design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

universal space time coding a universal framework is developed for constructing full rate and full diversity coherent space time codes for systems with arbitrary numbers of transmit and receive antennas the proposed framework combines space time layering concepts with algebraic component codes optimized for single input single output siso channels each component code is assigned to a thread in the space time matrix allowing it thus full access to the channel spatial diversity in the absence of the other threads diophantine approximation theory is then used in order to make the different threads transparent to each other within this framework a special class of signals which uses algebraic number theoretic constellations as component codes is thoroughly investigated the lattice structure of the proposed number theoretic codes along with their minimal delay allow for polynomial complexity maximum likelihood ml decoding using algorithms from lattice theory combining the design framework with the cayley transform allows to construct full diversity differential and noncoherent space time codes the proposed framework subsumes many of the existing codes in the literature extends naturally to time selective and frequency selective channels and allows for more flexibility in the tradeoff between power efficiency bandwidth efficiency and receiver complexity simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios

symbol by symbol map demodulation of cpm and psk signals on rayleigh flat fading channels demodulation using the symbol by symbol maximum a posteriori probability map algorithm is presented the algorithm is derived for the case of continuous phase modulation cpm signals transmitted over rayleigh flat fading channels and a corresponding receiver structure is specified it is shown that the map algorithm requires computing for each trellis branch the sum of the products of the weights of all paths through the trellis which pass through that branch and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis simulation results are presented which show both the hard and soft decision performance of the map receiver to be robust even in the presence of fade rates of up to 30 of the symbol rate the application of the receiver concept to phase shift keying psk signals is also discussed and then evaluated via simulation the concept of joint demodulation and decoding using iterative processing techniques is introduced it is shown that the map receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions simulation results for the reception of quaternary psk qpsk show that the bit error rate ber performance of the iterative map receiver can approach that of a receiver operating with perfect knowledge of the fading process

bounding the firing synchronization problem on a ring in this paper we improve the upper and lower bounds on the complexity of solutions to the firing synchronization problem on a ring in this variant of the firing synchronization problem the goal is to synchronize a ring of identical finite automata initially all automata are in the same state except for one automaton that is designated as the initiator for the synchronization the goal is to define the set of states and the transition function for the automata so that all machines enter a special fire state for the first time and simultaneously during the final round of the computation in our work we present two solutions to the ring firing synchronization problem an 8 state minimal time solution and a 6 state non minimal time solution both solutions use fewer states than the previous best known minimal time automaton a 16 state solution due to culik we also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem we show that there is no 3 state solution and no 4 state symmetric minimal time solution for the ring

sensitivity to timing errors in egc and mrc techniques the effect of imperfect timing is analyzed in equal gain combining egc and maximal ratio combining mrc techniques over rayleigh and nakagami m fading channels with binary phase shift keying modulation in the case of egc the bit error probability is derived while in the case of mrc error rate bounds are presented theoretical results are justified by computer simulation numerical results demonstrate that both egc and mrc are fairly sensitive to timing errors and comparatively mrc is more sensitive

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

error probability analysis of bit interleaved coded modulation this correspondence presents a simple method to accurately compute the error probability of bit interleaved coded modulation bicm thanks to the binary input output symmetric bios nature of the channel the pairwise error probability pep is equal to the tail probability of a sum of random variables with a particular distribution this probability is in turn computed with a saddlepoint approximation its precision is numerically validated for coded transmission over standard gaussian noise and fully interleaved fading channels for both convolutional and turbo like codes

a six state minimal time solution to the firing squad synchronization problem abstract from balzer s work 1967 we know that the firing squad synchronization problem has a minimal time solution with eight states we show that such a solution exists with only six states our method is somewhat different from all previous ones the initial line is iteratively divided in two inequal parts so that each new right part can be treated as the homothetical image of a shorter initial line

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

the c algebra of singular integral operators with semi almost periodic coefficients abstract we establish a fredholm criterion for the operators belonging to the c algebra generated by singular integral operators with semi almost periodic matrix coefficients the result is applied to toeplitz like operators that are perturbed by integral operators with fixed singularities at infinity in which case it leads to an effectively verifiable fredholm criterion together with an index formula our approach is based on an isomorphism theorem for c algebras associated with c dynamical systems and the notion of canonical generalized ap factorization for almost periodic matrix functions

low complexity joint channel estimation and decoding for pilot symbol assisted modulation and multiple differential detection systems with correlated rayleigh fading joint channel estimation and decoding in a time varying rayleigh fading channel is considered knowing that the optimal solution or even the truncated near optimal solution using iterative processing has an exponential complexity which hinders the practicability a reduced complexity approach is proposed this approach keeps the existing channel estimation and decoding schemes almost intact while applying iterative processing to effectively exchange information between them thus the complexity is rendered linear and estimator adaptability can be easily established we apply this approach to pilot symbol assisted modulation psam and differentially modulated systems it turns out that the performance is improved and the robustness to fading parameters is enhanced through simulations we also show that the proposed method performs almost as well as the near optimal design

the firing squad synchronization problem on ca with multiple updating cycles abstract classical cellular automata have a single global clock that allows all the cells to update their states simultaneously at every clock cycle here we overturn this assumption and we study cellular automata where different cells can use different clocks cycles and as a consequence they update at different times we show how it is possible to solve the firing squad synchronization problem in this new setting and propose a synchronization algorithm operating in time linear with respect to the automata size

leader election on two dimensional periodic cellular automata this article explores the computational power of bi dimensional cellular automata acting on periodical configurations it extends in some sense the results of a similar paper dedicated to the one dimensional case more precisely we present an algorithm that computes a minimal pattern network i e a minimal pattern and the two translation vectors it can use to tile the entire configuration this problem is equivalent to the computation of a leader which is one equivalence class of the cells of the periodical configuration

iterative sphere detectors for imperfect channel state information this manuscript presents an iterative detector based on a generalized schnorr euchner enumeration for the case of imperfect channel state information the detector determines the most contributive n 1 2 terms in each of the two log sum exponents the objective function of the tree search is modified to account for a the channel estimation error variance and b the input a priories due to a the decomposition of the objective into the form used in conventional tree search is not possible moreover both a and b invalidate the use of the progressive zigzag order because of this a generalized schnorr euchner enumeration is proposed where explicit sorting is done unlike the conventional tree search the node weights are not computed in an additive way where the weight of a child node is the sum of the weights of the parent and the branch connecting them the advantage of the proposed detectors compared to iterative channel estimation and decoding is that the repetition of the channel estimation and the qr decomposition is not needed also since they are based on the schnorr euchner enumeration they do not require an initial radius estimation and if channel estimation errors are small enough to be ignored the search step becomes division and square root free

effect of channel estimation error on qam systems with antenna diversity this paper studies the effect of channel estimation error and antenna diversity on multilevel quadrature amplitude modulation m qam systems over rayleigh fading channels based on the characteristic function method a general closed form bit error rate ber for m qam systems is presented the effect of the inaccurate channel estimation on the performance for pilot symbol assisted modulation m qam systems with antenna diversity is investigated simulation results for m qam m 4 16 64 256 etc show that the analytical method can accurately estimate the system performance moreover numerical results show that with the antenna diversity technique the ber performance improves significantly especially in perfect channel estimation cases it is also found that the channel estimation error limits the benefit of antenna diversity by increasing the length of the channel estimator and the amplitude of the pilot symbol more accurate channel estimation can be achieved so that the ber performance is improved

seven state solutions to the firing squad synchronization problem abstract we show that seven states are enough to implement minsky like solutions to the firing squad synchronization problem in a linear network of n finite state cellular automata with null transmission delay

effect of channel estimation error on m qam ber performance in rayleigh fading we determine the bit error rate ber of multilevel quadrature amplitude modulation m qam in flat rayleigh fading with imperfect channel estimates despite its high spectral efficiency m qam is not commonly used over fading channels because of the channel amplitude and phase variation since the decision regions of the demodulator depend on the channel fading estimation error of the channel variation can severely degrade the demodulator performance among the various fading estimation techniques pilot symbol assisted modulation psam proves to be an effective choice we first characterize the distribution of the amplitude and phase estimates using psam we then use this distribution to obtain the ber of m qam as a function of the psam and channel parameters by using a change of variables our exact ber expression has a particularly simple form that involves just a few finite range integrals this approach can be used to compute the ber for any value of m we compute the ber for 16 qam and 64 qam numerically and verify our analytical results by computer simulation we show that for these modulations amplitude estimation error leads to a 1 db degradation in average signal to noise ratio and combined amplitude phase estimation error leads to 2 5 db degradation for the parameters we consider

decoding of low density parity check codes over finite state binary markov channels we propose a modified algorithm for decoding of low density parity check codes over finite state binary markov channels the proposed approach clearly outperforms systems in which the channel statistics are not exploited in the decoding even when the channel parameters are not known a priori at the decoder

the performance of universal encoding universal coding theory is surveyed from the viewpoint of the interplay between delay and redundancy the price for universality turns out to be acceptably small

adaptive iterative detectors for phase uncertain channels via variational bounding the problem of iterative detection decoding of data symbols transmitted over an additive white gaussian noise awgn channel in the presence of phase uncertainty is addressed in this paper by modelling the phase uncertainty either as an unknown deterministic variable process or random variable process with a known a priori probability density function a number of non bayesian and bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem in this paper a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique especially applying the generic variational bayesian vb framework efficient iterative joint estimation and detection decoding schemes are derived for the constant phase model as well as for the dynamic phase model in addition the relation of the vb based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation maximization em algorithm is provided performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors furthermore an incremental scheduling of the vb or em algorithm is shown to reduce the overall complexity of the receiver

high rate concatenated space time block code m tcm designs in this paper a new technique to design improved high rate space time st codes is proposed based on the concept of concatenated st block code stbc and outer trellis coded modulation m tcm encoder constructions unlike the conventional rate lossy stbc mtcm schemes the proposed designs produce higher rate st codes by expanding the codebook of the inner orthogonal stbc the classic set partitioning concept is adopted to realize the stbc mtcm designs with large coding gains the proposed expanded stbc mtcm designs for the two three and four transmitter cases are illustrated simulation results show the proposed stbc mtcm designs significantly outperform the traditional st tcm schemes furthermore decoding complexity of the proposed scheme is low because signal orthogonality is exploited to ease data decoding

the firing squad synchronization problem on cayley graphs the firing squad synchronization problem fssp for short has been intensively studied in the one dimensional space the problem consists in the synchronization of a segment of automata we generalize this problem on cayley graphs we give minimal time solutions for a synchronizing all cells in all minimal paths between any pair of cells of a cayley graph b synchronizing all cells in all minimal paths starting at a given cell g the general and leading to all cells at a given distance from g in a cayley graph in solutions for b in some cases all cells of a ball in a cayley graph will be synchronized in other cases this is not possible because of the existence of culs de sac

global minimax approximations and bounds for the gaussian q function by sums of exponentials this paper presents a novel systematic methodology to obtain new simple and tight approximations lower bounds and upper bounds for the gaussian q function and functions thereof in the form of a weighted sum of exponential functions they are based on minimizing the maximum absolute or relative error resulting in globally uniform error functions with equalized extrema in particular we construct sets of equations that describe the behaviour of the targeted error functions and solve them numerically in order to find the optimized sets of coefficients for the sum of exponentials this also allows for establishing a trade off between absolute and relative error by controlling weights assigned to the error functions extrema we further extend the proposed procedure to derive approximations and bounds for any polynomial of the q function which in turn allows approximating and bounding many functions of the q function that meet the taylor series conditions and consider the integer powers of the q function as a special case in the numerical results other known approximations of the same and different forms as well as those obtained directly from quadrature rules are compared with the proposed approximations and bounds to demonstrate that they achieve increasingly better accuracy in terms of the global error thus requiring significantly lower number of sum terms to achieve the same level of accuracy than any reference approach of the same form

time optimal solution of the firing squad synchronization problem for n dimensional rectangles with the general at an arbitrary position a time optimal solution to the firing squad synchronization problem of n dimensional rectangles with the general at an arbitrary position is presented the solution uses one dimensional time optimal fssp algorithms which have a symmetrical transition function and use as few states as the best known non symmetrical transition functions the n dimensional case is demonstrated for n 2 and the straightforward generalization to larger n is outlined

c algebra of nonlocal convolution type operators abstract the c subalgebra b of all bounded linear operators on the space l 2 r which is generated by all multiplication operators by piecewise slowly oscillating functions by all convolution operators with piecewise slowly oscillating symbols and by the range of a unitary representation of the group of all affine mappings on r is studied a faithful representation of the quotient c algebra b b k in a hilbert space where k is the ideal of compact operators on the space l 2 r is constructed by applying an appropriate spectral measure decompositions a local trajectory method and the fredholm symbol calculus for the c algebra of convolution type operators without shifts this gives a fredholm symbol calculus for the c algebra b and a fredholm criterion for the operators b b

on maximum likelihood detection and the search for the closest lattice point maximum likelihood ml decoding algorithms for gaussian multiple input multiple output mimo linear channels are considered linearity over the field of real numbers facilitates the design of ml decoders using number theoretic tools for searching the closest lattice point these decoders are collectively referred to as sphere decoders in the literature in this paper a fresh look at this class of decoding algorithms is taken in particular two novel algorithms are developed the first algorithm is inspired by the pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the viterbo boutros sphere decoder the connection between the proposed algorithm and the stack sequential decoding algorithm is then established this connection is utilized to construct the second algorithm which can also be viewed as an application of the schnorr euchner strategy to ml decoding aided with a detailed study of preprocessing algorithms a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near ml detection performance this claim is supported by intuitive arguments and simulation results in many relevant scenarios

iterative decoding of low density parity check codes over compound channels iterative decoding of low density parity check codes over compound channels we present a setting for decoding of low density parity check ldpc codes jointly with channel estimation suitable for transmission over memoryless compound channels we show that the performance of the combined scheme can be rigorously evaluated by means of density evolution and focus on density evolution as a tool for designing a channel estimator that matches not only to the channel but also to the ldpc ensemble as well the utility of the concept is exemplified for a compound binary symmetric channel and an unknown phase additive white gaussian channel

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 firing squad synchronization problem for graphs abstract in this paper we give a solution of the firing squad synchronization problem for graphs the synchronization times of solutions which have been obtained are proportional to the number of nodes of a graph the synchronization time of our solution is proportional to the radius rg of a graph g 3rg 1 or 3rg time units where rg is the longest distance between the general and any other node of g this synchronization time is minimum for an infinite number of graphs

the minimum firing time of the generalized firing squad synchronization problem for squares for almost all variations of the firing squad synchronization problem for elementary geometric figures such as lines rings squares rectangles and cubes minimal time solutions are known however in 2012 umeo and kubo introduced a very simple variation of this type and pointed out that its minimal time solutions are unknown in that variation a problem instance is a square array of n columns and n rows and the position of the general is arbitrary for this variation they constructed a solution that fires at time 2n 2 for any position of the general and wrote that it is not known whether this solution is minimal time or not we determine the exact value of the minimum firing time of this variation for some problem instances this value is smaller than 2n 2 and hence the 2n 2 time solution is not minimal time our result does not solve the problem of existence or non existence of minimal time solutions of the variation however the result gives one necessary condition for solutions to be minimal time

the llr metric for q ary ldpc codes with mpsk modulation over rayleigh channels with imperfect csi we consider the iterative decoding of low density parity check codes with m ary phase shift keying transmission and pilot symbol assisted channel estimation over time correlated rayleigh fading channels we present the correct conceptual approach for deriving the log likelihood ratio llr expression for a general q ary code its bit error probability bep performance is compared with that of the conventional metric which does not take into account the information concerning the channel estimation accuracy simulation results show that this llr metric outperforms the conventional metric in both bep performances and average number of decoding iterations required for convergence the work here demonstrates the importance of incorporating the knowledge of the channel estimation accuracy in the iterative decoding process

on time optimal solutions of the firing squad synchronization problem for two dimensional paths the firing squad synchronization problem for two dimensional paths 2 path fssp for short is a variation of the firing squad synchronization problem where finite automata are placed along a path in the two dimensional array space whether 2 path fssp has a time optimal solution or not is an open problem we introduce a combinatorial problem which we call the two dimensional path extension problem 2 pep for short and show that if 2 path fssp has a time optimal solution then 2 pep has a polynomial time algorithm the computational complexity of 2 pep is not well understood and the exhaustive search requiring exponential time is the only algorithm we know for it at present

pilot symbol assisted coded transmission over the block noncoherent awgn channel in this paper pilot symbol assisted transmission in conjunction with high performance coding over the block independent noncoherent additive white gaussian noise channel is investigated several approximate iterative receivers are proposed which either perform carrier phase estimation separately from detection or joint carrier phase estimation decoding in an iterative fashion the performance of the proposed receivers is analyzed using density evolution the power allocation to the pilot symbol is quantified and it is shown that an optimal allocation scheme exists that minimizes the overall information bit signal to noise ratio required for error free communication this optimal power allocation which could be utilized in code design is found to be sensitive to the channel coherence interval as well as to the particular receiver used in addition a simple upper bound on the performance of any receiver that performs joint iterative carrier phase estimation and detection is derived the obtained results are compared with the simulated performance of the proposed receivers

variable rate and variable power mqam system based on bayesian bit error rate and channel estimation techniques the impact of inaccurate channel state information at the transmitter for a variable rate variable power multilevel quadrature amplitude modulation vrvp mqam system over a rayleigh flat fading channel is investigated a system model is proposed with rate and power adaptation based on the estimates of instantaneous signal to noise ratio snr and bit error rate ber a pilot symbol assisted modulation scheme is used for snr estimation the ber estimator is derived using a maximum a posteriori approach and a simplified closed form solution is obtained as a function of only the second order statistical characterization of the channel state imperfection based on the proposed system model rate and power adaptation is derived for the optimization of spectral efficiency subject to an average power constraint and an instantaneous ber requirement the performance of the vrvp mqam system under imperfect channel state information csi is evaluated we show that the proposed vrvp mqam system that employs optimal solutions based on the statistical characterization of csi imperfection achieves a higher spectral efficiency as compared to an ideal csi assumption based method

bounds on rates of ldpc codes for bec with varying erasure rate a binary erasure channel with erasure probability which can take one of two values is considered transmission is done by using a low density parity check code under the requirement that completely successful decoding is possible when the channel is in its better state while tolerating some predetermined residual erasure fraction when the channel is in its worse state upper bounds on the achievable design rate under iterative decoding are derived for this setting these bounds are compared to rates obtained by practical code profiles it is also observed that when exceeding the capacity of the erasure channel the performance of such codes exhibits graceful degradation as measured by the residual erasure fraction

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

on the complexity of network synchronization we show that if a minimal time solution to a fundamental distributed computation primitive synchronizing a network path of finite state processors exists on the three dimensional undirected grid then we can conclude the purely complexity theoretic result p np every previous result on network synchronization for various network topologies either demonstrates the existence of fast synchronization solutions or proves that a synchronization solution cannot exist at all to date it is unknown whether there is a network topology for which there exists a synchronization solution but for which no minimal time synchronization solution exists under the assumption that p neq np this paper solves this longstanding open problem in the affirmative

a simple bit error probability analysis for square qam in rayleigh fading with channel estimation a new approach is presented for analyzing the bit error probability bep of square multilevel quadrature amplitude modulation over a nonselective rayleigh fading channel with imperfect channel estimation employing pilot symbol assisted modulation it is much simpler and more powerful than those in the literature and the average bep is obtained by calculating the bep for each individual bit the results are given in simple exact closed form expressions that do not require any numerical integration these expressions show explicitly the behavior of the bep as a function of various system parameters three channel estimation schemes are investigated it is shown that existing channel estimation schemes using sinc interpolation and gaussian interpolation can be improved

message passing algorithms for phase noise tracking using tikhonov mixtures phase noise poses a serious challenge for high speed digital communications systems mainly when going to higher and higher carrier frequencies such as in satellite communications traditionally phase noise estimation was performed separately from the decoding task and it was shown recently that there is much to be gained from joint estimation and decoding particularly when using ldpc low density parity check turbo codes however jointly estimating phase noise and decoding is a very complex and computationally demanding task in this paper we propose several algorithms based on the sum and product algorithm spa for low complexity joint decoding and estimation of coded information in strong phase noise channels these algorithms are based on a novel approximation of spa messages as tikhonov mixtures of a given order since mixture based bayesian inference such as spa creates an exponential increase in mixture order for consecutive messages a mixture reduction scheme is a must therefore in this paper we propose a low complexity mixture reduction algorithm which provably satisfies an upper bound on the kullback leibler kl divergence between the mixture and the reduced mixture we then reduce the complexity even further including limiting the model order and reducing the clustering effort to simple component selection as an extreme case it is even possible to reduce the number of modes to one we show the relation between the simplified algorithm to the phase locked loop pll finally we show simulation results and complexity analysis for the proposed algorithms which show superior performance over other state of the art low complexity algorithms

sphere decoding complexity exponent for decoding full rate codes over the quasi static mimo channel in the setting of quasi static multiple input multiple output channels we consider the high signal to noise ratio snr asymptotic complexity required by the sphere decoding sd algorithm for decoding a large class of full rate linear space time codes with sd complexity having random fluctuations induced by the random channel noise and codeword realizations the introduced sd complexity exponent manages to concisely describe the computational reserves required by the sd algorithm to achieve arbitrarily close to optimal decoding performance bounds and exact expressions for the sd complexity exponent are obtained for the decoding of large families of codes with arbitrary performance characteristics for the particular example of decoding the recently introduced threaded cyclic division algebra based codes the only currently known explicit designs that are uniformly optimal with respect to the diversity multiplexing tradeoff the sd complexity exponent is shown to take a particularly concise form as a non monotonic function of the multiplexing gain to date the sd complexity exponent also describes the minimum known complexity of any decoder that can provably achieve a gap to maximum likelihood performance that vanishes in the high snr limit

a linear speed up theorem for cellular automata abstract ibarra 1985 showed that given a cellular automaton of range 1 recognizing some language in time n 1 r n we can obtain another ca of range 1 recognizing exactly the same language but in time n 1 r n k k 2 arbitrary their proof proceeds indirectly through the simulation of cas by a special kind of sequential machines the stms and we think it misses that way some of the deep intuition of the problem we therefore provide here a direct proof of this result extended to the case of cas of arbitrary range involving the explicit construction of a ca working in time n 1 r n k this speeded up automaton first gathers the cells of the line k by k in n 1 steps which then enables it to start computing by leaps of k steps thus completing the r n remaining steps in time r n k the major problem arising from the obligation to pass from one phase to the other synchronously is solved using a synchronization process derived from the solutions of the well known firing squad synchronization problem fssp

augmented belief propagation decoding of low density parity check codes we propose an augmented belief propagation bp decoder for low density parity check ldpc codes which can be utilized on memoryless or intersymbol interference channels the proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the bp decoder the augmented decoder is a multistage iterative decoder where at each stage the original channel messages on select symbol nodes are replaced by saturated messages the key element of the proposed method is the symbol selection process which is based on the appropriately defined subgraphs of the code graph and or the reliability of the information received from the channel we demonstrate by examples that this decoder can be implemented to achieve substantial gains compared to the standard locally operating bp decoder for short ldpc codes decoded on both memoryless and intersymbol interference gaussian channels using the margulis code example we also show that the augmented decoder reduces the error floors finally we discuss types of bp decoding errors and relate them to the augmented bp decoder

a c algebra of singular integral operators with shifts admitting distinct fixed points abstract representations on hilbert spaces for a nonlocal c algebra b of singular integral operators with piecewise slowly oscillating coefficients extended by a group of unitary shift operators are constructed the group of unitary shift operators u g in the c algebra b is associated with a discrete amenable group g of orientation preserving piecewise smooth homeomorphisms g t t that acts topologically freely on t and admits distinct fixed points for different shifts a c algebra isomorphism of the quotient c algebra b k where k is the ideal of compact operators onto a c algebra of fredholm symbols is constructed by applying the local trajectory method spectral measures and a lifting theorem as a result a fredholm symbol calculus for the c algebra b or equivalently a faithful representation of the quotient c algebra b k on a suitable hilbert space is constructed and a fredholm criterion for the operators b b is established

theory of cellular automata a survey this article surveys some theoretical aspects of cellular automata ca research in particular we discuss classical and new results on reversibility conservation laws limit sets decidability questions universality and topological dynamics of ca the selection of topics is by no means comprehensive and reflects the research interests of the author the main goal is to provide a tutorial of ca theory to researchers in other branches of natural computing to give a compact collection of known results with references to their proofs and to suggest some open problems

universal serially concatenated trellis coded modulation for space time channels this paper presents serially concatenated trellis coded modulations sctcms that perform consistently close to the available mutual information for periodic erasure channel pec periodic fading channel pfc and the 2 times 2 compound matrix channel we use both the maximum likelihood decoding criteria and iterative decoding criteria to design universal sctcms for the pec and the pfc for the space time channel by demultiplexing the symbols across the antennas the proposed universal sctcms for the period 2 pfc deliver consistent performance over the eigenvalue skew of the matrix channel within the family of channels having the same eigenvalue skew a time varying linear transformation tvlt is used to mitigate the performance variation over different eigenvectors the proposed space time sctcms of 1 0 2 0 and 3 0 bits per transmission require excess mutual information in the ranges 0 11 0 15 0 23 0 26 and 0 35 0 53 bits per antenna respectively because of their consistent performance over all channels the proposed codes will have good frame error rate fer performance over any quasi static fading distribution in particular the codes provide competitive fer performance in quasi static rayleigh fading

soft decision metric generation for qam with channel estimation error the channel code bit log likelihood ratio llr for soft decision decoding is derived for quadrature amplitude modulated signals qam the effect of imperfect channel knowledge on soft decision decoding performance is studied our results indicate this effect increases with channel estimation error and or qam modulation level a metric based on generalized log likelihood ratio gllr is derived for soft decision channel decoding with imperfect channel knowledge numerical results show that the gllr based metric outperforms the conventional minimum distance decoding metric that does not take into account channel estimation error

comments on exact error rate analysis of diversity 16 qam with channel estimation error recently cao and beaulieu presented an insightful analysis on the bit error performance of 16 quadrature amplitude modulation qam scheme on rayleigh fading channels with maximal ratio combining diversity and channel estimation errors unfortunately although exact the results presented in that paper are based on a complicated parabolic cylinder function and a two dimensional numerical integration has to be performed to evaluate the average probability of bit error in this letter we present a surprisingly simple expression for the average probability of error in a well known closed form we point out that the error rates for any n ary square rectangular qam constellation with gray mapping can also be expressed in this form furthermore we show that the presented results can also be modified in a simple fashion for a generalized selection combining scheme in the presence of channel estimation errors

the synchronization of nonuniform networks of finite automata abstract the generalized firing squad synchronization problem gfssp is the well known firing squad synchronization problem fssp extended to arbitrarily connected networks of finite automata here the transmission delays associated with the links of a network are assumed to be 0 i e a signal can get through a link in no time when the delays are allowed to be arbitrary nonnegative integers the problem is called gfssp nud i e gfssp with nonuniform delays we give for the first time a solution of gfssp nud the solution is independent of the structure of the network and the actual delays of the links the firing time of the solution is bounded by o 3 max where max is the maximum transmission delay of any single link and is the maximum transmission delay between the general and any other node of a given network this answers an open question in mazoyer in automata networks c choffrut ed pp 82 93 springer verlag berlin new york 1986 our result is based on a strategy different from the one of balzer and waksman which is used in almost all existing solutions of fssp and gfssp the extension of gfssp and gfssp nud to networks with more than one general is also considered we show that 1 for any fixed k 2 gfssp with at most k generals has a solution whose firing time is bounded by o d where d is the maximum distance between any two nodes of a given network and gfssp nud with at most k generals has a solution whose firing time is bounded by o max 3 where is the maximum transmission delay between any two nodes of a given network 2 there are no solutions for gfssp and gfssp nud with an arbitrary number of generals

on the error probability of linearly modulated signals on frequency flat ricean rayleigh and awgn channels the method used in aghamohammadi and meyr 1990 for finding the error probability of linearly modulated signals on rayleigh frequency flat fading channels has been applied to the more general case of ricean fading a signal received on a fading channel is subject to a multiplicative distortion md and to the usual additive noise following a compensation of the md the signal provided to the detector may be thought to include only a single additive distortion term final noise which comprises the effects of the original additive noise the md and the error in md compensation an exact expression for the probability density function of the final noise is derived this allows calculation of error probability for arbitrary types of linear modulations results for many cases of interest are presented furthermore as special cases of ricean fading error probability for rayleigh fading and non fading channels are obtained which either match the results or complete the approximate derivations formerly known from the literature

firing squad synchronization problem in reversible cellular automata abstract we studied the firing squad synchronization problem fssp on reversible i e backward deterministic cellular automata rca first we proved that in the case of rca there is no solution under the usual condition for fssp where the firing state is only one so we defined a little weaker condition suitable for rca in which finite number of firing states are allowed we showed that minsky s solution in time 3n can be embedded in an rca with 99 states that satisfies the new condition we used the framework of partitioned ca pca which is regarded as a subclass of ca for making ease of constructing rca

ldpc codes over rings for psk modulation this paper describes the design and analysis of low density parity check ldpc codes over rings and shows how these codes when mapped onto appropriate signal constellations can be used to effect bandwidth efficient modulation specifically ldpc codes are constructed over the integer rings spl zopf sub m and g sub m sup 2 and mapped onto phase shift keying psk type signal sets to yield geometrically uniform signal space codes this paper identifies and addresses the design issues that affect code performance examples of codes over spl zopf sub 8 and g sub 64 mapped onto 8 ary and 64 ary signal sets at a spectral efficiency of 1 5 and 2 0 bits per second per hertz b s hz illustrate the approach simulation of these codes over the additive white gaussian noise awgn channel demonstrates that this approach is a good alternative to bandwidth efficient techniques based on binary ldpc codes e g bit interleaved coded modulation

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

spectral measures in c algebras of singular integral operators with shifts abstract the c subalgebra b of b l 2 t generated by all multiplication operators by slowly oscillating and piecewise continuous functions by the cauchy singular integral operator and by the range of a unitary representation of an amenable group of diffeomorphisms which acts topologically freely on t is studied a symbol calculus for the c algebra b and a fredholm criterion for the operators b b are established by using a generalization of the local trajectory method for studying c algebras associated with c dynamical systems this method is related to the allan douglas local principle and its generalization is based on the notion of spectral measure

exact error rate analysis of diversity 16 qam with channel estimation error the bit error rate ber performance of multilevel quadrature amplitude modulation with pilot symbol assisted modulation channel estimation in static and rayleigh fading channels is derived both for single branch reception and maximal ratio combining diversity receiver systems the effects of noise and estimator decorrelation on the received ber are examined the high sensitivity of diversity systems to channel estimation error is investigated and quantified the influence of the pilot symbol interpolation filter windowing is also considered

llr approximation for wireless channels based on taylor series and its application to bicm with ldpc codes a new approach for the approximation of the channel log likelihood ratio llr for wireless channels based on taylor series is proposed the approximation is applied to uncorrelated flat fading channels with unknown channel state information at the receiver it is shown that the proposed approximation greatly simplifies the calculation of channel llrs and yet provides results almost identical to those based on the exact calculation of channel llrs the results are obtained in the context of bit interleaved coded modulation bicm schemes with low density parity check ldpc codes and include threshold calculations and error rate performance of finite length codes compared to the existing approximations the proposed method is either significantly less complex or considerably more accurate

low complexity affine mmse detector for iterative detection decoding mimo ofdm systems iterative turbo processing between detection and decoding shows near capacity performance on a multiple antenna system combining iterative processing with optimum front end detection is particularly challenging because the front end maximum a posteriori map algorithm has a computational complexity that is exponential sub optimum detector such as the soft interference cancellation linear minimum mean square error sic lmmse detector with near front end map performance has been proposed in the literature the asymptotic computational complexity of sic lmmse is o nt 2nr ntnr 3 ntmc2mc per detection decoding cycle where nt is number of transmit antenna nr is number of receive antenna and mc is modulation size a lower complexity detector is the hard interference cancellation lmmse hic lmmse detector hic lmmse has asymptotic complexity of o nt 2nr ntmc2mc but suffers extra performance degradation in this paper two front end detection algorithms are introduced that not only achieve asymptotic computational complexity of o nt 2nr ntnr 2 gamma beta 1 ntmc2mc where gamma beta is a function with discrete output 1 2 3 nt and o ntmc2mc respectively simulation results demonstrate that the proposed low complexity detection algorithms offer exactly same performance as their full complexity counterpart in an iterative receiver while being computational more efficient

density evolution for asymmetric memoryless channels density evolution de is one of the most powerful analytical tools for low density parity check ldpc codes and graph codes with message passing decoding algorithms with channel symmetry as one of its fundamental assumptions density evolution has been widely and successfully applied to different channels including binary erasure channels becs binary symmetric channels bscs binary additive white gaussian noise biawgn channels etc this paper generalizes density evolution for asymmetric memoryless channels which in turn broadens the applications to general memoryless channels e g z channels composite white gaussian noise channels etc the central theorem underpinning this generalization is the convergence to perfect projection for any fixed size supporting tree a new iterative formula of the same complexity is then presented and the necessary theorems for the performance concentration theorems are developed several properties of the new density evolution method are explored including stability results for general asymmetric memoryless channels simulations code optimizations and possible new applications suggested by this new density evolution method are also provided this result is also used to prove the typicality of linear ldpc codes among the coset code ensemble when the minimum check node degree is sufficiently large it is shown that the convergence to perfect projection is essential to the belief propagation bp algorithm even when only symmetric channels are considered hence the proof of the convergence to perfect projection serves also as a completion of the theory of classical density evolution for symmetric memoryless channels

constructible functions in cellular automata and their applications to hierarchy results we investigate time constructible functions in one dimensional cellular automata ca it is shown that i if a function t n is computable by an o t n n time turing machine then t n is time constructible by ca and ii if two functions are time constructible by ca then the sum product and exponential functions of them are time constructible by ca as an application it is shown that if t1 n and t2 n are time constructible functions such that limnt1 n t2 n 0 and t1 n n then there is a language which can be recognized by a ca in t2 n time but not by any ca in t1 n time

achieving a vanishing snr gap to exact lattice decoding at a subexponential complexity this study identifies the first lattice decoding solution that achieves in the general outage limited multiple input multiple output mimo setting and in the high rate and high signal to noise ratio limit both a vanishing gap to the error performance of the exact solution of regularized lattice decoding as well as a computational complexity that is subexponential in the number of codeword bits and in the rate the proposed solution employs lenstra lenstra lovasz based lattice reduction lr aided regularized lattice sphere decoding and proper timeout policies these performance and complexity guarantees hold for most mimo scenarios most fading statistics all channel dimensions and all full rate lattice codes in sharp contrast to the aforementioned very manageable complexity the complexity of other standard preprocessed lattice decoding solutions is revealed here to be extremely high specifically this study has quantified the complexity of regularized lattice sphere decoding and has proved that the computational resources required by this decoder to achieve a good rate reliability performance are exponential in the lattice dimensionality and in the number of codeword bits and it in fact matches in common scenarios the complexity of ml based sphere decoders through this sharp contrast this study was able to for the first time rigorously demonstrate and quantify the pivotal role of lr as a special complexity reducing ingredient

smaller solutions for the firing squad in this paper we improve the bounds on the complexity of solutions to the firing squad problem also known as the firing synchronization problem in the firing synchronization problem we consider a one dimensional array of n identical finite automata initially all automata are in the same state except for one automaton designated as the initiator for the synchronization our results hold for the original problem where the initiator may be located at either endpoint and for the variant where any one of the automata may be the initiator called the generalized problem in both cases the goal is to define the set of states and transition rules for the automata so that all machines enter a special fire state simultaneously and for the first time during the final round of the computation in our work we improve the construction for the best known minimal time solution to the generalized problem by reducing the number of states needed and give non minimal time solutions to the original and generalized problem that use fewer states than the corresponding minimal time solutions

effect of channel estimation error on bit error probability in ofdm systems over rayleigh and ricean fading channels a characteristic function based method is used to derive closed form bit error probability bep expressions for orthogonal frequency division multiplexing ofdm systems in the presence of channel estimation error over frequency selective rayleigh fading channels and frequency selective ricean fading channels both single channel reception and diversity reception with maximal ratio combining mrc are examined the bep expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex gaussian random variable theory and a characteristic function method the closed form bep expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models the performances of two interpolation methods a sine interpolator with hamming windowing and a wiener interpolator are compared

linear speed up for cellular automata synchronizers and applications abstract simple cellular automata can be used as language recognizers or function calculators there exist several proofs of the linear speed up theorem in strong form for recognizers 7 6 11 but not for calculators in this paper we design a linear speed up method for a special kind of calculators namely the synchronizers which are different from recognizers as a consequence we extend a result from j mazoyer by proving that any polynomial with rational coefficients of a synchronization time is also a synchronization time provided that it be greater than a certain minimal time

ber evaluation of ofdm systems with joint effect of ti adc circuit s gain mismatch and channel estimation error the identification of maximum tolerable levels for potential mismatches is critical when designing communication systems in this paper we derive maximum tolerable levels for time interleaved analog to digital converter ti adc gain mismatch in orthogonal frequency division multiplexing ofdm systems to this end we first analytically evaluate the bit error rate ber for square quadrature amplitude modulated ofdm systems that are impaired by 1 the gain mismatch of a ti adc and 2 the channel estimation errors cees of a zero forcing equalizer our analysis includes the cases of a frequency selective rayleigh fading channel and a wired channel next built on the obtained ber expressions a threshold is established on the gain mismatch level at which an error floor caused by the gain mismatch is below a given ber value at high signal to noise ratios in the absence of cees finally numerical results further show that if and only if we set the gain mismatch level below 0 25 of this threshold there is essentially no ber performance degradation compared with the mismatch free case