the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

a family of distributed space time trellis codes with asynchronous cooperative diversity in current cooperative communication schemes to achieve cooperative diversity synchronization between terminals is usually assumed which may not be practical since each terminal has its own local oscillator in this paper based on the stack construction proposed by hammons and el gamal we first construct a family of space time trellis codes for bpsk modulation scheme that is characterized to possess the full cooperative diversity order without the synchronization assumption we then generalize this family of the space time trellis codes from bpsk to higher order qam and psk modulation schemes based on the unified construction proposed by lu and kumar some diversity product properties of space time trellis codes are studied and simplified decoding methods are discussed simulation results are given to illustrate the performance of the newly proposed codes

a unified construction of space time codes with optimal rate diversity tradeoff the problem of constructing space time st block codes over a fixed desired signal constellation is considered in this situation there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code the transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal to noise ratio snr in the setting of a quasi static channel model let n sub t denote the number of transmit antennas and t the block interval for any n sub t spl les t a unified construction of n sub t spl times t st codes is provided here for a class of signal constellations that includes the familiar pulse amplitude pam quadrature amplitude qam and 2 sup k ary phase shift keying psk modulations as special cases the construction is optimal as measured by the rate diversity tradeoff and can achieve any given integer point on the rate diversity tradeoff curve an estimate of the coding gain realized is given other results presented here include i an extension of the optimal unified construction to the multiple fading block case ii a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes iii the providing of a linear dispersion form for the underlying binary block codes iv a gray mapped version of the unified construction and v a generalization of construction of the ary case corresponding to constellations of size sup k items ii and iii are aimed at simplifying the decoding of this class of st codes

remarks on space time codes including a new lower bound and an improved code this article presents a new asymptotically exact lower bound on pairwise error probability of a space time code as well as an example code that outperforms the comparable orthogonal design based space time odst code also contained in the article are an exact expression for pairwise error probability pep signal design guidelines and some observations relating to the reception of odst codes

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

new families of m ary sequences with low correlation constructed from sidel nikov sequences in this correspondence for a positive integer m and a prime p such that m pn 1 three families of m ary sequences using the m ary sidel nikov sequences with period pn 1 are constructed two small families contain pn 1 2 m 2 or pn m 3 m ary sequences and both of their maximum magnitudes of correlation values are upper bounded by 2 radic pn 6 the largest family has its maximum magnitude of correlation values upper bounded by 3 radic pn 5 and the family size is m 1 2 2n 1 1 m 1 for p 2 or m 1 2 pn 3 2 m m 1 2 for an odd prime p

diversity multiplexing tradeoff and outage performance for rician mimo channels in this paper we analyze the diversity multiplexing tradeoff dmt originally introduced by zheng and tse and outage performance for rician multiple input multiple output mimo channels the dmt characteristics of rayleigh and rician channels are shown to be identical in a high signal to noise ratio snr regime the log log plot of outage probability versus snr curve for a rician channel is a shifted version of that for the corresponding rayleigh channel the snr gap between the outage curves of the rayleigh and rician channels is derived the dmt and outage performance are also analyzed for rician multiple input single output miso single input multiple output simo channels over a finite snr regime a closed form expression for the outage probability is derived and the finite snr dmt characteristic is analyzed it is observed that the maximum diversity gain can be achieved at some finite snr the maximum gain tends to increase linearly with the rician factor the finite snr diversity gain is shown to be a linear function of the finite snr multiplexing gain the consistency between the dmts for finite and infinite snrs is also shown

ucht based complex sequences for asynchronous cdma system the use of orthogonal spreading codes has attracted much attention due to their ability to suppress interference from other users compared with the nonorthogonal sequences in the synchronous case in this paper new sets of orthogonal sequences derived from the unified complex hadamard transforms uchts are investigated various correlation properties of the sequences are mathematically derived and analyzed it is shown that some ucht sequences provide better autocorrelation properties than orthogonal walsh hadamard sequences performance comparisons between ucht sequences gold small set of kasami and m sequences show that some ucht sequences outperform these well known spreading sequences under simulation of systems in the presence of multiple access interference and additive white gaussian noise

a unified framework for tree search decoding rediscovering the sequential decoder we consider receiver design for coded transmission over linear gaussian channels we restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search clps here a tree search framework for solving the clps is adopted in our framework the clps algorithm is decomposed into the preprocessing and tree search stages the role of the preprocessing stage is to expose the tree structure in a form matched to the search stage we argue that the forward and feedback matrix filters of the minimum mean square error decision feedback equalizer mmse dfe are instrumental for solving the joint detection and decoding problem in a single search stage it is further shown that mmse dfe filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity at the expense of a marginal performance loss for the search stage we present a generic method based on the branch and bound bb algorithm and show that it encompasses all existing sphere decoders as special cases the proposed generic algorithm further allows for an interesting classification of tree search decoders sheds more light on the structural properties of all known sphere decoders and inspires the design of more efficient decoders in particular an efficient decoding algorithm that resembles the well known fano sequential decoder is identified the excellent performance complexity tradeoff achieved by the proposed mmse dfe fano decoder is established via simulation results and analytical arguments in several multiple input multiple output mimo and intersymbol interference isi scenarios

