algebraic reflexivity of sets of bounded operators on vector valued lipschitz functions abstract in this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued lipschitz functions we also derive a representation for the generalized bi circular projections on these spaces

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

dynamic response optimization using an active set rqp algorithm a recently developed recursive quadratic programming rqp algorithm is applied to dynamic response design problems the algorithm incorporates updated hessians of the lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding qp subproblem hessian updating with dynamic response constraints presents some difficulties the primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration this can cause inconsistencies in hessian updating if proper numerical procedures are not used a numerical procedure to handle the situation is developed implemented and evaluated automatic restarting procedures are necessary for proper convergence of the algorithm the new algorithm is robust as well as more efficient than the purely linear algorithm the active set strategy plays an important role for application to dynamic response problems the rqp algorithms that do not use such a strategy are not applicable to this class of problems

rate compatible puncturing of low density parity check codes in this correspondence we consider puncturing of low density parity check ldpc codes for additive white gaussian noise awgn channels we show that good puncturing patterns exist and that the puncturing can be performed in a rate compatible fashion furthermore rate compatible puncturing results in a small loss of performance with respect to threshold namely the punctured code is good in terms of threshold across a range of rates when compared with the optimal codes for each rate this allows one to implement a single mother encoder and decoder that is good across a wide range of rates

coding schemes for user cooperation in low power regimes we consider the design of cooperation coding schemes for a two user multiaccess channel mac in particular we consider two block markov coding schemes namely the multiplexed coding and the superposition coding although the fully multiplexed fmp coding outperforms the superposition coding in theory it is difficult to implement with practical error correction codes we therefore introduce a partially multiplexed pmp coding scheme for code rate r 0 5 and propose a simplified superposition coding scheme the outage analysis shows that these cooperation schemes provide significant gains over the non cooperative mac in the low power regime when the bandwidth w rarr infin we then propose a pmp code design using irregular repeat accumulate ira codes the design method can be extended to build the low rate pmp codes using irregular repeat zigzag hadamard irzh codes a new class of capacity achieving low rate codes simulation results demonstrate that the block markov multiplexed coding using pmp ira codes outperforms the practical superposition coding by 2 db at 10 2 fer and it provides a 10 db gain over the noncooperative mac the multiplex coding using pmp irzh codes offers 1 db gain over the superposition coding and a 9 5 db gain over noncooperative mac at 10 2 fer moreover the pmp irzh coding performs only 0 5 db away from the outage capacity of multiplexed coding in the low power regime

short turbo codes over high order fields two classes of turbo codes constructed on high order finite fields are introduced the codes are derived from a particular protograph sub ensemble of the 2 3 regular low density parity check ldpc code ensemble the first construction results in a parallel concatenation of two non binary time variant accumulators the second construction consists of the serial concatenation of a non binary time variant differentiator with a non binary time variant accumulator and provides a highly structured flexible encoding scheme for 2 4 ldpc codes a cycle graph representation is also provided the proposed codes can be decoded efficiently either as ldpc codes via belief propagation decoding on their bipartite graphs or as turbo codes via the forward backward algorithm applied to the component code trellises by means of the fast fourier transform the proposed codes provide remarkable coding gains more than 1 db at a codeword error rate 10 4 over binary ldpc and turbo codes in the moderate short block length regime

generalized tricircular projections on minimal norm ideals in b h abstract a nonzero projection p on a complex banach space x is said to be a generalized tricircular projection if there exist distinct modulus one complex numbers and not equal to 1 and nonzero projections q and r on x such that p q r i and p q r is an isometry we determine the structure of generalized tricircular projections on minimal norm ideals in b h different from the hilbert schmidt class

homomorphisms between algebras of lipschitz functions with the values in function algebras abstract we give a characterization of algebra homomorphisms and isomorphisms between banach algebras of lipschitz functions with the values in unital commutative c algebras we prove that such homomorphisms are composition operators of the form and preserve some properties

algebraic reflexivity of some subsets of the isometry group let x be a compact first countable space in this paper we show that the set of isometries of c x that are involutions is algebraically reflexive as a consequence of a recent work of botelho and jamison this leads to the conclusion that the set of generalized bi circular projections on c x is also algebraically reflexive we also consider these questions for the space c x e where e is a uniformly convex banach space

algebraic reflexivity of the isometry group of some spaces of lipschitz functions abstract we show that the isometry groups of lip x d and lip x d with 0 1 for a compact metric space x d are algebraically reflexive we also prove that the sets of isometric reflections and generalized bi circular projections on such spaces are algebraically reflexive in order to achieve this we characterize generalized bi circular projections on these spaces

local automorphisms of nest subalgebras of factor von neumann algebras in this paper it is proved that every surjective weakly continuous linear local automorphism of nest subalgebras with non trivial nests of factor von neumann algebras is an automorphism and that every surjective linear 2 local automorphism of nest algebras with non trivial nests of factor von neumann algebras is an automorphism

exit functions of hadamard components in repeat zigzag hadamard rzh codes with parallel decoding the extrinsic information transfer exit functions of hadamard codes in the context of repeat zigzag hadamard rzh codes with parallel decoding are investigated exit functions over both the binary erasure channel bec and the binary input additive white gaussian noise biawgn channel are derived the application of these exit functions in the design of low rate capacity approaching irregular rzh irzh codes is also considered using the exit functions the bit error rate ber for a given code profile can be easily estimated and the differential evolution de technique can be employed to find the optimal degree profile for given design parameters the exit functions derived in this communication can serve as an effective tool for designing low rate irzh codes with parallel decoding in both bec and biawgn channels

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

on the robustness and efficiency of the sam algorithm for structural optimization a parameter study involving a feasibility factor adaptive tolerance refinement and active set and move limits is conducted on the interior feasible direction method with successive approximations sam the study involves the sizing design of five structural problems of which one is a large power transmission tower to be designed in adherence with a standard design code it is concluded that a move limit is dispensable for this application while adaptive tolerance refinement makes the algorithm more efficient optimal ranges for the feasibility factor and active set limits are suggested this study reaffirms and quantifies the exceptional stability and robustness of the sam algorithm

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

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

local isometries of function spaces abstract we show that for a large class of function spaces any isometry that coincides locally with a surjective isometry must be automatically surjective this class includes finite codimensional subspaces of c left x right and spaces c left x e right of e valued continuous functions for finite dimensional or uniformly convex and algebraically reflexive e

local derivations on operator algebras abstract when attempting to find sufficient conditions for a linear mapping to be a derivation an obvious candidate is the concept of a local derivation local derivations on operator algebras have been investigated in recent papers of kadison j algebra130 1990 494 509 and larson and sourour proc symp pure math 51 1990 187 194 a local derivation is a norm continuous linear map from an operator algebra a into an a bimodule m which agrees with some derivation at each point in the algebra we show that if a is the direct limit of finite dimensional csl algebras via extendable embeddings e g a triangular af algebra then a local derivation on a must be a derivation further we show that for many finite dimensional operator algebras any inner local derivation must be an inner derivation

weight distribution of low density parity check codes we derive the average weight distribution function and its asymptotic growth rate for low density parity check ldpc code ensembles we show that the growth rate of the minimum distance of ldpc codes depends only on the degree distribution pair it turns out that capacity achieving sequences of standard unstructured ldpc codes under iterative decoding over the binary erasure channel bec known to date have sublinearly growing minimum distance in the block length

expander codes using expander graphs we construct a new family of asymptotically good linear error correcting codes these codes have linear time sequential decoding algorithms and logarithmic time parallel decoding algorithms that use a linear number of processors we present both randomized and explicit constructions of these codes experimental results demonstrate the good performance of the randomly chosen codes

the design of rate compatible protograph ldpc codes this paper presents a simple yet effective method for designing nested families of ldpc codes rate compatible codes are essential for many communication applications e g hybrid automatic repeat request harq systems and their design is nontrivial due to the difficulty of simultaneously guaranteeing the quality of several related codes puncturing can be used to generate rate compatible ldpc codes but it produces a gap to capacity that in practice often significantly exceeds the gap of the mother code we propose an alternative method based on successively extending a high rate protograph the resulting codes not only inherit the advantages of protograph codes namely low encoding complexity and efficient decoding algorithms but also cover a wide range of rates and have very good performance with iterative decoding thresholds that are within 0 2 db of their capacity limits

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

asymptotic enumeration methods for analyzing ldpc codes we show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low density parity check ldpc codes in particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular ldpc code ensembles we then consider the binary erasure channel bec using these estimates we derive lower bounds on the error exponent under iterative decoding of ldpc codes used over the bec both regular and irregular code structures are considered these bounds are compared to the corresponding bounds when optimal maximum likelihood ml decoding is applied

raptor codes on binary memoryless symmetric channels in this paper we will investigate the performance of raptor codes on arbitrary binary input memoryless symmetric channels bimscs in doing so we generalize some of the results that were proved before for the erasure channel we will generalize the stability condition to the class of raptor codes this generalization gives a lower bound on the fraction of output nodes of degree 2 of a raptor code if the error probability of the belief propagation decoder converges to zero using information theoretic arguments we will show that if a sequence of output degree distributions is to achieve the capacity of the underlying channel then the fraction of nodes of degree 2 in these degree distributions has to converge to a certain quantity depending on the channel for the class of erasure channels this quantity is independent of the erasure probability of the channel but for many other classes of bimscs this fraction depends on the particular channel chosen this result has implications on the universality of raptor codes for classes other than the class of erasure channels in a sense that will be made more precise in the paper we will also investigate the performance of specific raptor codes which are optimized using a more exact version of the gaussian approximation technique

minimax multiobjective optimization in structural design summary the use of multiobjective optimization techniques which may be regarded as a systematic sensitivity analysis for the selection and modification of system parameters is presented a minimax multiobjective optimization model for structural optimization is proposed three typical multiobjective optimization techniques goal programming compromise programming and the surrogate worth trade off method are used to solve such a problem the application of multiobjective optimization techniques to the selection of system parameters and large scale structural design optimization problems is the main purpose of this paper

on 2 local isometries on continuous vector valued function spaces article history received 24 july 2008 available online 24 december 2008 submitted by j d m wright a not necessarily linear mapping from a banach space x to a banach space y is said to be a 2 local isometry if for any pair x y of elements of x t here is as urjective linear isometry t x y such that tx x and ty y we show that under certain conditions on locally compact hausdorff spaces q k and a banach space e e very 2 local isometry on c0 q e to c0 k e is linear and surjective we also show that every 2 local isometry on p is linear and surjective for 1 p p 2 but this fails for the hilbert space 2

optimizing transmission lengths for limited feedback with nonbinary ldpc examples this paper presents a general approach for optimizing the number of symbols in increments packets of incremental redundancy in a feedback communication system with a limited number of increments this approach is based on a tight normal approximation on the rate for successful decoding applying this approach to a variety of feedback systems using nonbinary nb low density parity check ldpc codes shows that greater than 90 of capacity can be achieved with average blocklengths fewer than 500 transmitted bits one result is that the performance with ten increments closely approaches the performance with an infinite number of increments the paper focuses on binary input additive white gaussian noise bi awgn channels but also demonstrates that the normal approximation works well on examples of fading channels as well as high snr awgn channels that require larger qam constellations this paper explores both variable length feedback codes with termination vlft and the more practical variable length feedback vlf codes without termination that require no assumption of noiseless transmitter confirmation for vlf we consider both a two phase scheme and crc based scheme

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

low rate repeat zigzag hadamard codes in this paper we propose a new class of low rate error correction codes called repeat zigzag hadamard rzh codes featuring simple encoder and decoder structures and flexible coding rate rzh codes are serially concatenated turbo like codes where the outer code is a repetition code and the inner code is a punctured zigzag hadamard zh code by analyzing the code structure of rzh codes we prove that both systematic and nonsystematic rzh codes are good codes in the sense that for an rzh code ensemble there exists a positive number gamma0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than the average block error probability of maximum likelihood ml decoding approaches zero two decoding algorithms serial and parallel decoders for rzh codes are proposed we then employ the extrinsic information transfer exit chart technique to design irregular rzh codes results show that the optimized irregular rzh codes exhibit a performance that is very close to capacity in the low rate regime

capacity achieving codes with bounded graphical complexity and maximum likelihood decoding in this paper the existence of capacity achieving codes for memoryless binary input output symmetric mbios channels under maximum likelihood ml decoding with bounded graphical complexity is investigated graphical complexity of a code is defined as the number of edges in the graphical representation of the code per information bit and is proportional to the decoding complexity per information bit per iteration under iterative decoding irregular repeat accumulate ira codes are studied first utilizing the asymptotic average weight distribution aawd of these codes and invoking divsalar s bound on the binary input additive white gaussian noise biawgn channel it is shown that simple nonsystematic ira ensembles outperform systematic ira and regular low density parity check ldpc ensembles with the same graphical complexity and are at most 0 124 db away from the shannon limit however a conclusive result as to whether these nonsystematic ira codes can really achieve capacity cannot be reached motivated by this inconclusive result a new family of codes is proposed called low density parity check and generator matrix ldpc gm codes which are serially concatenated codes with an outer ldpc code and an inner low density generator matrix ldgm code it is shown that these codes can achieve capacity on any mbios channel using ml decoding and also achieve capacity on any bec using belief propagation bp decoding both with bounded graphical complexity moreover it is shown that under certain conditions these capacity achieving codes have linearly increasing minimum distances and achieve the asymptotic gilbert varshamov bound for all rates

upper bounds to error probabilities of coded systems beyond the cutoff rate a family of upper bounds to error probabilities of coded systems was recently proposed by d divsalar see ieee communication theory workshop 1999 jpl tmo prog rep 42 139 1999 these bounds are valid for transmission over the additive white gaussian noise channel and require only the knowledge of the weight spectrum of the code words after illustrating these bounds we extend them to fading channels contrary to the union bound our bounds maintain their effectiveness below the signal to noise ratio snr at which the cutoff rate of the channel equals the rate of the code some applications are shown first we derive upper bounds to the minimum snr necessary to achieve zero error probability as the code block length increases to infinity next we use our bounds to predict the performance of turbo codes and low density parity check codes

local isometries on spaces of continuous functions let x and y be banach spaces and s a subset of the space of linear continuous operators from x to y we say that an operator t belongs locally to s if for every x x there is s s possibly depending on x such that tx sx pointwise should be better than locally but we have followed tradition if each operator that belongs locally to s belongs in fact to s we say that s is algebraically reflexive when y x and s iso x is the group of isometries of x we say that t is a local isometry of x in this paper isometry means linear surjective isometry similarly a local automorphism of a banach algebra is an operator which agrees at every point with some automorphism also we will consider approximate local isometries and automorphisms these are operators having with the following property given x x and e 0 there is an isometry respectively an automorphism s of x such that tx sx e the study of local isometries and automorphisms of banach algebras spurred a considerable interest in recent years see the bibliography of the dissertation 16 in this paper we deal with local isometries and automorphisms of the algebras c0 l as usual we write c0 l or c k 0 l for the banach algebra of all continuous k valued functions on the locally compact space l vanishing at infinity where k is either c or r if l is compact the subscript will be omitted by the banach stone theorem if t is local isometry of c0 l then for each f there are a homeomorphism of l and a continuous unitary u l k such that tf u f

projections as convex combinations of surjective isometries on c ω we study properties of operators that are in the convex hull of a finite set of surjective isometries on the banach space of complex valued continuous maps defined on a compact and connected topological space we characterize those projections that are in the convex combination of two surjective isometries and we show that they are generalized bi circular projections

construction of near capacity protograph ldpc code sequences with block error thresholds density evolution for protograph low density parity check ldpc codes is considered and it is shown that the message error rate falls double exponentially with iterations whenever the degree 2 subgraph of the protograph is cycle free and noise level is below threshold conditions for stability of protograph density evolution are established and related to the structure of the protograph using large girth graphs sequences of protograph ldpc codes with block error threshold equal to bit error threshold and block error rate falling near exponentially with blocklength are constructed deterministically small sized protographs are optimized to obtain thresholds near capacity for binary erasure and binary input gaussian channels

design of repeat accumulate codes for iterative detection and decoding extrinsic information transfer exit charts are used to design systematic and nonsystematic repeat accumulate ra codes for iterative detection and decoding the convergence problems of nonsystematic ra codes are solved by introducing a biregular or doped layer of check nodes as examples such nonsystematic codes are designed for multi input multi output mimo fading channels and are shown to operate close to capacity

designing a good low rate sparse graph code this paper deals with the design of low rate sparse graph codes having a linear minimum distance d min in the blocklength n its main contributions are a a necessary condition on a general family of sparse graph codes with linear d min b a justification of having degree 1 bits in the low rate code structure c a new efficient ensemble of low rate sparse graph codes with bits of degree 1 designed so that the necessary condition a is satisfied

coding theorems for turbo code ensembles this paper is devoted to a shannon theoretic study of turbo codes we prove that ensembles of parallel and serial turbo codes are good in the following sense for a turbo code ensemble defined by a fixed set of component codes subject only to mild necessary restrictions there exists a positive number spl gamma sub 0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than spl gamma sub 0 the average maximum likelihood ml decoder block error probability approaches zero at least as fast as n sup spl beta where spl beta is the interleaver gain exponent defined by benedetto et al in 1996

2 local automorphisms of operator algebras abstract a not necessarily continuous linear or multiplicative function from an algebra a into itself is called a 2 local automorphism if agrees with an automorphism of a at each pair of points in a in this paper we study when a 2 local automorphism of a c algebra or a standard operator algebra on a locally convex space is an automorphism

a counterexample to wood s conjecture abstract we prove that if the one point compactification of a locally compact noncompact hausdorff space l is the topological space called pseudoarc then c 0 l c is almost transitive we also obtain two necessary conditions on a metrizable locally compact hausdorff space l for c 0 l being almost transitive

selective avoidance of cycles in irregular ldpc code construction this letter explains the effect of graph connectivity on error floor performance of low density parity check ldpc codes under message passing decoding a new metric called extrinsic message degree emd measures cycle connectivity in bipartite graphs of ldpc codes using an easily computed estimate of emd we propose a viterbi like algorithm that selectively avoids small cycle clusters that are isolated from the rest of the graph this algorithm is different from conventional girth conditioning by emphasizing the connectivity as well as the length of cycles the algorithm yields codes with error floors that are orders of magnitude below those of random codes with very small degradation in capacity approaching capability

algebraic reflexivity of isometry groups of algebras of lipschitz maps abstract we study groups of surjective linear isometries on banach algebras of lipschitz maps with values in some unital c algebras in this paper these spaces are endowed with the sum norm for the case where the c algebras are commutative whose groups of all surjective isometries are algebraically reflexive we prove that the group of all surjective isometries on the corresponding banach algebra of lipschitz maps are algebraically reflexive we also prove that the group of unital surjective isometries between matrix valued lipschitz algebras are reflexive

concatenated zigzag hadamard codes in this correspondence we introduce a new class of low rate error correction codes called zigzag hadamard zh codes and their concatenation schemes each member of this class of codes is specified by a highly structured zigzag graph with each segment being a hadamard codeword the zh codes enjoy extremely simple encoding and very low complexity soft input soft output siso decoding based on a posteriori probability app fast hadamard transform fht technique we present an asymptotic performance analysis of the proposed concatenated zh codes using the extrinsic mutual information transfer exit chart for infinite length codes we also provide a union bound analysis of the error performance for finite length codes furthermore the concatenated zh codes are shown to be a good class of codes in the low rate region specifically a rate 0 0107 concatenated code with three zh components and an interleaver size of 65536 can achieve the bit error rate ber performance of 10 sup 5 at 1 15db which is only 0 44 db away from the ultimate shannon limit the proposed concatenated zh codes offer similar performance as another class of low rate codes the turbo hadamard codes and better performance than superorthogonal turbo codes with much lower encoding and decoding complexities

regular and irregular progressive edge growth tanner graphs we propose a general method for constructing tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge by edge manner called progressive edge growth peg algorithm lower bounds on the girth of peg tanner graphs and on the minimum distance of the resulting low density parity check ldpc codes are derived in terms of parameters of the graphs simple variations of the peg algorithm can also be applied to generate linear time encodeable ldpc codes regular and irregular ldpc codes using peg tanner graphs and allowing symbol nodes to take values over gf q q 2 are investigated simulation results show that the peg algorithm is a powerful algorithm to generate good short block length ldpc codes

closed ideals of finite codimension in regular self adjoint banach algebras soit 7b a une algebre de banach unitaire et 7b m un sous espace clos de codimension finie n soit s le spectre de 7b a on suppose que pour chaque x dans 7b m la transformee de gelfand x a au moins k zeros distincts dans s alors il existe un sous ensemble z de s de cardinalite k tel que x t 0 pour tout x dans 7b m et tout t dans z

the performance of serial turbo codes does not concentrate minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed it is shown that for a fraction of interleavers approaching one as the block length grows large the minimum distance of serial turbo codes grows as a positive power of their block length while their error probability decreases exponentially fast in some positive power of their block length on sufficiently good memoryless channels such a typical code behavior contrasts the performance of the average serial turbo code whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers and decays only as a negative power of the block length the analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code whose scaling law is shown to depend both on the free distance of its outer constituent encoder which determines the exponent of its sub linear growth in the block length and on the effective free distance of its inner constituent encoder the latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two and appears as a linear scaling factor for the minimum distance of the typical serial turbo code hence despite the lack of concentration of the maximum likelihood error probability around its expected value the main design parameters suggested by the average code analysis turn out to characterize also the performance of the typical serial turbo code by showing for the first time that the typical serial turbo code s minimum distance scales linearly in the effective free distance of the inner constituent encoder the presented results generalize and improve upon the probabilistic bounds of kahale and urbanke as well as the deterministic upper bound of bazzi mahdian and spielman where only the dependence on the outer encoder s free distance was proved

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

performance of some sqp algorithms on structural design problems this paper describes the basic ideas of sequential quadratic programming sqp algorithms for design optimization there are two fundamental differences between the various algorithms i the difinition of the qp subproblem solved at each iteration and ii the descent function used during step size determination the performances of the algorithms can change dramatically depending on how the two steps are executed numerical implementation details of various computational steps are discussed three programs based on sqp algorithms are used to solve 17 structural design problems having 7 to 96 design variables and 10 to 1051 performance constraints besides design variable bounds based on the performance of these programs efficient procedures to execute various steps of the sqp methods are determined it is concluded that the potential constraint strategy where only a subset of the constraints is used to define the qp subproblem is essential for large scale engineering design applications with this strategy the sqp methods are quite robust and have great potential for routine application in engineering design

raptor codes in the low snr regime in this paper we revisit the design of raptor codes for binary input additive white gaussian noise channels where we are interested in very low signal to noise ratios snrs a linear programming degree distribution optimization problem is defined for raptor codes in the low snr regime through several approximations we also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum output node degree in the low snr regime which enables us to calculate the exact value of the fractions of output nodes of small degrees a more practical degree distribution design is also proposed for raptor codes in the low snr regime where we include the rate efficiency and the decoding complexity in the optimization problem and an upper bound on the maximum rate efficiency is derived for given design parameters simulation results show that the raptor code with the designed degree distributions can approach rate efficiencies larger than 0 95 in the low snr regime

new successive approximation method for optimum structural design a new procedure using only first order explicit information and consisting of the successive solution of approximate subproblems is proposed the method differs from established sequential quadratic programming methods by not utilizing the lagrangian form and not attempting to store full and explicit hessian information instead each constraint is individually approximated by a quadratic function involving only one coefficient in the quadratic term this coefficient is determined from a two point collocation a novel feature of the method is that each quadratic subproblem is solved by a recently proposed interior feasible direction method an auxiliary problem is formulated to generate a feasible starting point for each subproblem

isometries between function spaces surjective isometries between some classical function spaces are investigated we give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding hausdorff compact spaces in particular the answer is positive for the c x ac 0 1 lip0 x and lip0 x spaces provided with various natural norms

on banach spaces whose group of isometries acts micro transitively on the unit sphere abstract we study banach spaces whose group of isometries acts micro transitively on the unit sphere we introduce a weaker property inherited by one complemented subspaces that we call uniform micro semitransitivity we prove a number of results about both micro transitive and uniformly micro semitransitive spaces in particular they are uniformly convex and uniformly smooth and form a self dual class to this end we relate the fact that the group of isometries acts micro transitively with a property of operators called the pointwise bishop phelps bollobas property and use some known results on it besides we show that if there is a non hilbertian non separable banach space with uniform micro semitransitive or micro transitive norm then there is a non hilbertian separable one finally we show that an l p space is micro transitive or uniformly micro semitransitive only when p 2

rate compatible punctured low density parity check codes with short block lengths we consider the problem of rate compatible puncturing of low density parity check ldpc codes over additive white gaussian noise awgn channels in previous work it was shown that good puncturing distributions exist for ldpc codes but the code length was large in this correspondence we give a procedure for determining the puncturing distributions for ldpc codes with short block lengths a few thousand bits and show that careful puncturing can produce good performance we compare the performance of the rate compatible punctured ldpc codes with dedicated ldpc codes across a range of rates and see that the rate compatible codes have a favorable complexity performance tradeoff

convex transitivity and function spaces abstract it is shown that if x is a convex transitive banach space and 1 p then l p 0 1 x and l s 0 1 x are convex transitive here l s 0 1 x is the closed linear span of the simple functions in the bochner space l 0 1 x if h is an infinite dimensional hilbert space and c 0 l is convex transitive then c 0 l h is convex transitive some new fairly concrete examples of convex transitive spaces are provided

g invariant norms and bicircular projections abstract it is shown that for many finite dimensional normed vector spaces v over c a linear projection p v v will have nice structure if p i p is an isometry for some complex unit not equal to one from these results one can readily determine the structure of bicircular projections i e those linear projections p such that p i p is an isometry for every complex unit the key ingredient in the proofs is the knowledge of the isometry group of the given norm the proof techniques also apply to real vector spaces in such cases characterizations are given to linear projections p such that p i p 2p i is an isometry

bandwidth efficient and rate matched low density parity check coded modulation a new coded modulation scheme is proposed at the transmitter the concatenation of a distribution matcher and a systematic binary encoder performs probabilistic signal shaping and channel coding at the receiver the output of a bitwise demapper is fed to a binary decoder no iterative demapping is performed rate adaption is achieved by adjusting the input distribution and the transmission power the scheme is applied to bipolar amplitude shift keying ask constellations with equidistant signal points and it is directly applicable to two dimensional quadrature amplitude modulation qam the scheme is implemented by using the dvb s2 low density parity check ldpc codes at a frame error rate of 10 3 the new scheme operates within less than 1 1 db of the awgn capacity frac 1 2 log 2 1 mathsf snr at any spectral efficiency between 1 and 5 bits s hz by using only 5 modes i e 4 ask with code rate 2 3 8 ask with 3 4 16 ask and 32 ask with 5 6 and 64 ask with 9 10

finite length rate compatible ldpc codes a novel puncturing scheme transactions letters in this paper we study rate compatible puncturing of finite length low density parity check ldpc codes we present a novel rate compatible puncturing scheme that is easy to implement our scheme uses the idea that the degradation in performance is reduced by selecting a puncturing pattern wherein the punctured bits are far apart from each other in the tanner graph of the code although the puncturing scheme presented is tailored to regular codes it is also directly applicable to irregular parent ensembles by simulations the proposed rate compatible puncturing scheme is shown to be superior to the existing puncturing methods for both regular and irregular ldpc codes over the binary erasure channel bec and the additive white gaussian noise awgn channel

concatenated tree codes a low complexity high performance approach this paper is concerned with a family of concatenated tree ct codes ct codes are special low density parity check ldpc codes consisting of several trees with large spans they can also be regarded as special turbo codes with hybrid recursive nonrecursive parts and multiple constituent codes ct codes are decodable by the belief propagation algorithm they combine many advantages of ldpc and turbo codes such as low decoding cost fast convergence speed and good performance

reflexivity of the automorphism and isometry groups of the suspension of b h the aim of this paper is to show that the automorphism and isometry groups of the suspension of b h h being a separable infinite dimensional hilbert space are algebraically reflexive this means that every local automorphism respectively every local surjective isometry ofc0 r b h is an automorphism respectively a surjective isometry

on the conjecture of wood and projective homogeneity abstract in 2005 kawamura and rambla independently constructed a metric counterexample to wood s conjecture from 1982 we exhibit a new nonmetric counterexample of a space l such that c 0 l c is almost transitive and show that it is distinct from a nonmetric space whose existence follows from the work of greim and rajagopalan in 1997 up to our knowledge this is only the third known counterexample to wood s conjecture we also show that contrary to what was expected if a one point compactification of a space x is r h bing s pseudo circle then c 0 x c is not almost transitive for a generic choice of points finally we point out close relation of these results on wood s conjecture to a work of irwin and solecki on projective fraisse limits and projective homogeneity of the pseudo arc and addressing their conjecture we show that the pseudo circle is not approximately projectively homogeneous

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

generalized bi circular projections abstract recall that a projection p on a complex banach space x is a generalized bi circular projection if p i p is a surjective isometry for some such that 1 and 1 it is easy to see that every hermitian projection is generalized bi circular a generalized bi circular projection is said to be nontrivial if it is not hermitian botelho and jamison showed that a projection p on c 0 1 is a nontrivial generalized bi circular projection if and only if p i p is a surjective isometry in this article we prove that if p is a projection such that p i p is a surjective isometry for some then either p is hermitian or is an n th unit root of unity we also show that for any n th unit root of unity there are a complex banach space x and a nontrivial generalized bi circular projection p on x such that p i p is an isometry

protograph based raptor like ldpc codes this paper proposes protograph based raptor like pbrl codes as a class of rate compatible low density parity check codes for binary input awgn channels as with the raptor codes exclusive or operations on precoded bits produce additional parity bits providing extensive rate compatibility unlike raptor codes each additional parity bit in the protograph is explicitly designed to optimize the density evolution threshold during the lifting process approximate cycle extrinsic message degree ace and circulant progressive edge growth cpeg constraints are used to avoid undesirable graphical structures some density evolution performance is sacrificed to obtain lower error floors particularly at short blocklengths simulation results are shown for information block sizes of k 1032 hbox and 16 384 for a target frame error rate of 10 5 at each rate the k 1032 hbox and 16 384 code families perform within 1 db and 0 4 db of both the gallager bound and the normal approximation respectively the 16 384 code family outperforms the best known standardized code family namely the ar4ja codes the pbrl codes also outperform dvb s2 codes that have the advantages of longer blocklengths and outer bch codes performance is similar to rc code families designed by nguyen et al that do not constrain codes to have the pbrl structure and involve simulation in the optimization process at each rate

design of low density parity check codes for modulation and detection a coding and modulation technique is studied where the coded bits of an irregular low density parity check ldpc code are passed directly to a modulator at the receiver the variable nodes of the ldpc decoder graph are connected to detector nodes and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder the code is optimized by performing a curve fitting on extrinsic information transfer charts design examples are given for additive white gaussian noise channels as well as multiple input multiple output mimo fading channels where the receiver but not the transmitter knows the channel for the mimo channels the technique operates within 1 25 db of capacity for various antenna configurations and thereby outperforms a scheme employing a parallel concatenated turbo code by wide margins when there are more transmit than receive antennas

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes

improved low density parity check codes using irregular graphs we construct new families of error correcting codes based on gallager s 1973 low density parity check codes we improve on gallager s results by introducing irregular parity check matrices and a new rigorous analysis of hard decision decoding of these codes we also provide efficient methods for finding good irregular structures for such decoding algorithms our rigorous analysis based on martingales our methodology for constructing good irregular codes and the demonstration that irregular structure improves performance constitute key points of our contribution we also consider irregular codes under belief propagation we report the results of experiments testing the efficacy of irregular codes on both binary symmetric and gaussian channels for example using belief propagation for rate 1 4 codes on 16000 bits over a binary symmetric channel previous low density parity check codes can correct up to approximately 16 errors while our codes correct over 17 in some cases our results come very close to reported results for turbo codes suggesting that variations of irregular low density parity check codes may be able to match or beat turbo code performance

an analysis of belief propagation on the turbo decoding graph with gaussian densities motivated by its success in decoding turbo codes we provide an analysis of the belief propagation algorithm on the turbo decoding graph with gaussian densities in this context we are able to show that under certain conditions the algorithm converges and that somewhat surprisingly though the density generated by belief propagation may differ significantly from the desired posterior density the means of these two densities coincide since computation of posterior distributions is tractable when densities are gaussian use of belief propagation in such a setting may appear unwarranted indeed our primary motivation for studying belief propagation in this context stems from a desire to enhance our understanding of the algorithm s dynamics in a non gaussian setting and to gain insights into its excellent performance in turbo codes nevertheless even when the densities are gaussian belief propagation may sometimes provide a more efficient alternative to traditional inference methods