optimal domain for the hardy operator abstract we study the optimal domain for the hardy operator considered with values in a rearrangement invariant space in particular this domain can be represented as the space of integrable functions with respect to a vector measure defined on a ring a precise description is given for the case of the minimal lorentz spaces

the greatest fixed points and rational omega tree languages abstract rational omega tree languages are defined by extending the notion of rational or regular expressions for languages and their properties are investigated they are characterized by means of greatest fixed points of certain functions and are shown to be precisely the omega tree languages recognized by rabin s special automata a simple normal form for rational omega tree languages is also presented

kantorovich wright integration and representation of vector lattices abstract the aim of this work is to introduce a purely order based kantorovich wright type integration of scalar functions with respect to a vector measure defined on a ring and taking values in a dedekind complete vector lattice and use it for obtaining general representation theorems for dedekind complete vector lattices

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

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

some block and trellis coded modulations for the rayleigh fading channel the error performance of a modulation code over a channel depends on several distance parameters and the path multiplicity of the code for the awgn channel the error performance of a modulation code depends mainly on its minimum squared euclidean distance and path multiplicity for the rayleigh fading channel however the error performance of a modulation code depends strongly on its minimum symbol distance minimum product distance and path multiplicity it depends on the minimum squared euclidean distance in a lesser degree this paper is concerned with the construction of block and trellis mpsk modulation codes for the rayleigh fading channel in each construction the distance parameters are chosen to achieve good error performance with reduced decoding complexity

a komlos theorem for abstract banach lattices of measurable functions abstract consider a banach function space x of classes of locally integrable functions over a finite measure space with the weak fatou property day and lennard 2010 9 proved that the theorem of komlos on convergence of cesaro sums in l 1 0 1 holds also in these spaces i e for every bounded sequence f n n in x there exists a subsequence f n k k and a function f x such that for any further subsequence h j j of f n k k the series 1 n j 1 n h j converges a e to f in this paper we generalize this result to a more general class of banach spaces of classes of measurable functions spaces l 1 of integrable functions with respect to a vector measure on a ring and explore to which point the fatou property and the komlos property are equivalent in particular we prove that this always holds for ideals of spaces l 1 with the weak fatou property and provide an example of a banach lattice of measurable functions that is fatou but do not satisfy the komlos theorem

minimal and maximal methods of interpolation abstract we show that several interpolation functors including the widely used real and complex methods are minimal or maximal extensions from a single couple of banach spaces various consequences are drawn from this property

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

on the spectrum of distances of a multilevel code decoded by a multistage decoder in this correspondence we are concerned with the error rates contributed by component codes in a multilevel code decoded by a multistage decoder these error rates are required for estimating the performance of the structure but more importantly they can serve as a design tool for achieving high coding gain the latter objective can be reached by approaching a balance among these error rates for evaluating the error rate contributed by a component code it is essential to calculate the corresponding spectrum of euclidean distances a method for computing this spectrum is developed in this correspondence the method is general and applicable to any signal constellation and convolutional as well as block component codes the error coefficient available in the literature for some multilevel codes with an infinite size signal constellation is shown to be significantly different from that of a practical finite constellation note that the complete spectrum is essential when codewords of a component code with hamming distance beyond the minimum distance affect the error rate see e g turbo codes

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

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

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

factorizing operators on banach function spaces through spaces of multiplication operators abstract in order to extend the theory of optimal domains for continuous operators on a banach function space x over a finite measure we consider operators t satisfying other type of inequalities than the one given by the continuity which occur in several well known factorization theorems for instance pisier factorization theorem through lorentz spaces p th power factorable operators we prove that such a t factorizes through a space of multiplication operators which can be understood in a certain sense as the optimal domain for t our extended optimal domain technique does not need necessarily the equivalence between and the measure defined by the operator t and by using rings is allowed to be infinite classical and new examples and applications of our results are also given including some new results on the hardy operator and a factorization theorem through hilbert spaces

