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

multi edge type low density parity check codes for bandwidth efficient modulation a method of designing low density parity check codes for bandwidth efficient high order modulation is proposed a multi edge type ldpc code ensemble is used to improve the correspondence between modulation bit channel capacity and bit level protection in a bit interleaved coded modulation system a key innovation is the development of a multi dimensional extrinsic information transfer exit vector field technique for the analysis and design of multi edge type codes a condition sufficient for the decoder to converge is derived on the multi dimensional exit vector field and this condition is used as a constraint in code optimization code designs indicate that the proposed method produces codes matching the performance of codes designed using best available methods in ensemble threshold and is capable of achieving identical finite length error rates with shorter block lengths in addition to simplified design complexity the resulting codes allow for low complexity implementation and rate adaptivity and hence are well suited for adaptive modulation systems

fundamental groups of character varieties surfaces and tori we compute the fundamental group of moduli spaces of lie group valued representations of surface and torus groups

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

on calderon s conjecture with constants cfi p1 p2 depending only on fi p1 p2 and p p1p2 p1 p2 hold the flrst result of this type is proved in 4 and the purpose of the current paper is to extend the range of exponents p1 and p2 for which 2 is known in particular the case p1 2 p2 1 is solved to the a rmative this was

reliability based coded modulation with low density parity check codes in this letter we consider the interleaver design in bit interleaved coded modulation bicm with low density parity check ldpc codes the design paradigm is to provide more coding protection through iterative decoding to bits that are less protected by modulation and are thus less reliable at the output of the demodulator the design is carried out by an ad hoc search algorithm over the column permutations of the parity check matrix our simulations show that the proposed reliability based coded modulation scheme can improve the error rate performance of conventional bicm schemes based on regular ldpc codes by a few tenths of a decibel with no added complexity

a martingale approach for testing diffusion models based on infinitesimal operator abstract i develop an omnibus specification test for diffusion models based on the infinitesimal operator the infinitesimal operator based identification of the diffusion process is equivalent to a martingale hypothesis for the processes obtained by a transformation of the original diffusion model my test procedure is then constructed by checking the martingale hypothesis via a multivariate generalized spectral derivative based approach that delivers a n 0 1 asymptotical null distribution for the test statistic the infinitesimal operator of the diffusion process is a closed form function of drift and diffusion terms consequently my test procedure covers both univariate and multivariate diffusion models in a unified framework and is particularly convenient for the multivariate case moreover different transformed martingale processes contain separate information about the drift and diffusion specifications this motivates me to propose a separate inferential test procedure to explore the sources of rejection when a parametric form is rejected simulation studies show that the proposed tests have reasonable size and excellent power performance an empirical application of my test procedure using eurodollar interest rates finds that most popular short rate models are rejected and the drift misspecification plays an important role in such rejections

multilevel codes theoretical concepts and practical design rules this paper deals with 2 sup l ary transmission using multilevel coding mlc and multistage decoding msd the known result that mlc and msd suffice to approach capacity if the rates at each level are appropriately chosen is reviewed using multiuser information theory it is shown that there is a large space of rate combinations such that mlc and full maximum likelihood decoding mld can approach capacity it is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of mld the capacity rule the balanced distances rules and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies moreover topics relevant in practical applications such as signal set labeling dimensionality of the constituent constellation and hard decision decoding are emphasized bit interleaved coded modulation proposed by caire et al see ibid vol 44 p 927 46 1998 is reviewed in the context of mlc finally the combination of signal shaping and coding is discussed significant shaping gains are achievable in practice only if these design rules are taken into account

dirichlet forms and semilinear elliptic equations with measure data we propose a probabilistic definition of solutions of semilinear elliptic equations with possibly nonlocal operators associated with regular dirichlet forms and with measure data using the theory of backward stochastic differential equations we prove the existence and uniqueness of solutions in the case where the right hand side of the equation is monotone and satisfies mild integrability assumption and the measure is smooth we also study regularity of solutions under the assumption that the measure is smooth and has finite total variation some applications of our general results are given

hilbert poincare series for spaces of commuting elements in lie groups in this article we study the homology of spaces mathrm hom mathbb z n g of ordered pairwise commuting n tuples in a lie group g we give an explicit formula for the poincare series of these spaces in terms of invariants of the weyl group of g by work of bergeron and silberman our results also apply to mathrm hom f n gamma n m g where the subgroups gamma n m are the terms in the descending central series of the free group f n finally we show that there is a stable equivalence between the space mathrm comm g studied by cohen stafa and its nilpotent analogues

on the structure of general mean variance hedging strategies we provide a new characterization of mean variance hedging strategies in a general semimartingale market the key point is the introduction of a new probability measure p which turns the dynamic asset allocation problem into a myopic one the minimal martingale measure relative to p coincides with the variance optimal martingale measure relative to the original probability measure p

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

gradient estimates for sdes driven by multiplicative levy noise abstract gradient estimates are derived for the first time for the semigroup associated to a class of stochastic differential equations driven by multiplicative levy noise in particular the estimates are sharp for stable type noises to derive these estimates a new derivative formula of bismut elworthy li s type is established for the semigroup by using the malliavin calculus and a finite jump approximation argument

on the design of bit interleaved turbo coded modulation with low error floors in this paper we introduce an algorithm to optimize the performance in the error floor region of bit interleaved turbo coded modulation bitcm on the additive white gaussian noise channel the key ingredient is an exact turbo code weight distribution algorithm producing a list of all codewords in the underlying turbo code of weight less than a given threshold in bitcm the information sequence is turbo encoded bit interleaved and mapped to signal points in a signal constellation using the union bounding technique we show that a well designed bit interleaver is crucial to have a low error floor furthermore the error rate performance in the waterfall region depends on the bit interleaver since the level of protection from channel noise on the bit level depends on the bit position and the neighboring bit values within the same symbol in the transmitted sequence we observe a tradeoff between error rate performance in the waterfall and error floor regions as illustrated by an extensive case study of a high rate bitcm scheme this tradeoff is typical in iterative decoding of turbo like codes the reported case study shows that it is possible to design bit interleavers with our proposed algorithm with equal or better performance in the waterfall region and superior performance in the error floor region compared with randomly generated bit interleavers in particular we were able to design bitcm schemes with maximum likelihood decoding frame error rates of 10 12 and 10 17 at 2 6 and 3 8 db away from unconstrained channel capacity at spectral efficiencies of 3 10 and 6 20 b s hz using square 16 and 256 quadrature amplitude modulation signal constellations respectively

convergence rate of numerical solutions to sfdes with jumps abstract in this paper we are interested in numerical solutions of stochastic functional differential equations with jumps under a global lipschitz condition we show that the p th moment convergence of euler maruyama numerical solutions to stochastic functional differential equations with jumps has order 1 p for any p 2 this is significantly different from the case of stochastic functional differential equations without jumps where the order is 1 2 for any p 2 it is therefore best to use the mean square convergence for stochastic functional differential equations with jumps moreover under a local lipschitz condition we reveal that the order of mean square convergence is close to 1 2 provided that local lipschitz constants valid on balls of radius j do not grow faster than log j

t 1 theorem for dyadic singular integral forms associated with hypergraphs abstract this paper studies dyadic singular integral forms associated with r partite r uniform hypergraphs such that all their connected components are complete we characterize their l p boundedness by t 1 type conditions in two different ways we also dominate these forms by positive sparse forms and prove weighted estimates with multilinear muckenhoupt weights

one modification of the martingale transform and its applications to paraproducts and stochastic integrals abstract in this paper we introduce a variant of burkholder s martingale transform associated with two martingales with respect to different filtrations even though the classical martingale techniques cannot be applied we show that the discussed transformation still satisfies some expected l p estimates then we apply the obtained inequalities to general dilation twisted paraproducts particular instances of which have already appeared in the literature as another application we construct stochastic integrals 0 t h s d x s y s associated with certain continuous time martingales x t t 0 and y t t 0 the process x t y t t 0 is shown to be a good integrator although it is not necessarily a semimartingale or even adapted to any convenient filtration

a sharp and strict l p inequality for stochastic integrals on donne une nouvelle preuve d une inegalite lp pointue pour des integrales stochastiques qui permet de montrer que l inegalite stricte est maintenue dans tous les cas non triviaux

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

on the fundamental group of rm hom mathbb z k g let g be a compact lie group consider the variety rm hom mathbb z k g of representations of mathbb z k into g we can see this as a based space by taking as base point the trivial representation open image in new window the goal of this paper is to prove that pi 1 rm hom mathbb z k g is naturally isomorphic to 1 g k

weak tail conditions for local martingales the following conditions are necessary and jointly sufficient for an arbitrary c adl ag local martingale to be a uniformly integrable martingale a the weak tail of the supremum of its modulus is zero b its jumps at the first exit times from compact intervals converge to zero in l 1 on the events that those times are finite and c its almost sure limit is an integrable random variable

design of multi input multi output systems based on low density parity check codes we design serial concatenated multi input multi output systems based on low density parity check ldpc codes we employ a receiver structure combining the demapper detector and the decoder in an iterative fashion we consider the a posteriori probability app demapper as well as a suboptimal demapper incorporating interference cancellation with linear filtering extrinsic information transfer exit chart analysis is applied to study the convergence behavior of the proposed schemes we show that exit charts match very well with the simulated decoding trajectories and they help explain the impact of different mappings and different demappers it is observed that if the app demapper transfer characteristics are almost flat the ldpc codes optimized for binary input channels are good enough to achieve performance close to the channel capacity we also present a simple code optimization method based on exit chart analysis and we design a rate 1 2 ldpc code that achieves very low bit error rates within 0 15 db of the capacity of a two input two output rayleigh fading channel with 4 pulse amplitude modulation we next propose to use a space time block code as an inner code of our serial concatenated coding scheme by means of a simple example scheme using an alamouti inner code we demonstrate that the design optimization of the outer code e g ldpc code is greatly simplified

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

capacity approaching bandwidth efficient coded modulation schemes based on low density parity check codes we design multilevel coding mlc and bit interleaved coded modulation bicm schemes based on low density parity check ldpc codes the analysis and optimization of the ldpc component codes for the mlc and bicm schemes are complicated because in general the equivalent binary input component channels are not necessarily symmetric to overcome this obstacle we deploy two different approaches one based on independent and identically distributed i i d channel adapters and the other based on coset codes by incorporating i i d channel adapters we can force the symmetry of each binary input component channel by considering coset codes we extend the concentration theorem based on previous work by richardson et al see ibid vol 47 p 599 618 feb 2001 and kavc spl caron ic spl acute et al see ibid vol 49 p 1636 52 july 2003 we also discuss the relation between the systems based on the two approaches and show that they indeed have the same expected decoder behavior next we jointly optimize the code rates and degree distribution pairs of the ldpc component codes for the mlc scheme the optimized irregular ldpc codes at each level of mlc with multistage decoding msd are able to perform well at signal to noise ratios snr very close to the capacity of the additive white gaussian noise awgn channel we also show that the optimized bicm scheme can approach the parallel independent decoding pid capacity as closely as does the mlc pid scheme simulations with very large codeword length verify the accuracy of the analytical results finally we compare the simulated performance of these coded modulation schemes at finite codeword lengths and consider the results from the perspective of a random coding exponent analysis

design of bandwidth efficient unequal error protection ldpc codes this paper presents a strategy for the design of bandwidth efficient ldpc codes with unequal error protection bandwidth efficiency is obtained by appropriately designing the codes for higher order constellations assuming an awgn channel the irregularities of the ldpc code are designed using the gaussian approximation of the density evolution to enhance the unequal error protection property of the code as well as account for the different bit error probabilities given by the higher order constellation the proposed code design algorithm is flexible in terms of the number and proportions of protection classes it also allows arbitrary modulation schemes our method combines the design of unequal error protection ldpc codes for the binary input awgn channel with the code design for higher order constellations by dividing the variable node degree distribution into sub degree distributions for each protection class and each level of protection from the modulation the results show that appropriate code design for higher order constellations reduces the overall bit error rate significantly furthermore the unequal error protection capability of the code is increased especially for high snr

on the two dimensional bilinear hilbert transform we investigate the bilinear hilbert transform in the plane and the pointwise convergence of bilinear averages in ergodic theory arising from bf z 2 actions our techniques combine novel one and a half dimensional phase space analysis with more standard one dimensional theory