples are constructed to show that the proposed schemes outperform the best modified codes of the ungerboeck type due to significantly higher implicit time diversity yielding seven branches of built in time diversity whereas the ungerboeck code yields four branches of time diversity for a 64 state system the transmission delay is higher however the new schemes can provide three levels of unequal error protection when 8 psk or 8 differential phase shift keying 8 dpsk modulations are used they provide 10 14 db channel signal to noise ratio gain over uncoded 4 dpsk at a bit error rate of 10 sup 3 for a modest decoding complexity

performance evaluation of coded modulation schemes based on binary lattices we describe computational techniques for the evaluation of error probability of modulation schemes based on binary lattices and multilevel coding these techniques stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the binary lattice is based multilevel coded modulation schemes can also be described through a trellis by combining with this the trellis structure of the lattice constellation we obtain a single trellis that can be used for maximum likelihood decoding using the viterbi algorithm and for computing the error probability an upper bound to error probability can be obtained from the transfer function of the trellis with suitable labels and is applicable to both maximum likelihood and staged decoding

multilevel codes theoretical concepts and practical design rules this paper deals with 2 sup l ary transmission using multilevel coding mlc and multistage decoding msd the known result that mlc and msd suffice to approach capacity if the rates at each level are appropriately chosen is reviewed using multiuser information theory it is shown that there is a large space of rate combinations such that mlc and full maximum likelihood decoding mld can approach capacity it is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of mld the capacity rule the balanced distances rules and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies moreover topics relevant in practical applications such as signal set labeling dimensionality of the constituent constellation and hard decision decoding are emphasized bit interleaved coded modulation proposed by caire et al see ibid vol 44 p 927 46 1998 is reviewed in the context of mlc finally the combination of signal shaping and coding is discussed significant shaping gains are achievable in practice only if these design rules are taken into account

l sub 2 state feedback control with a prescribed rate of exponential convergence in this paper we consider the l sub 1 state feedback problem with an internal stability constraint in particular we establish the connection between controlled invariant contractive sets and static control laws that achieve a level of l sub 1 performance as well as a desired unforced rate of convergence we outline two algorithms for computing controlled invariant contractive sets the first is a modification of standard recursive techniques used in the literature whereas the second is based on dynamic games and involves solving an appropriate discrete isaacs recursion the latter approach results in a min max characterization of l sub 1 state feedback controllers we point out that the isaacs recursion provides a one shot as opposed to iterative computation of the optimal l sub 1 performance

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

an upper bound on the minimum euclidean distance for block coded phase shift keying we present an upper bound on the minimum euclidean distance d sub emin c for block coded psk the bound is an analytic expression depending on the alphabet size q the block length n and the number of codewords c of the code c the bound is valid for all block codes with q spl ges 4 and with medium or high rate codes where c q 3 sup n there are several well known block codes whose d sub emin c is equal to our upper bound hence these codes are the best possible in the sense that there does not exist a code with the same q n and c and with a larger d sub emin c it also follows that for many choices of q n and c in particular for high rates our upper bound on d sub emin c is optimal

multidimensional trellis coded phase modulation using a multilevel concatenation approach ii codes for the awgn and fading channels for pt i see ibid vol 45 no 1 p 64 72 1997 we use the construction technique proposed in part i to construct multidimensional trellis coded modulation tcm codes for both the additive white gaussian noise awgn and the fading channels analytical performance bounds and simulation results show that these codes perform very well and achieve significant coding gains over uncoded reference modulation systems in addition the proposed technique can be used to construct codes which have a performance decoding complexity advantage over the codes listed in literature

multistage decoding of multilevel block m psk modulation codes and its performance analysis multistage decoding of multilevel block multilevel phase shift keying m psk modulation codes for the additive white gaussian noise awgn channel is investigated several types of multistage decoding including a suboptimum soft decision decoding scheme are devised and analyzed upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes error probabilities of some specific multilevel block 8 psk modulation codes are evaluated and simulated the computation and simulation results for these codes show that with multistage decoding significant coding gains can be achieved with large reduction in decoding complexity in one example it is shown that the difference in performance between the proposed suboptimum multistage soft decision decoding and the single stage optimum decoding is small only a fraction of a db loss in snr at the block error probability of 10 sup 6

gilbert varshamov bound for euclidean space codes over distance uniform signal sets in this correspondence in an extension of piret s bound for codes over phase shift keying psk signal sets we investigate the application of the gilbert varshamov gv bound to a variety of distance uniform du signal sets in euclidean space it is shown that four dimensional signal sets matched to binary tetrahedral binary octahedral and binary icosahedral groups lead to better bounds compared to the bounds for signal sets matched to dicyclic groups with the same number of signal points and comparable symmetric psk signal sets

a new description of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of real or complex numbers that are input to a noisy transmission channel ungerboeck has constructed simple trellis codes that provide the same noise immunity as is given by increasing the power of uncoded transmission by factors ranging from two to four his method is to specify an underlying convolutional code and a rule mapping by set partitioning that maps the output of this code onto a fixed signal constallation a new description of a trellis code is given that combines these two steps into one the new description is analytic rather than graphical many practical codes can be described very simply and strict bounds on performance can be obtained a method for differential encoding trellis codes is presented that was suggested by the authors representation

on block coded modulation with interblock memory block coded modulation with interblock memory bcmim is a variation of block coded modulation bcm which is designed for multilevel coding by providing interblock memory between adjacent blocks the coding rate of a bcmim scheme can be increased without decreasing the minimum squared euclidean distance msed as compared to the original bcm in an early version of bcmim interblock coding is provided only between the first two coding levels of adjacent blocks in this paper we design bcmim with a more general form for which interblock coding can be introduced among many coding levels in this way we can further increase the coding rate of bcmim without decreasing the msed we provide many examples to show the advantages of bcmim with the general form most of the examples are designed based on multidimensional signal sets since a multidimensional signal set can provide more coding levels than a two dimensional 2 d signal set

trellis coding with multidimensional qam signal sets trellis coding using multidimensional quadrature amplitude modulation qam signal sets is investigated finite size 2d signal sets are presented that have minimum average energy are 90 degrees rotationally symmetric and have from 16 to 1024 points the best trellis codes using the finite 16 qam signal set with two four six and eight dimensions are found by computer search the multidimensional multi d signal set is constructed from the 2 d signal set the best moderate complexity trellis codes for infinite lattices with two four six and eight dimensions are also found the minimum free squared euclidean distance and number of nearest neighbors for these codes were used as the selection criteria many of the multi d codes are fully rotationally invariant and give asymptotic coding gains up to 6 0 db from the infinite lattice codes the best codes for transmitting j j 1 4 j 1 3 j 1 2 j 2 3 and j 3 4 b sym j an integer are presented

i 1 optimal control of multivariable systems with output norm constraints in this paper we consider the l1 optimal control problem for general rational plants it is shown that for plants with no poles or zeros on the unit circle an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs exactly or approximately optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed loop transfer function no assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators it is shown that constrained problems in which a set of outputs is regulated subject to l norm constraints on another set of outputs can be solved using a slight modification of the same algorithm

on multilevel block modulation codes the multilevel technique for combining block coding and modulation is investigated a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures a specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed given a multilevel block modulation code c with no interdependency among the binary component codes the proposed method gives a multilevel block modulation code c that has the same rate as c a minimum squared euclidean distance not less than that of c a trellis diagram with the same number of states as that of c and a smaller number of nearest neighbor codewords than that of c finally a technique is presented for analyzing the error performance of block modulation codes for an additive white gaussian noise awgn channel based on soft decision maximum likelihood decoding error probabilities of some specific codes are evaluated by simulation and upper bounds based on their euclidean weight distributions

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

persistent disturbance rejection via static state feedback in contrast with spl hscr sub spl infin and spl hscr sub 2 control theories the problem of persistent disturbance rejection l sup 1 optimal control leads to dynamic controllers even when the states of the plant are available for feedback using viability theory shamma showed 1993 in a nonconstructive way that in the state feedback case the same performance achieved by any dynamic linear time invariant controller can be achieved using memoryless nonlinear state feedback in this paper we give an alternative constructive proof of these results for discrete and continuous time systems the main result of the paper shows that in both cases the l sup 1 norm achieved by any stabilizing state feedback linear dynamic controller can be also achieved using a memoryless variable structure controller

suboptimum decoding of decomposable block codes to decode a long block code with a large minimum distance by maximum likelihood decoding is practically impossible because the decoding complexity is simply enormous however if a code can be decomposed into constituent codes with smaller dimensions and simpler structure it is possible to devise a practical and yet efficient scheme to decode the code this paper investigates a class of decomposable codes their distance and structural properties it is shown that this class includes several classes of well known and efficient codes as subclasses several methods for constructing decomposable codes or decomposing codes are presented a two stage soft decision or hard decision decoding scheme for decomposable codes their translates or unions of translates is devised and its error performance is analyzed for an awgn channel the two stage soft decision decoding is suboptimum error performances of some specific decomposable codes based on the proposed two stage soft decision decoding are evaluated it is shown that the proposed two stage suboptimum decoding scheme provides an excellent trade off between the error performance and decoding complexity for codes of moderate and long block length

algebraic construction of cyclic codes over z sub 8 with a good euclidean minimum distance let s 8 denote the set of the eight admissible signals of an 8psk communication system the alphabet s 8 is endowed with the structure of z sub 8 the set of integers taken modulo 8 and codes are defined to be z sub 8 submodules of z sub 8 sup n three cyclic codes over z sub 8 are then constructed their length is equal to 6 8 and 7 and they respectively contain 64 64 and 512 codewords the square of their euclidean minimum distance is equal to 8 16 4 spl radic 2 and 10 2 spl radic 2 respectively the size of the codes of length 6 and 7 can be doubled while the euclidean minimum distance remains the same

lsb coded 8psk signals an 8psk scheme with the least significant bit lsb golay coded is proposed and its performance is analyzed with hard decision decoding the proposed scheme can achieve 1 db asymptotic coding gain and also save 26 bandwidth as compared with uncoded qpsk scheme

l sub 1 analysis and design of sampled data systems the focus of this work is l sub 1 optimal control of sampled data systems a converging approximation procedure is derived to compute the l sub infinity induced norm of closed loop finite dimensional linear time invariant lti sampled data systems an approximation method is developed to synthesize l sub 1 optimal sampled data regulators finally an example is provided that illustrates the l sub 1 analysis and design techniques presented

asymptotic upper bounds on the minimum distance of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of signal points in rn when a trellis code is used to encode data at the rate of k bits channel symbol each channel input depends not only on the most recent block of k bits to enter the encoder but will also depend on a set of bits preceding this block the bits determine the state of the encoder and the most recent block of k bits generates the channel symbol conditional on the encoder state the performance of a trellis code depends on a suitably defined minimum distance property of that code this paper obtains upper bounds on this minimum distance that are better than any previously known

on static feedback for the l 1 and other optimal control problems although e 1 optimal linear state feedback controllers are known to be dynamic it has been shown that suboptimal performance arbitrarily closed to optimal can be achieved by using a static non linear feedback law in this paper this fact is established by using a novel approach which shows that the result is a natural consequence of elementary state space theory the approach is motivated by recent works in active vision systems which have considered a state feedback problem tightly connected with e 1 optimization this problem which has independent interest is discussed in some detail the new formulation of the problem provides additional insight in e 1 state feedback in particular it leads naturally to some extensions which do not follow in a straightforward manner from previous works on the subject

a coded modulation scheme with interblock memory proposes a coded modulation scheme with interblock memory the proposed scheme has a multi stage coding structure however at some coding stage the coding designs for every two adjacent blocks are related compared to coded modulation schemes for which each block is independent of the others the introduction of interblock coding provides additional flexibility in the design in this way for the proposed scheme one can achieve a large minimum euclidean distance while the number of nearest neighbors is not too large the authors also design a multi stage decoding algorithm which is optimum in each stage and has low decoding complexity three specific examples are provided to demonstrate the advantages of the proposed scheme

an upper bound on the volume of discrete spheres finite length sequences over a finite alphabet with weights are considered an information theoretic upper bound on the number of such sequences whose weight does not exceed some given threshold is presented

state feedback e 1 optimal controllers can be dynamic abstract this paper considers l 1 optimal control problems given by discrete time systems with full state feedback scalar control and scalar disturbance motivation stems from the central role that this problem structure played in the development of the h 2 and h theories first systems with a scalar regulated output are studied singular problems sufficient conditions are given based on the non minimum phase zeros of the transfer function from the control to the regulated output for the existence of a static l 1 optimal controller a simple way to compute the static gain is provided using pole placement ideas it is shown however that having full state information does not prevent the l 1 optimal controller from being dynamic in general and that examples with arbitrarily high order optimal controllers can be easily constructed second problems with two regulated outputs one of them being the scalar control are considered non singular problems it is shown by means of a class of fairly general examples for which exact l 1 optimal solutions are constructed that such problems may not have static controllers that are l 1 optimal thus concluding that a separation structure does not occur in these problems in general

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

performance of pll based optical oppm communication systems the power spectral density psd of a direct detected optical signal with overlapping pulse position modulation oppm scheme is derived it is demonstrated that this spectrum contains a strong periodic component at the signal symbol frequency thereby enabling a simple pll device to provide joint symbol and slot synchronization the variance of the timing error for a linearized pll synchronizer is shown to be mainly dominated by and is inversely proportional to the product of the pll closed loop bandwidth and symbol duration of the oppm signal the performance of a shot noise limited pll based optical oppm communication system is then assessed in terms of the overall system symbol error rate

block coded psk modulation using two level group codes over dihedral groups a length n group code over a group g is a subgroup of g sup n under component wise group operation group codes over dihedral groups d sub m with 2m elements that are two level constructible using a binary code and a code over z sub m residue class integer ring modulo m as component codes are studied for arbitrary m a set of necessary and sufficient conditions on the component codes for the two level construction to result in a group code over d sub m are obtained the conditions differ for m odd and even using two level group codes over d sub m as label codes the performance of a block coded modulation scheme is discussed under all possible matched labelings of 2m apsk and 2m spsk asymmetric and symmetric psk signal sets in terms of the minimum squared euclidean distance matched labelings that lead to automorphic euclidean distance equivalent codes are identified it is shown that depending upon the ratio of hamming distances of the component codes some labelings perform better than others the best labeling is identified under a set of restrictive conditions finally conditions on the component codes for phase rotational invariance properties of the signal space codes are discussed

complexity of matroid property algorithms a general theorem is proved which can be used to show that for a large number of matroid properties there is no good algorithm of a certain type for determining whether these properties hold for general matroids specifically there exists no algorithm in which the matroid is represented by an independence test oracle or an oracle polynomially related to an independence test oracle and which solves the problem in question after a number of calls on the oracle which is bounded by a polynomial in the number of elements of the ground set of the matroid

bounds on the minimum distance of trellis codes the performance of trellis codes is determined by their minimum euclidean distance upper bounds on this minimum distance valid for phase shift keyed psk signals that improve on previously derived bounds are derived although the bound is valid only for psk signals the bounding techniques developed here can be extended to other equal energy configurations and hence could pave the way to obtaining more general results