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

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

a note on ω regular languages abstract this paper is a continuation of the work by landweber 5 to clarify the relationship between classes of languages accepted by finite automata we study their properties in the topological framework introduced by boasson and nivat 1 we characterize the classes in terms of borel hierarchy and show some interrelation of them

diversity embedded space time codes rate and diversity impose a fundamental tradeoff in wireless communication high rate space time codes come at a cost of lower reliability diversity and high reliability diversity implies a lower rate however wireless networks need to support applications with very different quality of service qos requirements and it is natural to ask what characteristics should be built into the physical layer link in order to accommodate them in this paper we design high rate space time codes that have a high diversity code embedded within them this allows a form of communication where the high rate code opportunistically takes advantage of good channel realizations while the embedded high diversity code provides guarantees that at least part of the information is received reliably we provide constructions of linear and nonlinear codes for a fixed transmit alphabet constraint the nonlinear constructions are a natural generalization to wireless channels of multilevel codes developed for the additive white gaussian noise awgn channel that are matched to binary partitions of quadrature amplitude modulation qam and phase shift keying psk constellations the importance of set partitioning to code design for the wireless channel is that it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain we investigate the systems implications of embedded diversity codes by examining value to unequal error protection rate opportunism and packet delay optimization these applications demonstrate that diversity embedded codes have the potential to outperform traditional single layer codes in moderate signal to noise snr regimes

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

real interpolation method on spaces of scalar integrable functions with respect to vector measures abstract for a given measurable space and a vector measure m x with values in a banach space x we consider the spaces of p power integrable and weakly integrable respectively functions with respect to the measure m l p m and l w p m for 1 p in this note we describe the real interpolated spaces that we obtain when the k method is applied to any couple of these spaces

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

multiplication operators on spaces of integrable functions with respect to a vector measure we study continuity and other properties related to some kind of compactness of multiplication operators between different spaces of pth power integrable scalar functions with respect to a vector measure

characterization of ω regular languages by first order formulas abstract first order formulas are used to specify various ways of acceptance of languages by deterministic finite automata and we study the relationship between the arithmetic hierarchy of the formulas in prenex normal form and the topological hierarchy of the accepted languages among other things it is proved that the languages accepted by finite automata under the accepting conditions specified by 1 type formulas are precisely open regular languages those accepted under the conditions specified by 2 type formulas coincide with the regular languages which are denumerable unions of closed sets and that as long as the accepting conditions are specified by first order formulas the accepted languages remain to be regular

on trellis codes with a delay processor and a signal mapper it is already known that a trellis code t which is constructed by using the encoder of a convolutional code c with short constraint length followed by a delay processor and a signal mapper is equivalent to a trellis code with large constraint length in this paper we derive a new lower bound on the free distance of t which in some cases is better than the previously derived bound moreover instead of the decoding used in earlier publications we apply iterative decoding on both tailbiting and zero tail representations of t to take advantage of the new lower bound and in the meantime to decrease the associated error coefficient caused by the decoding used in earlier publications comparisons among various designs of such a trellis code and some well known coding methods are also provided

reflexivity of function spaces associated to a σ finite vector measure abstract for a vector measure defined on a ring with values in a banach space and 1 p we characterize the reflexivity of the different spaces l w p integrability in the weak sense l p integrability in the strong sense and l p integrability in the choquet sense

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

multilevel coded modulation for unequal error protection and multistage decoding ii asymmetric constellations in this paper theoretical upper bounds and computer simulation results on the error performance of multilevel block coded modulations for unequal error protection uep and multistage decoding are presented it is shown that nonstandard signal set partitionings and multistage decoding provide excellent uep capabilities beyond those achievable with conventional coded modulation the coding scheme is designed in such a way that the most important information bits have a lower error rate than other information bits the large effective error coefficients normally associated with standard mapping by set partitioning are reduced by considering nonstandard partitionings of the underlying signal set the bits to signal mappings induced by these partitionings allow the use of soft decision decoding of binary block codes moreover parallel operation of some of the staged decoders is possible to achieve high data rate transmission so that there is no error propagation between these decoders hybrid partitionings are also considered that trade off increased intraset distances in the last partition levels with larger effective error coefficients in the middle partition levels the error performance of specific examples of multilevel codes over 8 psk and 64 qam signal sets are simulated and compared with theoretical upper bounds on the error performance

combination of bcm and tcm with 90 spl deg 180 spl deg and 270 spl deg phase rotational invariance two systematic schemes to combine block coded modulation bcm and trellis coded modulation tcm are proposed in the first scheme the signal points which are used in tcm should be partitioned by the proper bcm systems constructed by a multilevel construction method the asymptotic coding gain will be 6 02 3 01 n db where n is the length of the bcm systems since the average transmission power can be reduced by using a denser signal lattice the main idea of the second scheme is to construct the tcm system based on the signal points of a denser lattice formed by a proper bcm system hence we can get a higher coding gain which is a combination of both the distance gain of tcm and the density gain of bcm theoretically the net coding gain of this proposed scheme can reach 5 27 db in the case of an 8 d constellation and 7 15 db in the case of a 16 d constellation for practical implementation the phase ambiguity problems for both schemes are considered and solved by a differential encoder decoder

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

multilevel construction of block and trellis group codes the theory of group codes has been shown to be a useful starting point for the construction of good geometrically uniform codes in this paper we study the problem of building multilevel group codes i e codes obtained combining separate coding at different levels in such a way that the resulting code is a group code a construction leading to multilevel group codes for semi direct and direct products is illustrated the codes that can be obtained in this way are identified new geometrically uniform euclidean space codes obtained from multilevel codes over abelian and nonabelian groups are presented

multilevel trellis mpsk modulation codes for the rayleigh fading channel the multilevel coding technique is used for constructing multilevel trellis m ary phase shift keying mpsk modulation codes for the rayleigh fading channel in the construction of a code all the factors which affect the code performance and its decoding complexity are considered the error performance of some of these codes based on both one stage optimum decoding and multistage suboptimum decoding has been simulated the simulation results show that these codes achieve good error performance with small decoding complexity

the measure theoretic aspects of entropy part i abstract let p be a countably additive probability measure and be any 0 valued countably additive measure both on a algebra u over a space we define a p dependent countably additive measure h on the ring u a a u and a with values in with the property that in case u h is the total entropy of p relative to we study the lebesque decomposition of h with respect to

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

an improvement to generalized minimum distance decoding a novel acceptance criterion that is less stringent than previous criteria is developed the criterion accepts the codeword that is closest to the received vector for many cases where previous criteria fail to accept any codeword as a result the performance of generalized minimum distance gmd decoding is better if the new criterion is used for m ary signaling the weights used in gmd decoding are generalized to permit each of the possible m symbol values to have a different weight

multiple symbol differentially detected multilevel codes for the rayleigh fading channel conventional differential detection is known to perform poorly on the fast fading rayleigh fading channel due to the rapid variation of the channel state the technique of multiple symbol differential detection msdd improves the error performance by detecting over a sequence of symbols and exploiting the inherent correlation of the fading process to further reduce the error rate we need to introduce some form of coding successful coding for the rayleigh fading channel requires interleaving to decorrelate the channel a conflicting requirement to msdd we propose a solution consisting of interleaving blocks of l m ary phase shift keying mpsk symbols that are multiple symbol differentially detected the blocks are treated as elements of an m sup l symbol alphabet over which a multilevel code based on geometrically uniform partitions is defined

x automata on ω words abstract for any storage type x the languages accepted by x automata are investigated six accepting conditions including those introduced by landweber are compared for x automata the inclusions between the corresponding six families of languages are essentially the same as for finite state automata apart from unrestricted automata also real time and deterministic automata are considered the main tools for this investigation are 1 a characterization of the languages accepted by x automata in terms of inverse x transductions of finite state languages and 2 the existence of topological upper bounds on some of the families of accepted languages independent of the storage type x

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

new multilevel codes over gf q set partitioning is applied to multidimensional signal spaces over gf q i e gf sup n1 q n1 or d are presented these codes use reed solomon codes as component codes longer multilevel block codes are also constructed using q ary block codes with block length longer than q 1 as component codes some quaternary multilevel block codes are presented with the same length and number of information symbols as but larger distance than the best previously known quaternary one level block codes it is proved that if all the component block codes are linear the multilevel block code is also linear low rate q ary convolutional codes word error correcting convolutional codes and binary to q ary convolutional codes can also be used to construct multilevel trellis codes over gf q or binary to q ary trellis codes

the three subfamilies of rational ω languages closed under ω transduction abstract the transductions defined by gire as bimorphisms coincide with the compositions of non erasing morphisms and inverse non erasing morphisms we prove that there are exactly three subfamilies of rational languages which are closed under transduction the family of rational adherences the family of rational languages whose complementary is deterministic and the whole family of rational languages

a note on real interpolation of lp spaces of vector measures on δ rings abstract we describe the real interpolation spaces obtained when we apply the real k method of lions peetre to banach lattices of p integrable and weakly p integrable functions with respect to a banach space valued measure defined on a ring in general the obtained results are quite different from those in the case of vector measures on algebras described in 9 however we find a wide class of vector measures on rings for which the results on algebras hold true