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

generic construction of binary sequences of period 2n with optimal odd correlation magnitude based on quaternary sequences of odd period n binary sequences with low odd correlation have important applications in communication systems to reduce interference in this paper using the interleaving technique we present a generic connection between binary sequences with low odd correlation and quaternary sequences with low even correlation as a result some new binary sequences with optimal odd auto correlation magnitude are obtained besides two sets consisting of 2 n 1 binary sequences of period 2 2 n 1 with the maximum odd correlation magnitude 2 n 1 2 2 are derived which are the first two optimal classes of binary sequence sets achieving the sarwate bound on the odd correlation magnitude in the literature

translates of linear codes over z sub 4 we give a method to compute the complete weight distribution of translates of linear codes over z sub 4 the method follows known ideas that have already been used successfully by others for hamming weight distributions for the particular case of quaternary preparata codes we obtain that the number of distinct complete weights for the dual preparata codes and the number of distinct complete coset weight enumerators for the preparata codes are both equal to ten independent of the code length

prime phase sequences with periodic correlation properties better than binary sequences for the case where p is an odd prime n or 2 is an integer and omega is a complex primitive pth root of unity a construction is presented for a family of p sup n p phase sequences symbols of the form omega sup i where each sequence has length p sup n 1 and where the maximum nontrivial correlation value c sub max does not exceed 1 square root p sup n a complete distribution of correlation values is provided as a special case of this construction a previous construction due to sidelnikov 1971 is obtained the family of sequences is asymptotically optimum with respect to its correlation properties and in comparison with many previous nonbinary designs the present design has the additional advantage of not requiring an alphabet of size larger than three the new sequences are suitable for achieving code division multiple access and are easily implemented using shift registers they wee discovered through an application of deligne s bound 1974 on exponential sums of the weil type in several variables the sequences are also shown to have strong identification with certain bent functions

two new families of optimal binary sequences obtained from quaternary sequences in this paper we present two optimal binary families of sequences of length 2n 1 and 2 2n 1 for odd integer n they are obtained as the images of proposed optimal quaternary sequences under the most significant bit and the gray maps the first family has 2n 1 sequences of length 2n 1 and the identical correlation distribution to that of gold sequences and gold like sequences and the second family of sequences of length 2 2n 1 has 2n sequences and the same correlation values as those of kerdock sequences

growth problems for avoidable words abstract a word w is said to avoid a word u if no block subword factor of w is the image of u under a homomorphism of free semigroups without unit the theory of words avoiding xx square free words has been much studied the word u is said to be avoidable on n letters if there are arbitrarily long words on an n letter alphabet that avoid u if u is avoidable on n letters for some n let u be the minimum possible such n we show that u has a linear bound in terms of the alphabet size of u we further show that there exists a word that is avoidable on four letters but not on three letters moreover if u is this word the number of words of length l on a u letter alphabet that avoid u has a polynomial bound in terms of l so that the question of the existence of such an example is resolved in the affirmative in contrast for xx the bound is known to be exponential

new optimal quadriphase sequences with larger linear span in this paper two new optimal families s and u of quadriphase sequences are presented compared to the family a constructed by boztas and the family d investigated by tang respectively the proposed families have the same optimal correlation properties and family size but larger linear spans

performance of ds cdma downlink systems with orthogonal ucht complex sequences this letter investigates a transmitted signaling technique using orthogonal unified complex hadamard transform ucht spreading sequences and the coherent rake receiver in direct sequence code division multiple access ds cdma downlinks to maintain the orthogonality between users and reduce the effect of multipath fading and interference from other users a general multipath fading channel model is assumed system performance is evaluated by means of signal to interference plus noise ratio sinr at the rake receiver it is shown that the sinr of the system employing ucht complex sequences is independent of the phase offsets between different paths while the sinr of the system using walsh hadamard wh sequences is related to the squared cosine of path phase offsets as a result the bit error ratio performance of the ds cdma downlink system employing ucht complex sequences is better than that of the system with wh sequences at high sinrs

letter frequency in infinite repetition free words we estimate the extremal letter frequency in infinite words over a finite alphabet avoiding some repetitions for ternary square free words we improve the bounds of tarannikov on the minimal letter frequency and prove that the maximal letter frequency is 255653 kolpakov et al have studied the function r such that r x is the minimal letter frequency in an infinite binary x free word in particular they have shown that r is discontinuous at 73 and at every integer at least 3 we answer one of their questions by providing some other points of discontinuity for r finally we propose stronger versions of dejean s conjecture on repetition threshold in which unequal letter frequencies are required

on the theory of space time codes for psk modulation the design of space time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas the lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords which is difficult to relate to traditional code designs over finite fields and rings we present general binary design criteria for psk modulated space time codes for linear bpsk qpsk codes the rank of binary projections of the unmodulated codewords as binary matrices over the binary field is a sufficient design criterion full binary rank guarantees full spatial diversity this criterion accounts for much of what is currently known about psk modulated space time codes we develop new fundamental code constructions for both quasi static and time varying channels these are perhaps the first general constructions other than delay diversity schemes that guarantee full spatial diversity for an arbitrary number of transmit antennas

on repetition free binary words of minimal density we study the minimal proportion density of one letter in n th power free binary words first we introduce and analyse a general notion of minimal letter density for any infinite set of words which don t contain a specified set of prohibited subwords we then prove that for n th power free binary words the density function is frac 1 n frac 1 n 3 frac 1 n 4 cal o frac 1 n 5 we also consider a generalization of n th power free words for fractional powers exponents a word is x th power free for a real x if it does not contain subwords of exponent x or more we study the minimal proportion of one letter in x th power free binary words as a function of x and prove in particular that this function is discontinuous at frac 7 3 as well as at all integer points n geq 3 finally we give an estimate of the size of the jumps

optimal throughput diversity delay tradeoff in mimo arq block fading channels in this paper we consider an automatic repeat request arq retransmission protocol signaling over a block fading multiple input multiple output mimo channel unlike previous work we allow for multiple fading blocks within each transmission arq round and we constrain the transmitter to fixed rate codes constructed over complex signal constellations in particular we examine the general case of average input power constrained con stellations with a fixed signaling alphabet of finite cardinality this scenario is a suitable model for practical wireless communications systems employing orthogonal frequency division multiplexing ofdm techniques over a mimo arq channel two cases of fading dynamics are considered namely short term static fading where channel fading gains change randomly for each arq round and long term static fading where channel fading gains remain constant over all arq rounds pertaining to a given message as our main result we prove that for the block fading mimo arq channel with a fixed signaling alphabet satisfying a short term power constraint the optimal signal to noise ratio snr exponent is given by a modified singleton bound relating all the system parameters to demonstrate the practical significance of the theoretical analysis we present numerical results showing that practical singleton bound achieving maximum distance separable codes achieve the optimal snr exponent

new families of binary sequences with low correlation for a positive integer n new families s and u of binary sequences of period 2 sup n 1 with low correlations are proposed where for some positive integer e s is defined for odd n e and u for even n e the family s has four valued correlations and is a generalization of the family of gold like sequences introduced by s boztas and p v kumar see ibid vol 40 p 532 7 1994 the family u which is also a generalization of the sequence family defined by p udaya polyphase and frequency hopping sequences obtained from finite rings ph d dissertation dept elec eng indian inst technol kanpur 1992 has six valued correlations the relationship between gold like sequences and gold sequences is the same as the relationship between the family s and the family constructed from the binary sequences partially contributed by r gold see ibid vol it 14 p 154 6 1968 t kasami see coordinated sci lab univ of illinois urbana champaign tech rep r 285 ad 632574 1966 and welch using a lifting idea no j s and kumar p v ibid vol 35 p 371 9 1989 for the families s and u families of binary sequences with the same correlation distributions and large linear span are also constructed

new constructions of quadratic bent functions in polynomial form new quadratic bent functions in polynomial form are constructed in this paper the constructions give new boolean bent generalized boolean bent and p ary bent functions based on z 4 valued quadratic forms a simple method provides several new constructions of generalized boolean bent functions from these generalized boolean bent functions a method is presented to transform them into boolean bent and semi bent functions moreover many new p ary bent functions can also be obtained by applying similar methods

bbz _4 valued quadratic forms and quaternary sequence families in this paper zopf4 valued quadratic forms defined on a vector space over gf 2 are studied a classification of such forms is established distinguishing zopf4 valued quadratic forms only by their rank and whether the associated bilinear form is alternating this result is used to compute the distribution of certain exponential sums which occur frequently in the analysis of quaternary codes and quaternary sequence sets the concept is applied as follows when t 0 or m is odd the correlation distribution of family s t consisting of quaternary sequences of length 2 m 1 is established then motivated by practical considerations a subset s t of family s t is defined and the correlation distribution of family s t is given for odd and even m

several classes of codes and sequences derived from a bbz_ 4 valued quadratic form let m and k be positive integers with m gcd m k being odd for a r and b l the exponential sum x litr ax 2bx2k 1 is studied systematically in this paper where i 1 r gr 4 m is a galois ring l is the teichmuller set of r and tr is the trace function from the galois ring r to z4 through the discussions on the solutions of certain equations and the newly developed theory of z4 valued quadratic forms the distribution of the exponential sum is completely determined as its applications we can determine the lee weight and hamming weight distributions of a class of codes ck over z4 and the correlation distribution of a quaternary sequence family uk respectively furthermore the hamming weight distributions of the binary codes obtained from ck under the most significant bit msb and gray maps are also determined for the msb map sequences of uk the nontrivial maximal correlation value is given and the correlation distribution is determined for the gray map sequences of uk it should be noted that the distribution of the exponential sum for the case gcd m k 1 is obtained for the first time and then the corresponding codes and sequences are novel

the predictable degree property and row reducedness for systems over a finite ring motivated by applications in communications we consider linear discrete time systems over the finite ring z p r we solve the open problem of deriving a theory of row reduced representations for these systems we introduce a less restrictive form of representation than the adapted form introduced by fagnani and zampieri we call this form the composed form we define the concept of p predictable degree property and p row reduced we demonstrate that these concepts coupled with the composed form provide a natural setting that extends several classical results from the field case to the ring case in particular the classical rank test on the leading row coefficient matrix is generalized we show that any annihilator of a behavior mathfrak b of a pre specified degree is uniquely parametrized with finitely many coefficients in terms of a kernel representation in p row reduced composed form the underlying theory is the theory of reduced p basis for submodules of z q p r xi that is developed in this paper we show how to construct a p row reduced kernel representation in composed form by constructing a reduced p basis for the module mathfrak b perp

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

optimal biphase sequences with large linear complexity derived from sequences over z sub 4 new families of biphase sequences of size 2 sup r 1 1 r being a positive integer are derived from families of interleaved maximal length sequences over z sub 4 of period 2 2 sup r 1 these sequences have applications in code division spread spectrum multiuser communication systems the families satisfy the sidelnikov bound with equality on spl theta sub max which denotes the maximum magnitude of the periodic cross correlation and out of phase autocorrelation values one of the families satisfies the welch bound on spl theta sub max with equality the linear complexity and the period of all sequences are equal to r r 3 2 and 2 2 sup r 1 respectively with an exception of the single m sequence which has linear complexity r and period 2 sup r 1 sequence imbalance and correlation distributions are also computed

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

imposing curvature restrictions on flexible functional forms abstract a general computational method for estimating the parameters of a flexible functional form subject to convexity quasi convexity concavity or quasi concavity at a point at several points or over a region is set forth and illustrated with an example

multiple phase codes for detection without carrier phase reference we consider the construction and analysis of linear block codes for m ary phase shift keying that can be decoded without carrier phase synchronization under these circumstances the function that has a significant impact on performance is the noncoherent distance analogous to the euclidean distance for the coherent case the major difficulty in constructing and analyzing such codes lies in the fact that the noncoherent distance is not a true metric for this reason prior work mainly relies on numerical approaches to search for good codes and to determine the corresponding minimum noncoherent distance we first present a theorem that links the noncoherent distance with the euclidean and lee 1958 distances this theorem allows us to construct good codes and determine their minimum noncoherent distances analytically based on this theorem we classify the codes whose duals consist of a cyclic group these codes are of minimum redundancy we further investigate codes with the flavor of hamming and shortened hamming codes many of these new codes provide significantly larger coding gains than previously known codes linear codes derived from code division multiple access cdma sequences are considered as well these codes in general provide rather large coding gains finally an algorithm is introduced that can be appended to any suboptimal decoding technique to enhance the performance

improved binary codes and sequence families from z sub 4 linear codes a bound on exponential sums over galois rings is used to construct a nested chain of z sub 4 linear binary codes and binary sequences when compared with the chain of delsarte goethals 1975 codes the codes in the new chain offer a larger minimum distance for the same code size the binary sequence families constructed also make use of nechaev s 1991 construction of a cyclic version of the kerdock code for a given value of maximum correlation the binary sequences are shown to have a family size considerably larger than the best sequence families known

an asymptotic analysis of ds ssma communication systems with random polyphase signature sequences direct sequence spread spectrum multiple access ds ssma communication systems with random m phase sequences for even m are considered by examining the asymptotic behavior of the normalized multiple access interference mai the authors find that a system with random m phase sequences for m 4 should have the same performance as one with random quadriphase sequences asymptotically however a system with random m phase sequences for m spl ges 4 may perform better than one with random binary sequences when the number of simultaneous users is relatively small a new gaussian approximation is proposed to estimate the probabilities of error in these systems in two cases the new approximation reduces to established results which have been shown to provide close estimates to the probabilities of error

new m ary sequence families with low correlation from the array structure of sidelnikov sequences in this paper we extend the construction by vu and gong for families of m ary sequences of period q 1 from the array structure of an m ary sidelnikov sequence of period q 2 1 where q is a prime power and m q 1 the construction now applies to the cases of using any period q d 1 for 3 d 27 the proposed construction results in a family of m ary sequences of period q 1 with 1 the correlation magnitudes which are upper bounded by 2 d 1 q 1 and 2 the asymptotic size of m 1 q d 1 d as q increases we also characterize some subsets of the above of size r 1 q d 1 d but with a tighter upper bound 2d 2 q 2 on its correlation magnitude we discuss reducing both time and memory complexities for the practical implementation of such constructions in some special cases we further give some approximate size of the newly constructed families in general and an exact count when d is a prime power or a product of two distinct primes the main results of this paper now give more freedom of tradeoff in the design of m ary sequence family between the family size and the correlation magnitude of the family

a linear construction for certain kerdock and preparata codes the nordstrom robinson kerdock and slightly modified preparata codes are shown to be linear over z4 the integers mod 4 the kerdock and preparata codes are duals over z4 and the nordstrom robinson code is self dual all these codes are just extended cyclic codes over z4 this provides a simple definition for these codes and explains why their hamming weight distributions are dual to each other firstand second order reed muller codes are also linear codes over z4 but hamming codes in general are not nor is the golay code

asymptotic information lossless designs and the diversity multiplexing tradeoff it is known that neither the alamouti nor the v blast scheme achieves the zheng tse diversity multiplexing tradeoff dmt of the multiple input multiple output mimo channel with respect to the dmt curve the alamouti scheme achieves the point corresponding to maximum diversity gain only whereas v blast meets only the point corresponding to maximum multiplexing gain it is also known that d blast achieves the optimal dmt for n transmit and n receive antennas but only under the assumption that the leading and trailing zeros are ignored when these zeros are taken into account d blast achieves the point corresponding to zero multiplexing gain but not the point corresponding to zero diversity gain the first scheme to achieve the dmt is the coding scheme of yao and wornell for the case of two transmit and two receive antennas in this paper we introduce the notion of an asymptotic information lossless aill design and obtain a necessary and sufficient condition under which a design is aill analogous to the result that full rank designs achieve the point corresponding to the zero multiplexing gain of the optimal dmt curve we show aill to be a necessary and sufficient condition for a design to achieve the point on the dmt curve corresponding to zero diversity gain we also derive a lower bound on the tradeoff achieved by designs from field extensions and show that the tradeoff is very close to the optimal tradeoff in the case of a single receive antenna a lower bound to the tradeoff achieved by designs from division algebras is presented which indicates that these designs achieve both extreme points corresponding to zero diversity and zero multiplexing gain of the optimal dmt curve finally we present simulations results for n transmit and n receive antennas for n 2 3 4 which suggest that designs from division algebras are likely to have the property of being dmt achieving

z4 kerdock codes orthogonal spreads and extremal euclidean line sets when m is odd spreads in an orthogonal vector space of type omega 2m 2 2 are related to binary kerdock codes and extremal line sets in rr 2 m 1 with prescribed angles spreads in a 2m dimensional binary symplectic vector space are related to kerdock codes over zz 4 and extremal line sets in cc 2 m with prescribed angles these connections involve binary real and complex geometry associated with extraspecial 2 groups a geometric map from symplectic to orthogonal spreads is shown to induce the gray map from a corresponding zz 4 kerdock code to its binary image these geometric considerations lead to the construction for any odd composite m of large numbers of zz 4 kerdock codes they also produce new zz 4 linear kerdock and preparata codes 1991 mathematics subject classification primary 94b60 secondary 51m15 20c99

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

generalized cross correlation properties of chu sequences in this paper detailed cross correlation properties for chu sequences are investigated all possible values of the cross correlation function of chu sequences are derived for any given sequence length and lag and the maximum magnitude distribution function n x which is defined as the number of all chu sequence pairs with length n whose maximum magnitude of the cross correlation function is nx is obtained also good lower and upper bounds on the maximum number of available chu sequences and a construction algorithm for the corresponding partial chu sequence set are proposed when the maximum magnitude of the cross correlation among the sequences is constrained numerical examples show that the proposed bounds are quite tight and the proposed construction algorithm is near optimal up to fairly large value of n

on the construction of binary sequence families with low correlation and large sizes in this paper we revisit a method to produce binary sequences using the most significant bit map from z4 to the binary field this method is useful for the construction of binary sequences with low correlation and large family size there may be more cases where starting with z4 could help researchers design new low correlation sequences for code division multiple access application

a construction of a space time code based on number theory we construct a full data rate space time st block code over m 2 transmit antennas and t 2 symbol periods and we prove that it achieves a transmit diversity of 2 over all constellations carved from z i sup 4 further we optimize the coding gain of the proposed code and then compare it to the alamouti code it is shown that the new code outperforms the alamouti see ieee j select areas commun vol 16 p 1451 58 1998 code at low and high signal to noise ratio snr when the number of receive antennas n 1 the performance improvement is further enhanced when n or the size of the constellation increases we relate the problem of st diversity gain to algebraic number theory and the coding gain optimization to the theory of simultaneous diophantine approximation in the geometry of numbers we find that the coding gain optimization is equivalent to finding irrational numbers the furthest from any simultaneous rational approximations

a construction of ofdm 16 qam sequences having low peak powers using a realization of 16 qam as set addition of two scaled versions of the 4 psk constellation we construct 16 qam sequences having low peak to mean envelope power ratios pmepr from 4 psk golay sequences various upper bounds on the peak envelope powers of these sequences are established transmission using these sequences provides twice as much rate as transmission using complementary golay sequences with a maximum pmepr of 3 6 5 56 db

performances of ds ssma communications with mpsk signaling and complex signature sequences we study a direct sequence spread spectrum multiple access ds ssma communication system with m ary phase shift keyed mpsk signaling users in the system employ complex signature sequences which are modeled as deterministic sequences we present upper and lower bounds for the probability of bit error p b e of a reference transmission first the conditional p b e given the multiple user interference mui is obtained then the conditioning is removed by averaging over the discretized probability density function p d f of the mui the result is an upper or lower bound when the discretized p d f is a shifted high or shifted low version of a sectioned p d f this process requires the two dimensional p d f of the mui which is derived arbitrarily tight bounds can be obtained at the cost of increased computation numerical results are presented for complex fzc and near optimal 4 phase sequences as well as real binary gold sequences for bpsk 4 psk and 8 psk gray code bit mapping is assumed although the analysis can be applied to other bit mappings results show that complex sequences can yield better performance than binary sequences in mpsk signaling using complex sequences the number of available signature sequences is greatly enlarged

optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings we construct new sequences over finite rings having optimal hamming correlation properties these sequences are useful in frequency hopping multiple access fhma spread spectrum communication systems our constructions can be classified into linear and nonlinear categories both giving optimal hamming correlations according to lempel greenberger 1974 bound the nonlinear sequences have large linear complexity and can be seen as a generalized version of gmw sequences over fields

further results on the optimal sequence family mathcal ip _ 8 over 8 ary q pam constellation a family mathcal ip 8 of sequences over the 8 ary quadrature pulse amplitude modulation q pam constellation with asymptotically optimal correlation property was presented by anand and kumar in 2008 this is the only known family of sequences over the quadrature amplitude modulation qam constellation whose correlation magnitude asymptotically achieves the welch bound in this paper a larger family mathcal ip 8 text new of sequences with the same correlation magnitude as that of mathcal ip 8 but double family size is obtained moreover the correlation distributions of mathcal ip 8 and mathcal ip 8 text new are also determined for two particular cases in terms of the property of a class of exponential sums over galois rings it is also shown that more classes of qam and q pam sequences with low correlation and larger family size can be obtained from our approach

orthogonal sets of quadriphase sequences with good correlation properties a general construction for orthogonal sets of quadriphase sequences based on the sequence family a discovered by sole 1989 boztas hammons and kumar 1992 is presented the sequence family a is equivalent to the s 0 family that belongs to a chain of sequence families s i i 0 1 2 m with each family in the chain containing the preceding family therefore a number of orthogonal subsets can be generated for an arbitrary family s m the algorithm for an efficient implementation of the bank of correlators corresponding to any orthogonal subset of family s m is derived as well

the correlation distribution of quaternary sequences of period 2 2 n 1 family a is a family of sequences of period 2n 1 over zi the ring of integers modulo 4 this family has optimal correlation properties and its correlation distribution is well known two related families of quaternary sequences are the families b and c these are families of sequences over z4 of period 2 2n 1 in recent years new families of quaternary sequences of period 2 2n 1 have been constructed by modifying the sequence families b and c in a nonlinear way this has resulted in a new family d of sequences of period 2 2n 1 which has optimal correlation properties but until now the correlation distribution of this family has not been known in this paper we completely determine the correlation distribution of family d by making use of properties of exponential sums

rate diversity tradeoff of space time codes with fixed alphabet and optimal constructions for psk modulation we show that for any q spl times m space time code s having a fixed finite signal constellation there is a tradeoff between the transmission rate r and the transmit diversity gain spl nu achieved by the code the tradeoff is characterized by r spl les q spl nu 1 where q is the number of transmit antennas when either binary phase shift keying bpsk or quaternary phase shift keying qpsk is used as the signal constellation a systematic construction is presented to achieve the maximum possible rate for every possible value of transmit diversity gain

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

on the weight hierarchy of kerdock codes over z sub 4 the rth generalized hamming weight d sub r of the kerdock code of length 2 sup m over z sub 4 is considered a lower bound on d sub r is derived for any r and d sub r is exactly determined for r 0 5 1 1 5 2 2 5 in the case of length 2 sup 2m d sub r is determined for any r where 0 spl les r spl les m and 2r is an integer in addition it is shown that it is sometimes possible to determine the generalized hamming weights of the kerdock codes of larger length using the results of d sub r for a given length the authors also provide a closed form expression for the lee weight of a kerdock codeword in terms of the coefficients in its trace expansion

random properties of the highest level sequences of primitive sequences over z 2 sup e using the estimates of the exponential sums over galois rings we discuss the random properties of the highest level sequences spl alpha sub e 1 of primitive sequences generated by a primitive polynomial of degree n over z 2 sup e first we obtain an estimate of 0 1 distribution in one period of spl alpha sub e 1 on the other hand we give an estimate of the absolute value of the autocorrelation function c sub n h of spl alpha sub e 1 which is less than 2 sup e 1 2 sup e 1 1 spl radic 3 2 sup 2e 1 2 sup n 2 2 sup e 1 for h spl ne 0 both results show that the larger n is the more random spl alpha sub e 1 will be

on the autocorrelation distributions of sidel nikov sequences for a prime p and positive integers m and n such that m p sup n 1 sidel nikov introduced m ary sequences called sidel nikov sequences of period p sup n 1 the out of phase autocorrelation magnitude of which is upper bounded by 4 in this correspondence we derived the autocorrelation distributions i e the values and the number of occurrences of each value of the autocorrelation function of sidel nikov sequences the frequency of each autocorrelation value of an m ary sidel nikov sequence is expressed in terms of the cyclotomic numbers of order m it is also pointed out that the total number of distinct autocorrelation values is dependent not only on m but also on the period of the sequence but always less than or equal to m 2 1

a note on the optimal quadriphase sequences families in this note by using a modification of the families b and c we obtain a larger family of optimal quadriphase sequences d over z4 in contrast to the families b and c the family d has the same length and the same maximal nontrival correlation value but with double the size

unitary space time constellations based on quasi orthogonal sequences in this paper we propose a novel class of unitary space time constellations based on quaternary quasi orthogonal sequences qoss minimizing the maximum correlation between the signal matrices the proposed design owing to the underlying algebraic structure of the qoss allows for an efficient decoder structure while offering performance virtually identical to the unitary space time constellation design by hochwald et al

on the design of algebraic space time codes for mimo block fading channels the availability of multiple transmit antennas allows for two dimensional channel codes that exploit the spatial transmit diversity these codes were referred to as space time codes by tarokh et al see ibid vol 44 p 744 765 mar 1998 most prior works on space time code design have considered quasi static fading channels we extend our earlier work on algebraic space time coding to block fading channels first we present baseband design criteria for space time codes in multi input multi output mimo block fading channels that encompass as special cases the quasi static and fast fading design rules the diversity advantage baseband criterion is then translated into binary rank criteria for phase shift keying psk modulated codes based on these binary criteria we construct algebraic space time codes that exploit the spatial and temporal diversity available in mimo block fading channels we also introduce the notion of universal space time codes as a generalization of the smart greedy design rule as a part of this work we establish another result that is important in its own right we generalize the full diversity space time code constructions for quasi static channels to allow for higher rate codes at the expense of minimal reductions in the diversity advantage finally we present simulation results that demonstrate the excellent performance of the proposed codes

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

construction of ofdm m qam sequences with low peak to average power ratio we present a technique to derive m quadrature amplitude modulation qam signals from quaternary phase shift keying qpsk constellations when m 2 sup n and n is an even number by utilizing qpsk golay sequences we have constructed m qam sequences with low peak to mean envelope power ratios several upper bounds for these m qam sequences were derived

generalized binary udaya siddiqi sequences in this correspondence we present a family of binary 2n sequences of period 2 2n 1 where n is an integer which can be seen as a generalization of nonlinear binary sequences obtained from z4 sequences and recently constructed gkw gold kasami and welch like sequences the sequences have low correlations and are useful in code division multiple access cdma communication systems and cryptography

quadriphase sequences for spread spectrum multiple access communication this paper studies constructions for quadriphase sequences that are suitable for use as signature sequences in quadriphase spread spectrum multiple access communications quadriphase sequences are closely related to biphase i e binary sequences and many of the properties of the former can be expressed in terms of properties of the latter methods of construction are presented which obtain sets of quadriphase sequences from sets of biphase sequences methods of construction of quadriphase sequences are provided based upon the properties of the multiplicative characters of the finite field gf q where q equiv 1 mod 4 these methods use codewords from low rate reed solomon codes which are mapped onto the fourth roots of unity 2q 2 sequences of period q 1 are constructed for which the maximum magnitudes of the periodic cross correlation and the periodic out of phase autocorrelation are bounded by 3 sqrt q 5

tests on the validity of static equilibrium models abstract this paper provides a framework to test the validity of static cost minimizing equilibrium assumptions that form the basis for much of the empirical literature on industrial production the point of departure in our model is to allow the observed technology to be at a short run equilibrium where firms minimize variable costs while being constrained by the utilization levels of quasi fixed factors the long run equilibrium is then inferred by minimizing total costs with the optimal adjustment of quasi fixed factor levels we use results from the optimization problem to form tests with respect to quantities and prices in the quantity space version departures between the actual and the optimal long run levels of quasi fixed factors are tested for statistical significance a significant non zero departure implies the rejection of a static equilibrium specification in the price space version the test is cast as a comparison of the market price and the long run shadow value of a quasi fixed factor although the two versions would give identical results in the non stochastic case the rejection powers of these two tests are found to depend on the particular functional form chosen to represent the production process i e cost function in an application based on aggregate u s manufacturing where capital is taken to be quasi fixed we were able to reject the static equilibrium specification these results cast doubt on the validity of a number of previous empirical studies

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

constructions of asymptotically optimal space frequency codes for mimo ofdm systems constructions of space frequency sf codes for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems with nt transmit antennas and q subcarriers are considered in this paper following the pairwise error probability analysis it is known that in addition to the conventional rank distance criterion the minimum column distance of nttimesq sf codes serves as another benchmark in code design sf codes with larger minimum column distance are expected to have better performance following this principle the rate diversity tradeoff for the mimo ofdm channels as well as two sf code constructions are presented the first construction is obtained by right multiplying the code matrices in a maximal rank distance mrd code by a fixed qtimesq nonsingular matrix codes obtained from this construction are called linearly transformed mrd lt mrd codes minimum column distance of the lt mrd codes when averaged over all code ensembles is shown to meet the gilbert varshamov bound for the case of constructing the 2times256 quadrature phase shift keying qpsk modulated sf codes it is shown that the lt mrd codes can provide a much larger minimum column distance at the value of ges50 compared to the values of 3 5 or 6 obtained by other available constructions the second code construction termed cyclotomic construction is reminiscent of the construction of the reed solomon codes except that the code polynomials are now selected according to the cyclotomic cosets of the underlying field exact minimum rank distances of the resultant codes are presented it is shown that this newly constructed code is asymptotically optimal in terms of rate diversity tradeoff bounds on the minimum column distance of these codes are also given

optimal phases for a family of quadriphase cdma sequences signature sequences with good even even and odd or polyphase correlations are crucial for asynchronous code division multiple access cdma when the data sequence is random the even and odd or polyphase correlations are equally important however for most known signature sequences only their even correlations were analyzed it appears that determining the odd or the polyphase correlations is generally a very hard problem since the odd or the polyphase correlations depend on the phases of the signature sequences sole 1989 boztas hammons and kumar 1992 found a family of quadriphase sequences that are asymptotically optimal these sequences gain a factor spl radic 2 in terms of their maximum periodic even correlations when compared with the best possible binary phase shift keying bpsk sequences we find the optimal phases of these sequences the optimality is in the sense that at these phases the mean square values of the even odd and the polyphase correlations are minimal and achieve the welch 1974 bound equality simultaneously furthermore we show that at these phases the average user interference of these sequences is always smaller than that of the ideal random signature sequences comprehensive analytical and numerical results show that good phase sequences can offer a nonnegligible amount of gain over bad phase sequences at modest and high signal to noise ratios

binary sequences with gold like correlation but larger linear span a new construction of optimal binary sequences identical to the well known family of gold sequences in terms of maximum nontrivial correlation magnitude and family size but having larger linear span is presented the distribution of correlation values is determined for every odd integer spl tau spl ges 3 the construction provides a family that contains 2 sup spl tau 1 cyclically distinct sequences each of period 2 sup spl tau 1 the maximum nontrivial correlation magnitude equals 2 spl tau 1 sup 2 1 with one exception each of the sequences in the family has linear span at least spl tau sup 2 spl tau 2 compared to 2 spl tau for gold sequences the sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity

signal set design with constrained amplitude spectrum and specified time bandwidth product a new method for designing signals with a given time bandwidth product such that all the signals in the set have a flat amplitude spectrum and have low cross correlation function values is introduced it is shown that these signals lie on a signal parameter space ellipse for a given duration and bandwidth it is possible to trade off the cardinality of the set for better cross correlation properties between remaining members of the set proof that the cross correlation between these signals is bounded from above by a factor proportional to the square root of inverse distance between these signals along one of the axes of the ellipse is given it is also shown that the cross correlation between two signals that are furthest apart is bounded by the square root of inverse time bandwidth product of the signals in the set an example design is then given and a comparison of this signal set to some well known signal sets illustrates that it performs better when the metric is maximum cross correlation value the proposed signal set also has the advantage that it can be designed for any time bandwidth product instead of discrete values

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

testing for separable functional structure using temporary equilibrium models abstract the importance that functional structure plays in the analysis of producer behavior is well known and responsible for the empirical tests of input separability hypotheses found in the contemporary literature unfortunately to our knowledge all such tests have been conducted under the maintained assumption of full factor input equilibrium in this paper we propose and implement a method for testing functional structure hypotheses when the behavioral units are permitted to be in disequilibrium the results of this more general test provide less support for the existence of input separability in two digit manufacturing than previously reported by the authors using tests assuming full equilibrium

low correlation sequences over the qam constellation this paper presents the first concerted look at low correlation sequence families over quadrature amplitude modulation qam constellations of size and their potential applicability as spreading sequences in a code division multiple access cdma setting five constructions are presented and it is shown how such sequence families have the ability to transport a larger amount of data as well as enable variable rate signaling on the reverse link canonical family has period normalized maximum correlation parameter bounded above by where ranges from in the 16 qam case to for large in a cdma setting each user is enabled to transfer bits of data per period of the spreading sequence which can be increased to bits of data by halving the size of the sequence family the technique used to construct is easily extended to produce larger sequence families and an example is provided selected family has a lower value of but permits only bit data modulation the interleaved 16 qam sequence family has and supports 3 bit data modulation the remaining two families are over a quadrature pulse amplitude modulation q pam subset of size of the qam constellation family has a lower value of in comparison with family while still permitting bit data modulation interleaved family over the 8 ary q pam constellation permits 3 bit data modulation and interestingly achieves the welch lower bound on

on the correlation distributions of the optimal quaternary sequence family cal u and the optimal binary sequence family cal v recently new optimal families s and u of quaternary sequences have been presented and the optimal binary sequence family v obtained from family s under gray map has been investigated as well the two sequence families u and v are optimal with respect to the well known sidelnikov bound and welch bound but their exact correlation distributions are not known until now in this paper their exact correlation distributions are completely determined in some cases by making use of exponential sums and the theory of z4 valued quadratic forms

generic construction of quaternary sequences of period 2n with low correlation from quaternary sequences of odd period n in this paper a simple but generic method is proposed for transforming any family of quaternary sequences with low correlation of any odd period n to another family of quaternary sequences of period 2n with low correlation as an application of the generic method to sequence family a a new optimal quaternary sequence family with length 2 2n 1 family size 2n 1 and maximal nontrivial correlation value 2 n 1 2 2 where n is an odd integer is obtained most notably unlike all the known optimal quaternary sequence families the new family has a unique property that the odd integers 1 3 and the even integers 0 2 are allocated alternatively in all the sequences

on the aperiodic and odd correlations of the binary shanbhag kumar helleseth sequences a previously derived upper bound on hybrid sums over galois rings is combined with a method due to vinogradov 1954 to obtain an upper bound for the maximum aperiodic and odd correlations of the binary sequences constructed by shanbhag kumar and helleseth see proc 1995 ieee int symp on information theory 1995

quasi orthogonal sequences for code division multiple access systems the notion of quasi orthogonal sequence qos as a means of increasing the number of channels in synchronous code division multiple access cdma systems that employ walsh sequences for spreading information signals and separating channels is introduced it is shown that a qos sequence may be regarded as a class of bent almost bent functions possessing in addition a certain window property such sequences while increasing the system capacity minimize interference to the existing set of walsh sequences the window property gives the system the ability to handle variable data rates a general procedure of constructing qoss from well known families of binary sequences with good correlation including the kasami and gold 1967 sequence families as well as from the binary kerdock code is provided examples of qoss are presented for small lengths some examples of quaternary qoss drawn from family a are also included

multiple access interference reduction for qs cdma systems with a novel class of polyphase sequences in this paper a new class of polyphase sequences for cdma systems and its generation method are suggested and the correlation properties of the sequence are investigated the performance of the sequence in quasi synchronous cdma qs cdma systems is investigated under a frequency selective time nonselective slow nakagami fading channel with additive white gaussian noise awgn it is shown that the performance of the qs cdma systems using the suggested sequence is independent of the number of users and is much better than that using the pn sequence

upper bound for a hybrid sum over galois rings with applications to aperiodic correlation of some q ary sequences an upper bound for a hybrid exponential sum over galois rings is derived this bound is then used to obtain an upper bound for the maximum aperiodic correlation of some sequence families over galois rings the bound is of the order of spl radic qlnq where q 1 is the period of the sequences

cocyclic simplex codes of type spl alpha over z sub 4 and z sub 2 sup s over the past decade cocycles have been used to construct hadamard and generalized hadamard matrices this in turn has led to the construction of codes self dual and others here we explore these ideas further to construct cocyclic complex and butson hadamard matrices and subsequently we use the matrices to construct simplex codes of type spl alpha over z 4 and z 2 sup s respectively

linear threaded algebraic space time constellations space time st constellations that are linear over the field of complex numbers are considered relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established the fundamental tradeoff between rate and diversity is investigated under different constraints on the peak power receiver complexity and rate scaling with the signal to noise ratio snr a new family of constellations that achieve optimal or near optimal performance with respect to the different criteria is presented the proposed constellations belong to the threaded algebraic st tast signaling framework and achieve the optimal minimum squared euclidean distance and the optimal delay for systems with one receive antenna these constellations also achieve the optimal peak to average power ratio for quadrature amplitude modulation qam and phase shift keying psk input constellations as well as optimal coding gains in certain scenarios the framework is general for any number of transmit and receive antennas and allows for realizing the optimal tradeoff between rate and diversity under different constraints simulation results demonstrate the performance gains offered by the proposed designs in average power and peak power limited systems

diagonal algebraic space time block codes we construct a new family of linear space time st block codes by the combination of rotated constellations and the hadamard transform and we prove them to achieve the full transmit diversity over a quasi static or fast fading channels the proposed codes transmit at a normalized rate of 1 symbol s when the number of transmit antennas n 1 2 or n is a multiple of four we spread a rotated version of the information symbol vector by the hadamard transform and send it over n transmit antennas and n time periods for other values of n we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n spl times n st code matrix the codes maintain their rate diversity and coding gains for all real and complex constellations carved from the complex integers ring z i and they outperform the codes from orthogonal design when using complex constellations for n 2 the maximum likelihood ml decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity it is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity