on acceptance criterion for efficient successive errors and erasures decoding of reed solomon and bch codes we describe an efficient algorithm for successive errors and erasures decoding of bch codes the decoding algorithm consists of finding all necessary error locator polynomials and errata evaluator polynomials choosing the most appropriate error locator polynomial and errata evaluator polynomial using these two polynomials to compute a candidate codeword for the decoder output and testing the candidate for optimality via an originally developed acceptance criterion even in the most stringent case possible the acceptance criterion is only a little more stringent than forney s 1966 criterion for generalised minimum distance gmd decoding we present simulation results on the error performance of our decoding algorithm for binary antipodal signals over an awgn channel and a rayleigh fading channel the number of calculations of elements in a finite field that are required by our algorithm is only slightly greater than that required by hard decision decoding while the error performance is almost as good as that achieved with gmd decoding the presented algorithm is also applicable to efficient decoding of product rs codes

vanishing viscosity solutions of nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n system in one space dimension ut a u ux 0 assuming that the initial data have small total variation we show that the solutions of the viscous approximations ut a u ux euxx are defined globally in time and satisfy uniform bv estimates independent of e moreover they depend continuously on the initial data in the l 1 distance with a lipschitz constant independent of t e letting e 0 these viscous solutions converge to a unique limit depending lipschitz continuously on the initial data in the conservative case where a df is the jacobian

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

a unified method for evaluating the error correction radius of reliability based soft decision algorithms for linear block codes this paper presents a unified method for evaluating the error correction radii of many reliability based soft decision decoding algorithms for binary linear block codes based on this unified method these decoding algorithms as well as their potential improvements can be compared directly the error correction radius for each of these decoding algorithms is determined by finding the closest point on the boundary of the decision region of the soft decision decoder to the transmitted signal sequence it is shown that this problem can be formulated as a constrained optimization problem although no general closed form expression is possible a simple algorithm that always converges to the optimum solution of this optimization problem is presented based on these results the error correction radii of some well known reliability based soft decision decoding algorithms are revisited and compared

on space time code design with a conditional pic group decoding space time code designs based on a partial interference cancellation pic group decoding have been recently proposed the pic group decoding complexity depends on the group size and is between the lowest linear receiver complexity and the highest ml decoding complexity the symbol rate for a space time code achieving full diversity with the pic group decoding is also between those for the linear receivers and the ml decoding in this paper we propose a new decoding called conditional pic group decoding that is between the pic group decoding and the ml decoding with the proposed new decoding we obtain a new design criterion for space time codes to achieve full diversity which is also between the one with the pic group decoding and the one with the ml decoding we then present some designs that satisfy the new criterion and in the meantime have higher symbol rates than that for the pic group decoding

extinction rates for fluctuation induced metastabilities a real space wkb approach the extinction of a single species due to demographic stochasticity is analyzed the discrete nature of the individual agents and the poissonian noise related to the birth death processes result in local extinction of a metastable population as the system hits the absorbing state the fokker planck formulation of that problem fails to capture the statistics of large deviations from the metastable state while approximations appropriate close to the absorbing state become in general invalid as the population becomes large to connect these two regimes a real space wkb method based on the master equation is presented and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to the absorbing state the details of the underlying microscopic process smeared out in a mean field treatment are shown to be crucial for an exact determination of the extinction exponent this general scheme is shown to reproduce the known results in the field to yield new corollaries and to fit quite precisely the numerical solutions moreover it allows for systematic improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable state

linear decoupled and quasi decoupled space time codes space time transmit diversity results in coupling of transmitted symbols across different antennas which increases the complexity of maximum likelihood decoding symbol coupling can be completely or partially avoided if the space time code stc satisfies specific decoupling conditions examples of such codes are orthogonal space time block codes and quasi orthogonal codes in this letter we study decoupling conditions for a linear full diversity stc quasi decoupled codes are proposed as a partially decoupled full diversity stc of any rate for any number of transmit antennas with minimum decoding delay by optimizing the coding gain of quasi decoupled codes it is shown that quasi orthogonal codes have competitive performance with respect to the alamouti code and the more recent threaded algebraic space time tast codes and abba codes a general full diversity decoupling condition is considered and the general solution to this case which also encompasses previously known orthogonal stcs is derived

blind channel identifiability for generic linear space time block codes linear space time block codes stbcs have proven their effectiveness in performance improvement of wireless multiple input multiple output communication systems their successful decoding however requires reliable channel knowledge at the receiver in this paper we present a semiblind channel estimation method for linear stbc without the usual code orthogonality condition we provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration we also present a simple channel estimation algorithm finally we provide simulation results that illustrate the performance of the proposed scheme

on the complexity of sphere decoding in digital communications sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications in some cases the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure another claim is that although worst case complexity is exponential the expected complexity of the algorithm is polynomial herein we study the expected complexity where the problem size is defined to be the number of symbols jointly detected and our main result is that the expected complexity is exponential for fixed signal to noise ratio snr contrary to previous claims the sphere radius which is a parameter of the algorithm must be chosen to ensure a nonvanishing probability of solving the detection problem this causes the exponential complexity since the squared radius must grow linearly with problem size the rate of linear increase is however dependent on the noise variance and thus the rate of the exponential function is strongly dependent on the snr therefore sphere decoding can be efficient for some snr and problems of moderate size even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size

global bv entropy solutions to the gauss codazzi system abstract the gauss codazzi system for the given metric whose gauss curvature is negative is considered in the present paper we provide some suitable conditions on the given metric such that the system admits a global bv entropy solution our main approach is applying the method of seeking global bv entropy solutions to the hyperbolic system of balance laws to the gauss codazzi system the global existence of bv solutions to the gauss codazzi system yields a c 1 1 isometric immersion of two dimensional manifold into r 3

quadratic extension field codes for free space optical intensity communications in this paper we propose a space time code construction with a symbol rate of two for free space optical multiple input multiple output fso mimo communication systems unlike the radio frequency space time coding design that deals with complex symbols holding phase and magnitude information the phase detection in wireless optical communications remains very challenging this restricts optical mimo codes to carry positive magnitude information belonging to a finite range to meet these requirements we propose to design the fso mimo codes considering first the whole real space mathbb r followed by a bipolar to unipolar conversion to fit in the intensity margin we consider the mimo configurations with two or four transmitters lasers we base our shape preserving construction on quadratic extension fields that linearly combine the real symbols to form a full diversity space time code with a symbol rate equal to two for each configuration we show how to optimize the choice of the algebraic field numbers to jointly optimize the non vanishing code determinant and the bipolar to unipolar attenuation factor

mathematical structures for long range dynamics and symmetry breaking the algebraic dynamics of systems with long range instantaneous interactions requires an enlargement of the quasi local algebra which in most relevant cases includes variables at infinity that enter in an essential way in the time evolution of local variables the mathematical structures emerging for the treatment of long range dynamics are investigated also in connection with spontaneous symmetry breaking

a new generic maximum likelihood metric expression for space time block codes with applications to decoding the metric expression for a generic linear space time block code stbc is studied using a different approach to vectorization and a new representation of the metric the new representation lends itself to a simple measure of reliability based on the sum of inner products and provides a quantifiable definition for minimum distance of a stbc this provides the framework for a new family of near maximum likelihood ml and ml decoding algorithms it also has applications in the development of optimality test criteria for stbcs as well as in the design of stbcs with low decoding complexity

quasi orthogonal time reversal space time block coding for frequency selective fading channels quasi orthogonal space time block codes qo stbcs are a powerful code family designed for more than two transmit antennas in contrast to their orthogonal counterparts designed for the same number of transmit antennas qo stbcs are able to provide full rate transmission rate while original qo stbcs enjoy only a partial diversity the recently proposed rotated versions of qo stbcs achieve the maximum diversity order which is equal to the number of transmit antennas since qo stbcs have been originally proposed for frequency flat fading channels it is a challenging design problem to apply them over frequency selective channels the dispersive nature of such channels results in intersymbol interference which needs to be carefully handled at the receiver in this paper we investigate time domain equalization for qo stbc exploiting the embedded quasi orthogonal structure to design low complexity receivers we also present diversity gains for the proposed scheme through pairwise error probability pep derivation and analysis which are further confirmed by monte carlo simulations

low complexity maximum likelihood decoder for four transmit antenna quasi orthogonal space time block code this letter proposes a very low complexity maximum likelihood ml detection algorithm based on qr decomposition for the quasi orthogonal space time block code qstbc with four transmit antennas called the lc ml decoder the proposed algorithm enables the qstbc to achieve ml performance with significant reduction in computational load for any high level modulation scheme

distributed differential space time coding for wireless relay networks distributed space time coding is a cooperative transmission scheme for wireless relay networks with this scheme antennas of the distributive relays work as transmit antennas of the sender and generate a space time code at the receiver it achieves the maximum diversity although the scheme needs no channel information at relays it does require full channel information both the channels from the transmitter to relays and the channels from relays to the receiver at the receiver in this paper we propose a differential transmission scheme which requires channel information at neither relays nor the receiver for wireless relay networks as distributed space time coding can be seen as the counterpart of space time coding in the network setting this scheme is the counterpart of differential space time coding compared to coherent distributed space time coding the differential scheme is 3db worse in addition we show that alamouti square real orthogonal and sp 2 codes can be used differentially in networks with corresponding numbers of relays we also propose distributed differential space time codes that work for networks with any number of relays using circulant matrices

constellation space invariance of orthogonal space time block codes in this correspondence we prove an interesting property of orthogonal space time block codes ostbcs for flat block fading channels it is shown that the internal structure of the vector space of the input constellation remains invariant to the effects of both the ostbc and the channel except for certain scaling factors this property sheds light on the mechanism of maximum likelihood ml decoding of ostbcs and in particular provides an alternative explanation of why optimal decoding can be reduced to symbol by symbol decoding new simple expressions for the ml decoder are obtained which clarify its intrinsic structure

reliability based code search algorithms for maximum likelihood decoding of block codes efficient code search maximum likelihood decoding algorithms based on reliability information are presented for binary linear block codes the codewords examined are obtained via encoding the information set utilized for encoding comprises the positions of those columns of a generator matrix g of the code which for a given received sequence constitute the most reliable basis for the column space of g substantially reduced computational complexity of decoding is achieved by exploiting the ordering of the positions within this information set the search procedures do not require memory the codeword to be examined is constructed from the previously examined codeword according to a fixed rule consequently the search algorithms are applicable to codes of relatively large size they are also conveniently modifiable to achieve efficient nearly optimum decoding of particularly large codes

blind stbc identification for multiple antenna ofdm systems this paper addresses the problem of space time block code stbc identification for multiple antenna ma orthogonal frequency division multiplexing ofdm systems operating over frequency selective channels for the first time in literature previous investigations published on the topic of stbc identification were restricted to single carrier systems operating over frequency flat channels ofdm systems make this topic more challenging to handle since the identifiers work in frequency selective channels with little or no knowledge of the beginning of the ofdm blocks ofdm parameters and frequency selective channel coefficients we show that by taking advantage of the space time redundancy stbc identification can be performed by exploiting the cross correlation of the signals received from different antennas as a discriminating feature using this feature we develop a binary hypothesis test for decision making the proposed method does not require information about the channel coefficients modulation format noise power or timing of the ofdm and stbc blocks moreover it does not need accurate knowledge of either clock timing information or ofdm parameters including the number of sub carriers and cyclic prefix length extensive simulation experiments have verified the effectiveness of the proposed method

hyperbolic systems of balance laws via vanishing viscosity abstract global weak solutions of a strictly hyperbolic system of balance laws in one space dimension are constructed by the vanishing viscosity method of bianchini and bressan for global existence a suitable dissipativeness assumption has to be made on the production term g under this hypothesis the viscous approximations u that are globally defined solutions to u t a u u x g u u xx satisfy uniform bv bounds exponentially decaying in time furthermore they are stable in l 1 with respect to the initial data finally as 0 u converges in l loc 1 to the admissible weak solution u of the system of balance laws u t f u x g u 0 when a df

reliability based syndrome decoding of linear block codes in this correspondence various aspects of reliability based syndrome decoding of binary codes are investigated first it is shown that the least reliable basis lrb and the most reliable basis mrb are dual of each other by exploiting this duality an algorithm performing maximum likelihood ml soft decision syndrome decoding based on the lrb is presented contrarily to previous lrb based ml syndrome decoding algorithms this algorithm is more conveniently implementable for codes whose codimension is not small new sufficient conditions for optimality are derived these conditions exploit both the ordering associated with the lrb and the structure of the code considered with respect to mrr based sufficient conditions they present the advantage of requiring no soft information and thus can be preprocessed and stored based on these conditions low complexity soft decision syndrome decoding algorithms for particular classes of codes are proposed finally a simple algorithm is analyzed after the construction of the lrb this algorithm computes the syndrome of smallest hamming weight among o k sup i candidates where k is the dimension of the code for an order i of reprocessing at practical bit error rates for codes of length n spl les 128 this algorithm always outperforms any algebraic decoding algorithm capable of correcting up to t 1 errors with an order of reprocessing of at most 2 where t is the error correcting capability of the code considered

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

the icosian code and the e_8 lattice a new 4 times 4 space time code with nonvanishing determinant this paper introduces a new rate 2 full diversity space time code for four transmit antennas and one receive antenna the 4times4 codeword matrix consists of four 2times2 alamouti blocks with entries from q i radic5 and these blocks can be viewed as quaternions which in turn represent rotations in r 3 the alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron this algebraic structure is different from the golden code but the complex entries are taken from a common underlying field the minimum determinant is bounded below by a constant that is independent of the signal constellation and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the e 8 lattice

evolutionary dynamics with fluctuating population sizes and strong mutualism game theory ideas provide a useful framework for studying evolutionary dynamics in a well mixed environment this approach however typically enforces a strictly fixed overall population size deemphasizing natural growth processes we study a competitive lotka volterra model with number fluctuations that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games we show that in an appropriate limit the model describes standard evolutionary games with both genetic drift and overall population size fluctuations however there are also regimes where a varying population size can strongly influence the evolutionary dynamics we focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results we then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions taking into account the population size degree of freedom these results elucidate the interplay between population dynamics and evolutionary dynamics in well mixed systems

a squaring method to simplify the decoding of orthogonal space time block codes we present a squaring method to simplify the decoding of orthogonal space time block codes in a wireless communication system with an arbitrary number of transmit and receive antennas using this squaring method a closed form expression of signal to noise ratio after space time decoding is also derived it gives the same decoding performance as the maximum likelihood ratio decoding while it shows much lower complexity

low complexity sphere decoding algorithm for quasi orthogonal space time block codes space time codes can be decoded by the sphere decoding sd algorithm to reduce the complexity and retain maximum likelihood ml performance in this letter the ml metric of quasi orthogonal space time block codes is written into two independent euclidean norms thus sd can be applied to each function independently the new scheme reduces the complexity by at least 85 for systems with four or more transmit antennas compared with the conventional sd algorithm

multiuser detection of alamouti signals in a mimo multiple access channel where users employ space time block codes stbc interference cancellation can be used to suppress co channel interference and recover the desired signal of each user at the receiver leveraging the special properties of alamouti matrices we first show that spatial multiplexing of alamouti signals retains the space time diversity gain of alamouti signaling using our proposed low complexity alamouti blast mmse a blast algorithm next in contrast to traditional transmit diversity that focuses on stbc construction at the transmitter this paper looks at transmit diversity from the perspective of the receiver in other words the receiver gets to choose the stbciquests which are favourable to the channel assuming a fixed blast receive algorithm in a multiusermac setting we first present a systematic methodology to exploit different decomposition structure in alamouti matrices each with different tradeoff between performance and decoding complexity using possibly different mimo receive algorithms we then demonstrate that the notion of angles the inner product of two quaternionic vectors between multiuser channels determines the performance of mimo receive algorithms as an application of the general theory we transform the decoding problem for several types of quasi orthogonal stbc qostbc into multiuser detection of virtual alamouti users building upon our a blast algorithm we propose new algorithms for decoding single user and multiuser qostbc in particular we show that bit error probability is a function of the quaternionic angle between virtual users for a single user or multiple users this angle varies with the type of qostbc and leads to a new form of adaptive modulation called code diversity where feedback instructs the transmitter how to choose from a plurality of codes

bv weak solutions to gauss codazzi system for isometric immersions abstract the isometric immersion problem for surfaces embedded into r 3 is studied via the fluid dynamic framework introduced in chen et al 2010 6 as a system of balance laws of mixed type the techniques developed in the theory of weak solutions of bounded variation in continuum physics are employed to deal with the isometric immersions in the setting of differential geometry the so called bv framework is formed that establishes convergence of approximate solutions of bounded variation to the gauss codazzi system and yields the c 1 1 isometric realization of two dimensional surfaces into r 3 local and global existence results are established for weak solutions of small bounded variation to the gauss codazzi system for negatively curved surfaces that admit equilibrium configurations as an application the case of catenoidal shell of revolution is provided

how often is hard decision decoding enough the problem of decoding binary linear block codes has received much attention the two extremes are optimal high complexity soft decision or maximum likelihood decoding and lower performance much lower complexity hard decision or algebraic decoding this article considers a class of decoders which first implements hard decision decoding second tests to see if that is enough that its result matches the result of soft decision decoding and third continues to search if a match is not found the advantage of such a testing procedure is that if the hard decision decoding result is found to be enough called a success for the test then the computational effort expended by the decoder is low the performance as measured by the probability of a success of a variety of simple tests of the hard decision codeword are analyzed

two designs of space time block codes achieving full diversity with partial interference cancellation group decoding a partial interference cancellation pic group decoding based space time block code stbc design criterion was recently proposed by guo and xia where the decoding complexity and the code rate traeoff is dealt when the full diversity is achieved in this paper two designs of stbc are proposed for any number of transmit antennas that can obtain full diversity when a pic group decoding with a particular grouping scheme is applied at receiver with the pic group decoding and an appropriate grouping scheme for the decoding the proposed stbc are shown to obtain the same diversity gain as the ml decoding but have a low decoding complexity the first proposed stbc is designed with multiple diagonal layers and it can obtain the full diversity for two layer design with the pic group decoding and the rate is up to 2 symbols per channel use with pic sic group decoding the first proposed stbc can obtain full diversity for any number of layers and the rate can be full the second proposed stbc can obtain full diversity and a rate up to 9 4 with the pic group decoding some code design examples are given and simulation results show that the newly proposed stbc can well address the rate performance complexity tradeoff of the mimo systems

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

population genetics with fluctuating population sizes standard neutral population genetics theory with a strictly fixed population size has important limitations an alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is reviewed we then study a situation such that the competing species are neutral at the equilibrium population size but population size fluctuations nevertheless favor fixation of one species over the other in this case a separation of timescales emerges naturally and allows adiabatic elimination of a fast population size variable to deduce the fluctuation induced selection dynamics near the equilibrium population size the results highlight the incompleteness of the standard population genetics with a strictly fixed population size

space time trellis code design based on super quasi orthogonal block codes with minimum decoding complexity in this letter we propose a new family of space time trellis codes which are constructed by combining a super set of quasi orthogonal space time block codes with minimum decoding complexity with an outer multiple trellis coded modulation encoder a systematic set partitioning method for quadratic amplitude modulation constellations is given the proposed scheme can be used for systems with four or more than four transmit antennas furthermore its decoding complexity is low because its branch metric calculation can be implemented in a symbolwise way simulation results demonstrate that the proposed scheme has a comparable performance as super quasi orthogonal space time trellis codes proposed by jafarkhani and hassanpour while providing a lower decoding complexity

efficient heuristic search algorithms for soft decision decoding of linear block codes efficient new algorithms are presented for maximum likelihood and suboptimal soft decision decoding algorithms for linear block codes the first algorithm ma improves the efficiency of the a decoding algorithm conducting the heuristic search through a code tree while exploiting code specific properties the second algorithm h reduces search space by successively estimating the cost of the minimum cost codeword with a fixed value at each of the most reliable and linearly independent components of the received message the third algorithm directed search finds the codeword closest to the received vector by exploring a continuous search space the strengths of these three algorithms are combined in a hybrid algorithm applied to the 128 64 the 256 131 and the 256 139 binary extended bose chaudhuri hocquenghem bch codes simulation results show that this hybrid algorithm can efficiently decode the 128 64 code for any signal to noise ratio with near optimal performance previously no practical decoder could have decoded this code with such a performance for all ranges of signal to noise ratio

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

spatially modulated orthogonal space time block codes with non vanishing determinants this paper proposes a multiple input multiple output mimo transmission scheme for m ary modulations called spatially modulated orthogonal space time block coding sm ostbc based on the concept of spatial constellation sc codewords introduced by le at el in the proposed scheme transmit codeword matrices are generated by multiplying sc matrices with codewords constructed from orthogonal space time block codes o stbc the maximum spectral efficiency of the proposed scheme is equal to n t 2 log 2 m bpcu where n t is the number of transmit antennas and m is the modulation order the sc matrices provide a means of carrying information bits together with the o stbc codewords and allow the sm ostbc scheme to achieve second order transmit diversity by satisfying the non vanishing determinant property a systematic method to design the sc codewords for an even number of transmit antennas greater than 3 is presented a single stream maximum likelihood ml decoder which requires a low computational complexity thanks to the structure of the sm ostbc codewords and to the orthogonality of the o stbcs and a sphere decoder with further reduced signal processing complexity are developed the bit error rate ber performance of the proposed scheme is studied by using both theoretical union bound analysis and computer simulations finally simulation results are presented in order to compare ber performance energy efficiency and decoding complexity of the proposed scheme with those of several existing mimo transmission schemes

a new reed solomon code decoding algorithm based on newton s interpolation a reed solomon code decoding algorithm based on newton s interpolation is presented this algorithm has as main application fast generalized minimum distance decoding of reed solomon codes it uses a modified berlekamp massey algorithm to perform all necessary generalized minimum distance decoding steps in only one run with a time domain form of the new decoder the overall asymptotic generalized minimum distance decoding complexity becomes o dn with n the length and d the distance of the code including the calculation of all error locations and values this asymptotic complexity is optimal other applications are the possibility of fast decoding of reed solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay

a new adaptive two stage maximum likelihood decoding algorithm for linear block codes in this paper we propose a new two stage ts structure for computationally efficient maximum likelihood decoding mld of linear block codes with this structure near optimal mld performance can be achieved at low complexity through ts processing the first stage of processing estimates a minimum sufficient set mss of candidate codewords that contains the optimal codeword while the second stage performs optimal or suboptimal decoding search within the estimated mss of small size based on the new structure we propose a decoding algorithm that systematically trades off between the decoding complexity and the bounded block error rate performance a low complexity complementary decoding algorithm is developed to estimate the mss followed by an ordered algebraic decoding oad algorithm to achieve flexible system design since the size of the mss changes with the signal to noise ratio the overall decoding complexity adaptively scales with the quality of the communication link theoretical analysis is provided to evaluate the potential complexity reduction enabled by the proposed decoding structure

reduced gmd decoding a framework is presented for generalized minimum distance gmd decoding with a limited number of decoding trials and a restricted set of reliability values in gmd decoding symbols received from the channel may be erased before being fed into an algebraic error erasure decoder for error correction in subsequent or simultaneous trials with different erasing patterns the decision whether or not to erase a symbol in a certain trial is taken by an erasure choosing algorithm which takes into account reliability information from the channel the final gmd decoder output is a codeword which results from a decoding trial and satisfies a certain distance criterion for various erasing strategies and reliability sets the guaranteed error correction radius and the unsuccessful decoding probability of this technique are studied both known and new results with applications to concatenated coding follow from the unified approach presented in this correspondence

on decoding of the 89 45 17 quadratic residue code in this paper three decoding methods of the 89 45 17 binary quadratic residue qr code to be presented are hard soft and linear programming decoding algorithms firstly a new hybrid algebraic decoding algorithm for the 89 45 17 qr code is proposed it uses the laplace formula to obtain the primary unknown syndromes as done in lin et al s algorithm when the number of errors v is less than or equal to 5 whereas gaussian elimination is adopted to compute the unknown syndromes when v 6 secondly an appropriate modification to the algorithm developed by chase is also given in this paper therefore combining the proposed algebraic decoding algorithm with the modified chase ii algorithm called a new soft decision decoding algorithm becomes a complete soft decoding of qr codes thirdly in order to further improve the error correcting performance of the code linear programming lp is utilized to decode the 89 45 17 qr code simulation results show that the proposed algebraic decoding algorithm reduces the decoding time when compared with lin et al s hard decoding algorithm and thus significantly reduces the decoding complexity of soft decoding while maintaining the same bit error rate ber performance moreover the lp based decoding improves the error rate performance almost without increasing the decoding complexity when compared with the new soft decision decoding algorithm it provides a coding gain of 0 2 db at ber 2 x 10 6

exact steady state distributions of multispecies birth death immigration processes effects of mutations and carrying capacity on diversity stochastic models that incorporate birth death and immigration also called birth death and innovation models are ubiquitous and applicable to many problems such as quantifying species sizes in ecological populations describing gene family sizes modeling lymphocyte evolution in the body many of these applications involve the immigration of new species into the system we consider the full high dimensional stochastic process associated with multispecies birth death immigration and present a number of exact and asymptotic results at steady state we further include random mutations or interactions through a carrying capacity and find the statistics of the total number of individuals the total number of species the species size distribution and various diversity indices our results include a rigorous analysis of the behavior of these systems in the fast immigration limit which shows that of the different diversity indices the species richness is best able to distinguish different types of birth death immigration models we also find that detailed balance is preserved in the simple noninteracting birth death immigration model and the birth death immigration model with carrying capacity implemented through death surprisingly when carrying capacity is implemented through the birth rate detailed balance is violated

toward a preferred 4 x 4 space time block code a performance versus complexity sweet spot with linear filter decoding we develop a new 4 4 hadamard precoded quasi orthogonal space time block code qo stbc that enables highly effective near maximum likelihood near ml reliability based prioritized symbol detection using linear filters approximate block error rate minimization is being used to optimize the code rotation angle detailed computational complexity evaluation of the decoder in terms of real multiplications and additions shows significant complexity reduction for symbol alphabet sizes of interest numerical and simulation studies demonstrate negligible bit error rate degradation compared to the state of the art in bit error rate by ml decoded 4 4 codewords

isometric immersions and compensated compactness a fundamental problem in differential geometry is to characterize intrinsic metrics on a two dimensional riemannian manifold mathcal m 2 which can be realized as isometric immersions into mathbb r 3 this problem can be formulated as initial and or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic hyperbolic type whose mathematical theory is largely incomplete in this paper we develop a general approach which combines a fluid dynamic formulation of balance laws for the gauss codazzi system with a compensated compactness framework to deal with the initial and or boundary value problems for isometric immersions in mathbb r 3 the compensated compactness framework formed here is a natural formulation to ensure the weak continuity of the gauss codazzi system for approximate solutions which yields the isometric realization of two dimensional surfaces in mathbb r 3

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

structured set partitions and multilevel concatenated coding for partial response channels we present a systematic way to construct multilevel concatenated codes for partial response pr channels using 1 a structured set partition ssp of multiple channel output sets and 2 a set of conventional block codes with different error correcting capabilities a lower bound on the minimum squared euclidean distance of the constructed codes is given this bound is based on the interset minimal euclidean distances of the ssp and the minimum hamming distances of the used block codes an example of ssp for the extended class 4 partial response channel epr4 is presented iterative suboptimal decoding which combines viterbi detection on the trellis of the pr channel with algebraic error detection correction can be applied to the constructed concatenated codes truncated versions of the iterative decoding scheme are simulated and compared with each other

rate one space time block codes with full diversity orthogonal space time block codes provide full diversity and maximum likelihood ml decoding for orthogonal codes can be realized on a symbol by symbol basis it has been shown that rate one complex orthogonal codes do not exist for systems with more than two transmit antennas for a general system with n transmit and m receive antennas it is very desirable to design rate one complex codes with full diversity in this letter we provide a systematic method of designing rate one codes real or complex for a general multiple input multiple output system full diversity of these codes is then achieved by constellation rotation a generalized reduced complexity decoding method for rate one codes is also provided

reliability based soft decision decoding with multiple biases in this paper a new reliability based soft decision decoding algorithm is presented this algorithm repeatedly uses biased reliability values to construct the most reliable basis mrb as a result this new method makes use of multiple information sets in a stochastic way compared to previously proposed competitive approaches this new method produces a more efficient mrb reprocessing type algorithm to achieve near maximum likelihood decoding mld performance with a proper choice of the bias value it can be combined with any mrb reprocessing type algorithm and in each case a tight performance analysis can be derived

an efficient maximum likelihood decoding algorithm for linear block codes with algebraic decoder a new soft decoding algorithm for linear block codes is proposed the decoding algorithm works with any algebraic decoder and its performance is strictly the same as that of maximum likelihood decoding mld since our decoding algorithm generates sets of different candidate codewords corresponding to the received sequence its decoding complexity depends on the received sequence we compare our decoding algorithm with chase 1972 algorithm 2 and the tanaka kakigahara 1983 algorithm in which a similar method for generating candidate codewords is used computer simulation results indicate for some signal to noise ratios snr that our decoding algorithm requires less average complexity than those of the other two algorithms but the performance of ours is always superior to those of the other two

complementary reliability based decodings of binary linear block codes this correspondence presents a hybrid reliability based decoding algorithm which combines the reprocessing method based on the most reliable basis and a generalized chase type algebraic decoder based on the least reliable positions it is shown that reprocessing with a simple additional algebraic decoding effort achieves significant coding gain for long codes the order of reprocessing required to achieve asymptotic optimum error performance is reduced by approximately 1 3 this significantly reduces the computational complexity especially for long codes also a more efficient criterion for stopping the decoding process is derived based on the knowledge of the algebraic decoding solution

semiorthogonal space time block codes in this paper a new class of full diversity rate one space time block codes stbcs called semiorthogonal algebraic space time block codes sast codes is proposed sast codes are delay optimal when the number of transmit antennas is even the sast codeword matrix has a generalized alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols sast codes with maximal coding gain are constructed by using rate one linear threaded algebraic space time ltast codes compared with ltsat codes sast codes not only reduce the complexity of maximum likelihood detection but also provide remarkable performance gain they also outperform other stbc with rate one or less sast codes also perform well with suboptimal detectors such as the vertical bell laboratories layered space time v blast nulling and cancellation receiver finally sast codes attain nearly 100 of the shannon capacity of open loop multiple input single output miso channels

capacity approaching space time codes for systems employing four transmitter antennas the design of space time codes that are capable of approaching the capacity of multiple input single output miso antenna systems is a challenging problem yet one of high practical importance while a remarkably simple scheme of alamouti 1998 is capable of attaining the channel capacity in the case of two transmitter and one receiver antennas 2 1 no such schemes are known for the case of more than two transmitter antennas we propose a family of space time codes that are especially designed for the case of four transmitter antennas and that are shown to allow the attainment of a significant fraction of the open loop shannon capacity of the 4 1 channel

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

group decodable space time block codes with code rate 1 high rate space time block codes stbc with code rate 1 in multi input multi output mimo systems are able to provide both spatial multiplexing gain and diversity gain but have high maximum likelihood ml decoding complexity since group decodable quasi orthogonal code structure can reduce the decoding complexity we present in this paper systematic methods to construct group decodable high rate stbc with full symbol wise diversity gain for arbitrary transmit antenna number and code length we show that the proposed group decodable stbc can achieve high code rate that increases almost linearly with the transmit antenna number and the slope of this near linear dependence increases with the code length comparisons with existing low rate and high rate codes such as orthogonal stbc and algebraic stbc are conducted to show the decoding complexity reduction and good code performance achieved by the proposed codes

on channel orthogonalization using space time block coding with partial feedback orthogonal space time block codes ostbcs yield full diversity gain even while requiring only a linear receiver such full rate rate one orthogonal designs are available for complex symbol constellations only for n 2 transmit antennas in this paper we propose a new family of full rate space time block codes stbcs using a single parameter feedback for communication over rayleigh fading channels for n 3 4 transmit antennas and m receive antennas the proposed rate one codes achieve full diversity and the performance is similar to maximum receiver ratio combining the decoding complexity of these codes are only linear even while performing maximum likelihood decoding the partial channel information is a real phase parameter that is a function of all the channel gains and has a simple closed form expression for n 3 4 this feedback information enables us to derive channel orthogonal designs starting from quasi orthogonal stbcs the feedback complexity is significantly lower than conventional closed loop transmit beamforming we compare the proposed codes with the open loop ostbcs and also with the closed loop equal gain transmission egt scheme which uses equal power loading on all antennas simulated error rate performances indicate that the proposed channel orthogonalized stbcs significantly outperform the open loop orthogonal designs for the same spectral efficiency moreover even with significantly lower feedback and computational complexity the proposed scheme outperforms the egt technique for m n

code automorphisms and permutation decoding of certain reed solomon binary images we consider primitive reed solomon rs codes over the field f2m of length n 2m 1 building on lacan s results for the case of binary extension fields we show that the binary images of certain two parity symbol rs n n 2 3 code have a code automorphism subgroup related to the general linear group gl m 2 for these codes we obtain a code automorphism subgroup of order m gl m 2 an explicit algorithm is given to compute a code automorphism if it exists that sends a particular choice of m binary positions into binary positions that correspond to a single symbol of the rs code if one such automorphism exists for a particular choice of m binary symbol positions we show that there are at least m of them computationally efficient permutation decoders are designed for the two parity symbol rs n n 2 3 codes simulation results are shown for the additive white gaussian noise awgn channel for the finite fields f23 and f24 we go on to derive subgroups of code automorphisms belonging to binary images of certain rs codes that have three parity symbols a table of code automorphism subgroup orders computed using the groups algorithms and programming gap software is tabulated for the fields f23 f24 and f25

on algebraic soft decision decoding algorithms for bch codes three algebraic soft decision decoding algorithms are presented for binary bose chaudhuri hocquengham bch codes two of these algorithms are based on the bounded distance bd 1 generalized minimum distance gmd decoding presented by berlekamp 1984 and the other is based on chase 1972 decoding a simple algebraic algorithm is first introduced and it forms a common basis for the decoding algorithms presented next efficient bd 1 gmd and bd 2 gmd decoding algorithms are presented it is shown that for binary bch codes with odd designed minimum distance d and length n both the bd 1 gmd and the bd 2 gmd decoding algorithms can be performed with complexity o nd the error performance of these decoding algorithms is shown to be significantly superior to that of conventional gmd decoding by computer simulation finally an efficient algorithm is presented for chase decoding of binary bch codes like a one pass gmd decoding algorithm this algorithm produces all necessary error locator polynomials for chase decoding in one run

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

on the reliability order based decoding algorithms for binary linear block codes in this correspondence we consider the decoding of binary block codes over the additive white gaussian noise awgn channel with binary phase shift keying bpsk signaling by a reliability order based decoding algorithm robda we mean a soft decision decoding algorithm which decodes to the best most likely codeword of the form that is the sum of the hard decision tuple and an error pattern in a set determined only by the order of the reliabilities of the hard decisions examples of robdas include many well known decoding algorithms such as the generalized minimum distance gmd decoding algorithm chase decoding algorithms and the reliability based decoding algorithms proposed by fossorier and lin it is known that the squared error correction radii of robdas can be computed from the minimal squared euclidean distances mseds between the all one sequence and the polyhedra corresponding to the error patterns for the computation of such mseds we give a new method which is more compact than the one proposed by fossorier and lin these results are further used to show that any bounded distance robda is asymptotically optimal the ratio between the probability of decoding error of a bounded distance robda and that of the maximum likelihood ml decoding approaches 1 when the signal to noise ratio snr approaches infinity provided that the minimum hamming distance of the code is greater than 2

generalized distributive law for ml decoding of space time block codes the problem of designing good space time block codes stbcs with low maximum likelihood ml decoding complexity has gathered much attention in the literature all the known low ml decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast decodable conditionally multigroup decodable structure of a code we refer to this well known technique of decoding stbcs as conditional ml cml decoding in this paper we introduce a new framework to construct ml decoders for stbcs based on the generalized distributive law gdl and the factor graph based sum product algorithm we say that an stbc is fast gdl decodable if the order of gdl decoding complexity of the code with respect to the constellation size m is strictly less than m where is the number of independent symbols in the stbc we give sufficient conditions for an stbc to admit fast gdl decoding and show that both multigroup and conditionally multigroup decodable codes are fast gdl decodable for any stbc whether fast gdl decodable or not we show that the gdl decoding complexity is strictly less than the cml decoding complexity for instance for any stbc obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable the gdl decoder provides about 12 times reduction in complexity compared to the cml decoder similarly for the golden code which is conditionally multigroup decodable the gdl decoder is only half as complex as the cml decoder

widely linear alamouti receiver for the reception of real valued constellations corrupted by interferences the alamouti saic maic concept orthogonal space time block codes stbc and the alamouti scheme in particular are of particular interest in multiple input multiple output mimo systems since they achieve full spatial diversity over fading channels and are decoded from linear processing at the receiver nevertheless due to the expensive spectral resource increasing network capacity requires the development of interference cancellation ic techniques allowing several users to share the same spectral resources without impacting the transmission quality in this context several ic schemes have been developed during this last decade where each user is equipped with multiple antennas and employs stbc at transmission however these ic techniques require multiple antennas at reception which remains a challenge at the handset level due to cost and size limitations for this reason low complexity single antenna interference cancellation saic techniques currently operational in gsm handsets have been developed recently for single antenna users using real valued modulations or complex filtering of real valued modulations by using a widely linear wl filtering at reception extension to multiple antennas at reception is called multiple antenna interference cancellation maic technique the purpose of this paper is to extend the saic maic technology to users using both real valued constellations such as amplitude shift keying ask constellations and the alamouti scheme at transmission a wl minimum mean square error mmse receiver completely new for ic purposes in the context of radio communications systems using the alamouti scheme is proposed and analyzed this receiver which corresponds to the maximum likelihood ml receiver for synchronous intranetwork interferences is able to separate up to 2 n alamouti users from n antennas at reception hence saic capability for n 1

single symbol ml decoding for orthogonal and quasi orthogonal stbc in clipped mimo ofdm systems using a clipping noise model with gaussian approximation an efficient way to reduce the peak to average power ratio papr in ofdm systems is clipping after the clipping in an mimo ofdm system the additive noise may not be white in this paper we develop fast single symbol ml decoding algorithms for orthogonal space time block codes ostbc and linearly transformed quasi orthogonal space time block codes qostbc in clipped mimo ofdm systems by using a clipping noise model with gaussian approximation by using the statistics of the clipping distortions our newly developed fast ml decoding algorithms improve the performance for clipped mimo ofdm systems with ostbc and qostbc while the decoding complexities are not increased simulation results are presented to illustrate the improvement

an adaptive two stage algorithm for ml and sub ml decoding of binary linear block codes two distinct codeword searching procedures based on iterative bounded distance decoding bdd are combined to form an adaptive two stage maximum likelihood ml decoder for binary linear block codes during the first stage of the algorithm a tight upper bound on an error likelihood metric discrepancy is established iteratively for the ml codeword first stage processing requires sorting and storage adaptive switching to the second stage removes the sorting and storage requirements and allows to rule out redundant bdds efficiently second stage processing accounts for all codewords with discrepancy lower bound below the upper bound of the ml codeword and guarantees ml performance in addition the proposed two stage algorithm is inherently tunable for controlled suboptimum operation under sub ml operation the overall scheme can be interpreted as a generalization of the chase 1972 algorithm simulation studies for the 24 12 8 extended golay and the 64 30 14 and 128 64 22 extended bose chaudhuri hocquenghem bch codes illustrate and support these theoretical developments

worst case robust mimo transmission with imperfect channel knowledge in this paper we consider robust transmit strategies against the imperfectness of the channel state information at the transmitter csit for multi input multi output mimo communication systems following a worst case deterministic model the actual channel is assumed to be inside an ellipsoid centered at a nominal channel the objective is to maximize the worst case received signal to noise ratio snr or to minimize the worst case chernoff bound of the error probability thus leading to a maximin problem moreover we also consider the qos problem as a complement of the maximin design which minimizes the transmit power consumption and meanwhile keeps the received snr above a given threshold for any channel realization in the ellipsoid it is shown that for a general class of power constraints both the maximin and qos problems can be equivalently transformed into convex problems or even further into semidefinite programs sdps thus efficiently solvable by the numerical methods the most interesting result is that the optimal transmit directions i e the eigenvectors of the transmit covariance are just the right singular vectors of the nominal channel under some mild conditions this result leads to a channel diagonalizing structure as in the cases of perfect csit and statistical csit with mean or covariance feedback and reduces the complicated matrix valued problem to a scalar power allocation problem then we provide the closed form solution to the resulting power allocation problem

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

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

on full diversity space time block codes with partial interference cancellation group decoding in this paper we propose a partial interference cancellation pic group decoding strategy scheme for linear dispersive space time block codes stbc and a design criterion for the codes to achieve full diversity when the pic group decoding is used at the receiver a pic group decoding decodes the symbols embedded in an stbc by dividing them into several groups and decoding each group separately after a linear pic operation is implemented it can be viewed as an intermediate decoding between the maximum likelihood ml receiver that decodes all the embedded symbols together i e all the embedded symbols are in a single group and the zero forcing zf receiver that decodes all the embedded symbols separately and independently i e each group has and only has one embedded symbol after the zf operation is implemented the pic group decoding provides a framework to adjust the complexity performance tradeoff by choosing the sizes of the information symbol groups our proposed design criterion group independence for the pic group decoding to achieve full diversity is an intermediate condition between the loosest ml full rank criterion of codewords and the strongest zf linear independence condition of the column vectors in the equivalent channel matrix we also propose asymptotic optimal ao group decoding algorithm which is an intermediate decoding between the mmse decoding algorithm and the ml decoding algorithm the design criterion for the pic group decoding can be applied to the ao group decoding algorithm because of its asymptotic optimality it is well known that the symbol rate for a full rank linear stbc can be full i e nt for nt transmit antennas it has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver the intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the pic group decoding this therefore provides a complexity performance rate tradeoff some design examples are given

generalized minimum distance decoding of euclidean space codes and lattices it is shown that multistage generalized minimum distance gmd decoding of euclidean space codes and lattices can provide an excellent tradeoff between performance and complexity we introduce a reliability metric for gaussian channels that is easily computed from an inner product and prove that a multistage gmd decoder using this metric is a bounded distance decoder up to the true packing radius the effective error coefficient of multistage gmd decoding is determined two simple modifications in the gmd decoding algorithm that drastically reduce this error coefficient are proposed it is shown that with these modifications gmd decoding achieves the error coefficient of maximum likelihood decoding for block codes and for generalized construction a lattices multistage gmd decoding of the lattices d sub 4 e sub 8 k sub 12 bw sub 16 and spl lambda sub 24 is investigated in detail for k sub 12 bw sub 16 and spl lambda sub 24 the gmd decoders have considerably lower complexity than the best known maximum likelihood or bounded distance decoding algorithms and appear to be the most practically attractive decoders available for high dimensional codes and lattices spl ges 64 dimensions maximum likelihood decoding becomes infeasible while gmd decoding algorithms remain quite practical as an example we devise a multistage gmd decoder for a 128 dimensional sphere packing with a nominal coding gain of 8 98 db that attains an effective error coefficient of 1365760 this decoder requires only about 400 real operations in addition to algebraic errors and erasures decoding of certain bch and hamming codes it therefore appears to be practically feasible to implement algebraic multistage gmd decoders for high dimensional sphere packings and thus achieve high effective coding gains

high rate multisymbol decodable stbcs from clifford algebras it is well known that space time block codes stbcs obtained from orthogonal designs ods are single symbol decodable ssd and from quasi orthogonal designs qods are double symbol decodable dsd however there are ssd codes that are not obtainable from ods and dsd codes that are not obtainable from qods in this paper a method of constructing g symbol decodable g sd stbcs using representations of clifford algebras are presented which when specialized to g 1 2 gives ssd and dsd codes respectively for the number of transmit antennas 2a the rate in complex symbols per channel use of the g sd codes presented in this paper is a 1 g 2a g the maximum rate of the dsd stbcs from qods reported in the literature is a 2a 1 which is smaller than the rate a 1 2a 2 of the dsd codes of this paper for 2a transmit antennas in particular the reported dsd codes for 8 and 16 transmit antennas offer rates 1 and 3 4 respectively whereas the known stbcs from qods offer only 3 4 and 1 2 respectively the construction of this paper is applicable for any number of transmit antennas the diversity sum and diversity product of the new dsd codes are studied it is shown that the diversity sum is larger than that of all known qods and hence the new codes perform better than the comparable qods at low signal to noise ratios snrs for identical spectral efficiency simulation results for dsd codes at various spectral efficiencies are provided

an improvement of soft decision maximum likelihood decoding algorithm using hard decision bounded distance decoding a new soft decision maximum likelihood decoding algorithm is proposed which generates a set of candidate codewords using hard decision bounded distance decoding by improving the generating method of input vectors for the bounded distance decoding due to kaneko et al see ibid vol 40 no 3 p 320 27 1994 the decoding time complexity is reduced without degradation of the performance the space complexity is dependent on the bounded distance decoding

soft decision decoding of reed solomon codes this paper presents a maximum likelihood decoding mld and a suboptimum decoding algorithm for reed solomon rs codes the proposed algorithms are based on the algebraic structure of the binary images of rs codes theoretical bounds on the performance are derived and shown to be consistent with simulation results the proposed suboptimum algorithm achieves near mld performance with significantly lower decoding complexity it is also shown that the proposed suboptimum algorithm has better performance compared with generalized minimum distance decoding while the proposed mld algorithm has significantly lower decoding complexity than the well known vardy be ery 1991 mld algorithm

on the existence of c 1 1 isometric immersions of several classes of negatively curved surfaces into mathbb r 3 we prove the existence of c 1 1 isometric immersions of several classes of negatively curved riemannian surfaces mathcal m g into the 3 dimensional euclidean space mathbb r 3 including the standard hyperbolic plane the generalised helicoid type metrics and the generalised enneper metrics our proof is based on the theory of compensated compactness and the method of invariant regions in hyperbolic conservation laws together with several new observations on relevant geometric quantities gauss curvature metric components etc for negatively curved surfaces

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

a bounded distance decoding algorithm for binary linear block codes achieving the minimum effective error coefficient a new bounded distance bd decoding algorithm is presented for binary linear n k d block codes on additive white gaussian noise channels the algorithm is based on the generalized minimum distance gmd decoding algorithm of forney 1989 using the acceptance criterion of taipale and pursley gmd tp proposed in 1991 it is shown that the gmd tp decoding algorithm is a bd decoding algorithm with effective error coefficient sup n sub d it is also shown that the decision regions of gmd tp are good inner approximations of those of full gmd decoding and therefore full gmd decoding is bd and has an effective error coefficient that is well approximated by sup n sub d moreover by adding a d erasure correction step to gmd decoding the effective error coefficient can be reduced to a sub d the number of minimum weight codewords which is the same as the effective error coefficient of maximum likelihood decoding the decoding algorithm is mainly based on algebraic errors and erasures decoding and therefore has polynomial rather than exponential complexity

design of fully diverse multiple antenna codes based on sp 2 fully diverse constellations i e sets of unitary matrices whose pairwise differences are nonsingular are useful in multiple antenna communications especially in multiple antenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we construct four transmit antenna constellations appropriate for differential modulation based on the symplectic group sp 2 they can be regarded as extensions of alamouti s celebrated two transmit antenna orthogonal design which can be constructed from the group sp 1 we further show that the structure of sp 2 codes lends itself to efficient maximum likelihood ml decoding via the sphere decoding algorithm finally the performance of sp 2 codes is compared with that of other existing codes including alamouti s orthogonal design a 4 spl times 4 complex orthogonal design cayley differential unitary space time codes and group based codes

two time scale population evolution on a singular landscape under the effect of strong genetic drift it is highly probable to observe gene fixation or gene loss in a population shown by singular peaks on a potential landscape the genetic drift induced noise gives rise to two time scale diffusion dynamics on the bipeaked landscape we find that the logarithmically divergent singular peaks do not necessarily imply infinite escape times or biological fixations by iterating the wright fisher model and approximating the average escape time our analytical results under weak mutation and weak selection extend kramers s escape time formula to models with b beta function like equilibrium distributions and overcome constraints in previous methods the constructed landscape provides a coherent description for the bistable system supports the quantitative analysis of bipeaked dynamics and generates mathematical insights for understanding the boundary behaviors of the diffusion model