language theoretical representations of ω languages abstract in this paper we give language theoretical representations for some classes of languages defined by finite automata the classes considered in this paper are proved to be the classes of languages represented as f f pf or p p where p and p are prefix free regular languages and f and f are prefix free finite languages

automata on infinite objects and their applications to logic and programming abstract we introduce various types of automata top down automata and bottom up automata on infinite trees we study the power of determinstic and nondeterministic tree automata and prove that deterministic and non deterministic bottom up tree automata accept the same infinite tree sets we establish a relationship between tree automata logic programs recursive program schemes and the monadic second order theory of the tree we prove that the equivalence of two rational logic programs is decidable

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

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 coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

accepting conditions for automata on ω languages abstract in this paper we study the languages accepted by finite automata under a new type of accepting conditions which are based on whether the automaton enters all of its accepting states infinitely many times or not we investigate the classes of languages defined thereby in relation to other well known subclasses of the class of regular languages

projection lemmas for ω languages abstract the paper presents projection lemmas relating the infinite behaviour of deterministic and unboundedly branching nondeterministic infinite automata

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

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

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

topological characterizations of infinite tree languages abstract in this paper we define several types of acceptance of finite automata for infinite trees and study the topological properties of the tree languages accepted thereby as a consequence we show that the two classes of tree languages accepted by nondeterministic tree automata in the following two types of acceptance coincide 1 1 an infinite tree is accepted iff there is a run for such that on each path an accepting state is contained 2 2 an infinite tree is accepted iff every run for contains an accepting state

coded phase frequency modulation channel coding combined with expanded signal sets has been shown 1 to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals in this paper new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented the new schemes combine fsk and psk modulation and make use of trellis coding and viterbi decoding to improve error performance over uncoded modulation the free euclidean distance is calculated for several classes of codes and upper bounds and simulation results are also presented for some simple codes the spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two dimensional modulation formats differential encoding and various extensions of the basic scheme are also discussed

infinite word languages and continuous mappings abstract languages with infinite words have often been studied as subsets of a topological space the topology used for this purpose was always the natural topology of sequences this paper suggests that another topology may be more useful it is obtained by taking lim w as the derived set of w the resulting topological space is shown to be completely regular strongly zero dimensional and not normal the languages appearing in the theory of automata are shown to be closely related to functionally closed sets continuous inverse images of the set 0 as a consequence a number of known results can be expressed and proved in terms of continuous mappings

when and where the orlicz and luxemburg quasi norms are equivalent abstract we study the equivalence between the orlicz and luxemburg quasi norms in the context of the generalized orlicz spaces associated to an n function and a quasi banach function space x over a positive finite measure we show that the orlicz and the luxemburg spaces do not coincide in general and also that under mild requirements fatou property strictly monotone renorming the coincidence holds we use as a technical tool the classes l w m l m and l m of orlicz spaces of scalar integrable functions with respect to a banach space valued countably additive vector measure m providing also some new results on these spaces

the integration theory of banach space valued measures and the tonelli fubini theorems ii pettis integration in this part of the paper we turn to the concepts of gelfand and pettis integrability and integration of scalar valued functions with respect to a banach space valued measure the problem before us and our method for solving it have been outlined in section 1 of part i of this paper in what follows we adhere to the notation of part i and continue the trend set in that part all references with numbers such as 1 2 2 3 and a5 are to the items in sections 1 and 2 and appendix a in part i

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

two level coding based on trellis coded modulation and reed solomon codes a number of two level codes based on trellis coded modulation tcm schemes and their matched single or double error correcting reed solomon codes using qam constellations are presented and evaluated compared to the well known 4d 16 state tcm scheme with a comparable bandwidth efficiency these two level codes provide greater immunity from both gaussian and impulse noise at the cost of a reasonably higher complexity and a longer decoding delay on the order of a few hundred symbols the authors also show how to cope with phase ambiguities of the constellation in these two level codes both rotationally invariant coding and rotation detecting techniques are considered

various hierarchies of wω regular sets barua 1992 studied a hierarchy rn n 1 2 3 where rn is a class of regular sets which are decomposed into n rational g sets forming a decreasing sequence on the other hand kaminski 1985 defined a hierarchy bm m 1 2 3 where bm is a class of regular sets which are decomposed into 2m rational g sets not necessarily forming a decreasing sequence we prove that r2n bn in spite of the difference of defining conditions

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

complex interpolation of lp spaces of vector measures on δ rings abstract we apply the calderon interpolation methods to banach lattices of p integrable and weakly p integrable functions with respect to a banach space valued measure defined on a ring in general the results we obtain are quite different from those in the case of vector measures on algebras however we find a wide class of vector measures on rings for which the results on algebras hold true

further results on noncoherent block coded mpsk transactions papers a novel noncoherent block coding scheme called noncoherent block coded mpsk nbc mpsk was proposed recently in this paper we present further research results on nbc mpsk we first focus on the rotational invariance ri of nbc mpsk based on the ri property of nbc mpsk with multistage decoding a noncoherent near optimal linear complexity multistage decoder for nbc mpsk is proposed then we investigate a tree search ml decoding algorithm for nbcmpsk the derived algorithm is shown to have low complexity and excellent error performance in this paper we also utilize the idea of the nbc mpsk to design noncoherent space time block codes called noncoherent space time block coded mpsk nstbc mpsk for two transmit antennas we propose a signal set with set partitioning and derive the minimum noncohent distance of nstbc mpsk with this signal set for the decoding of nstbc mpsk we modify the ml decoding algorithm of nbc mpsk and propose an iterative hard decision decoding algorithm compared with training codes and unitary space time modulation nbc mpsk and nstbc mpsk have larger minimum noncoherent distance and thus better error performance for the noncoherent ml decoder

local rule distributions language complexity and non uniform cellular automata this paper investigates a variant of cellular automata namely n ca indeed n ca are cellular automata which can have different local rules at each site of their lattice the assignment of local rules to sites of the lattice completely characterizes n ca in this paper sets of assignments sharing some interesting properties are associated with languages of bi infinite words the complexity classes of these languages are investigated providing an initial rough classification of n ca

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

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

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

an approach to ungerboeck coding for rectangular signal sets corresp a method of finding good ungerboeck codes for large rectangular quadrature amplitude modulation qam signal sets is described using the concept of euclidean weights due to ungerboeck we prove that a 2 n point basic constellation may be employed to determine exactly the free distance for an ungerboeck coded rectangular 2 m point set when m n 1 bits are uncoded and the remaining bits pass through a rate n 1 n convolutionai encoder it is shown that rate 2 3 encoders may be used to achieve most of the theoretically possible coding gain in the proposed scheme where the effect of the error coefficient on the coding gain has been considered

trellis codes for the optical direct detection channel it is observed that the reduced complexity minimum distance search method of zehavi and wolf 1987 can be extended from codes designed using the squared euclidean distance measure to any measure which is additive over the code branches c n georghiades 1989 has derived such a metric for codes for the direct detection optical channel the search method is applied to find codes for four and eight point overlapping pulse position modulation oppm with large minimum distance and a small number of codewords at that distance

reduced lists of error patterns for maximum likelihood soft decoding a method whereby a substantially reduced family of error patterns called survivors may be created for maximum likelihood soft decoding is introduced the family of survivor depends on the received word a decoder based on this approach first forms the survivors then scores them rather than obtaining the survivors by online elimination of error patterns the use of predetermined lists that represent all families of survivors is proposed

techniques of bounding the probability of decoding error for block coded modulation structures two techniques for upper bounding the average probability of decoding error in coded modulation structures are presented the first bound which is applicable to the additive white gaussian noise awgn channel is tighter than the well known union bound and the minimum distance bound especially for low signal to noise ratio it is shown that for the leech lattice this upper bound is very close to a sphere lower bound for the second upper bound which is applicable to any memoryless channel not necessarily awgn a method of random coset coding is presented for the awgn channel a tighter upper bound is obtained by employing the method of random coset coding for calculating the average spectrum of distances of the code which is required for the computation of the first upper bound

finite acceptance of infinite words abstract in this paper we consider the following two types of finite acceptance of infinite words by finite automata an infinite word is accepted if and only if there is a run on input for which 1 1 an accepting state is visited at least once or 2 2 an accepting state is visited at least once but only finitely often the resulting classes of regular languages are characterized by language theoretic means and they are positioned into the known hierarchies of regular languages

reasoning about infinite computations we investigate extensions of temporal logic by connectives defined by finite automata on infinite words we consider three different logics corresponding to three different types of acceptance conditions finite looping and repeating for the automata it turns out however that these logics all have the same expressive power and that their decision problems are all pspace complete we also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem