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

a new upper bound on the minimum distance of turbo codes in this paper a new upper bound on the minimum distance of turbo codes is derived the new bound is obtained by construction of an undirected graph which reflects the characteristics of the constituent codes and the interleaver the resulting expression shows that the minimum distance of a turbo code grows approximately with the base 3 logarithm of the information word length the new bound is easy to compute applies to rate k sub 0 n sub 0 constituent encoders and often improves over existing results

morphisms of f isocrystals and the finite monodromy theorem for unit root f isocrystals we discuss tate type problems for f isocrystals that is the full faithfulness of the natural restriction functors between categories of overconvergent f isocrystals on schemes of positive characteristic we prove it in the cases of unit root f isocrystals using this result we prove that an overconvergent unit root f isocrystal has a finite monodromy

analysis and design of tuned turbo codes it has been widely observed that there exists a fundamental tradeoff between the minimum hamming distance properties and the iterative decoding convergence behavior of turbo like codes while capacity achieving code ensembles typically are asymptotically bad in the sense that their minimum distance does not grow linearly with block length and they therefore exhibit an error floor at moderate to high signal to noise ratios asymptotically good codes usually converge further away from channel capacity in this paper we introduce the concept of tuned turbo codes a family of asymptotically good hybrid concatenated code ensembles where asymptotic minimum distance growth rates convergence thresholds and code rates can be tradedoff using two tuning parameters and by decreasing the asymptotic minimum distance growth rate is reduced in exchange for improved iterative decoding convergence behavior while increasing raises the asymptotic minimum distance growth rate at the expense of worse convergence behavior and thus the code performance can be tuned to fit the desired application by decreasing a similar tuning behavior can be achieved for higher rate code ensembles

joint permutor analysis and design for multiple turbo codes in this paper we study the problem of joint permutor analysis and design for j dimensional multiple turbo codes with j constituent encoders j 2 the concept of summary distance is extended to multiple permutors of size n and used as the design metric using the sphere packing concept we prove that the minimum length 2 summary distance spread dmin 2 is asymptoticly upper bounded by o n j 1 j we also show that the asymptotic minimum length 2l summary distance dmin 2l for the class of random permutors is lower bounded by o nj 2j epsi where epsi 0 can be arbitrarily small then using the technique of expurgating bad symbols we show that the spread of random permutors can achieve the optimum growth rate i e o nj 1 j and that the asymptotic growth rate of dmin 2l can also be improved the minimum length 2 and length 4 summary distances are studied for an important practical class of permutors linear permutors we prove that there exist j dimensional multiple linear permutors with optimal spread dmin 2 o nj 1j finally we present several joint permutor construction algorithms applicable to multiple turbo codes of short and medium lengths

a distance spectrum interpretation of turbo codes the performance of turbo codes is addressed by examining the code s distance spectrum the error floor that occurs at moderate signal to noise ratios is shown to be a consequence of the relatively low free distance of the code it is also shown that the error floor can be lowered by increasing the size of the interleaver without changing the free distance of the code alternatively the free distance of the code may be increased by using primitive feedback polynomials the excellent performance of turbo codes at low signal to noise ratios is explained in terms of the distance spectrum the interleaver in the turbo encoder is shown to reduce the number of low weight codewords through a process called spectral thinning this thinned distance spectrum results in the free distance asymptote being the dominant performance parameter for low and moderate signal to noise ratios

on an analogue of zarantonello s inequality and a nonlinear mean ergodic theorem abstract let x be a uniformly convex banach space c be a bounded closed subset of x and t c x be a contraction then it is shown that for all xi c i 0 i 1 2 n with i 1n i 1 there exists a strictly increasing convex function n of r with n 0 0 such that n t i 1n ixi i 1n itxi 1 i j n i j xi xj txi txj as an application of this inequality the mean ergodic theorem for contractions in uniformly convex banach spaces is proved

reliable channel regions for good binary codes transmitted over parallel channels we study the average error probability performance of binary linear code ensembles when each codeword is divided into j subcodewords with each being transmitted over one of j parallel channels this model is widely accepted for a number of important practical channels and signaling schemes including block fading channels incremental redundancy retransmission schemes and multicarrier communication techniques for frequency selective channels our focus is on ensembles of good codes whose performance in a single channel model is characterized by a threshold behavior e g turbo and low density parity check ldpc codes for a given good code ensemble we investigate reliable channel regions which ensure reliable communications over parallel channels under maximum likelihood ml decoding to construct reliable regions we study a modifed 1961 gallager bound for parallel channels by allowing codeword bits to be randomly assigned to each component channel the average parallel channel gallager bound is simplified to be a function of code weight enumerators and channel assignment rates special cases of this bound average union bhattacharyya ub shulman feder sf simplified sphere ss and modified shulman feder msf parallel channel bounds allow for describing reliable channel regions using simple functions of channel and code spectrum parameters parameters describing the channel are the average parallel channel bhattacharyya noise parameter the average channel mutual information and parallel gaussian channel signal to noise ratios snrs code parameters include the union bhattacharyya noise threshold and the weight spectrum distance to the random binary code ensemble reliable channel regions of repeat accumulate ra codes for parallel binary erasure channels becs and of turbo codes for parallel additive white gaussian noise awgn channels are numerically computed and compared with simulation results based on iterative decoding in addition an examp

on quasi cyclic interleavers for parallel turbo codes in this correspondence we present an interleaving scheme that yields quasi cyclic turbo codes we prove that randomly chosen members of this family yield with probability almost 1 turbo codes with asymptotically optimum minimum distance i e growing as a logarithm of the interleaver size these interleavers are also very practical in terms of memory requirements and their decoding error probabilities for small block lengths compare favorably with previous interleaving schemes

an upper bound on the minimum distance of serially concatenated convolutional codes this correspondence presents an upper bound on the minimum distance of serially concatenated codes with interleaver where the inner code is a systematic recursive convolutional encoder and the outer code is any convolutional encoder the resulting expression shows that the minimum distance of the concatenated code cannot grow more than o k1 1 df o where k is the information word length and df o is the free distance of the outer code the obtained upper bound is shown to agree with and in some cases improve over previously known results

optimal puncturing ratios and energy allocation for multiple parallel concatenated codes we propose a systematic design framework for optimal low complexity punctured multiple parallel concatenated codes mpccs based on minimizing the convergence threshold using extrinsic information transfer exit charts as the convergence threshold is related to the area between the two exit curves the corresponding optimization problem is equivalent to a curve fitting problem the exit curves are determined by the respective exit functions of the constituents which can be conveniently shaped through the use of random puncturing and unequal energy allocations across parallel coding streams the design task is therefore to find the optimal combination of constituents puncturing ratios and energy allocation for matching the exit curves a search over all rate one convolutional codes of memory length four or less is performed identifying 98 classes of codes with unique exit functions out of a total of 310 codes low complexity mpccs with up to four constituents are found where the convergence thresholds are observed to be within 0 1 db or less of the fundamental minimum signal to noise ratio snr corresponding to the binary phase shift keying bpsk capacity for code rates 1 3 les r les 7 8 further allowing for unequal energy allocation the convergence thresholds for lower code rates are similarly improved

on the asymptotic input output weight distributions and thresholds of convolutional and turbo like encoders we present a general method for computing the asymptotic input output weight distribution of convolutional encoders in some instances one can derive explicit analytic expressions in general though to determine the growth rate of the input output weight distribution for a particular normalized input weight spl kappa and output weight spl omega a system of polynomial equations has to be solved this method is then used to determine the asymptotic weight distribution of various concatenated code ensembles and to derive lower bounds on the thresholds of these ensembles under maximum likelihood ml decoding

overconvergent witt vectors let a be a finitely generated algebra over a field k of characteristic p 0 we introduce a subring w a w a which we call the ring of overconvergent witt vectors and prove its basic properties in a subsequent paper we use the results to define an overconvergent de rham witt complex for smooth varieties over k whose hypercohomology is the rigid cohomology

a logarithmic upper bound on the minimum distance of turbo codes we derive new upper bounds on the minimum distance which turbo codes can maximally attain with the optimum interleaver of a given length the new bounds grow approximately logarithmically with the interleaver length and they are tighter than all previously derived bounds for medium length and long interleavers an extensive discussion highlights the impacts of the new bounds in the context of interleaver design and provides some new design guidelines

asymptotic behavior of solutions of nonlinear volterra equations 0 recently baillon and clement 3 established mean ergodic theorems for solutions of nonlinear volterra equations in hilbert space in the present paper we study the asymptotic behavior of solutions of 1 1 by using nonlinear ergodic theorems the first mean ergodic theorem was given by baillon l and it was improved by several authors 3 8 141 163

improved upper bounds on the ml decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum the ensemble performance of parallel and serial concatenated turbo codes is considered where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time varying recursive systematic convolutional codes following the derivation of the input output weight enumeration functions of the ensembles of random parallel and serial concatenated turbo codes the tangential sphere upper bound is employed to provide improved upper bounds on the block and bit error probabilities of these ensembles of codes for the binary input additive white gaussian noise awgn channel based on coherent detection of equi energy antipodal signals and maximum likelihood decoding the influence of the interleaver length and the memory length of the component codes is investigated the improved bounding technique proposed here is compared to the conventional union bound and to a alternative bounding technique by duman and salehi 1998 which incorporates modified gallager bounds the advantage of the derived bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random recursive systematic convolutional component codes and it is especially pronounced in the region exceeding the cutoff rate where the performance of turbo codes is most appealing these upper bounds are also compared to simulation results of the iterative decoding algorithm

local monodromy of p divisible groups a p divisible group over a field k admits a slope decomposition associated to each slope is an integer m and a representation gal k gl m d where d is the p division algebra with brauer invariant we call m the multiplicity of in the p divisible group let go be a p divisible group over a field k suppose that is not a slope of g 0 but that there exists a deformation of g in which appears with multiplicity one assume that s 1 s for any natural number s 1 we show that there exists a deformation g r of g 0 k such that the representation gal fracr gl 1 d has a large image

on the minimum distance of turbo codes with quadratic permutation polynomial interleavers an interleaver is a critical component for the channel coding performance of turbo codes algebraic constructions are of particular interest because they admit analytical designs and simple practical hardware implementations also the recently proposed quadratic permutation polynomial qpp based interleavers by sun and takeshita have provided excellent performance for short to medium block lengths and have been selected for the 3gpp lte standard in this paper we derive some upper bounds on the best achievable minimum distance dmin of qpp based conventional binary turbo codes with tailbiting termination or dual termination when the interleaver length n is sufficiently large that are tight for larger block sizes in particular we show that the minimum distance is at most 2 2v 1 9 independent of the interleaver length when there exists an inverse polynomial of degree two where v is the degree of the primitive feedback and monic feedforward polynomials however allowing the qpp to have no inverse polynomials of degree two may give strictly larger minimum distances and lower multiplicities in particular we provide several qpps with no quadratic inverse for some of the 3gpp lte interleaver lengths giving a dmin with the 3gpp lte constituent encoders which is strictly larger than 50 for instance we have found a qpp for n 6016 which gives an estimated dmin of 57 furthermore we provide the exact minimum distances and the corresponding multiplicities for all 3gpp lte turbo codes with dual termination which shows that the best minimum distance is 51 finally we compute the best achievable minimum distances with qpp interleavers for all 3gpp lte interleaver lengths n 4096 and compare these minimum distances with the ones we get when using the 3gpp lte polynomials

a p adic local monodromy theorem we produce a canonical filtration for locally free sheaves on an open p adic annulus equipped with a frobenius structure using this filtration we deduce a conjecture of crew on p adic differential equations analogous to grothendieck s local monodromy theorem also a consequence of results of andre and of mebkhout namely given a finite locally free sheaf on an open p adic annulus with a connection and a compatible frobenius structure the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix

combinatorial analysis of the minimum distance of turbo codes in this paper new upper bounds on the maximum attainable minimum hamming distance of turbo codes with arbitrary including the best interleavers are established using a combinatorial approach these upper bounds depend on the interleaver length the code rate and the scramblers employed in the encoder examples of the new bounds for particular turbo codes are given and discussed the new bounds are tighter than all existing ones and prove that the minimum hamming distance of turbo codes cannot asymptotically grow at a rate more than the third root of the codeword length

design of interleavers for turbo codes iterative interleaver growth algorithms of polynomial complexity this paper addresses the problem of designing interleavers for parallel concatenated convolutional codes pcccs tailored to specific constituent codes we start by establishing the role of the interleaver in the pccc and the various parameters that influence the performance of the pccc with a given interleaver subsequently we define a canonical form of the interleaving engine denoted as the finite state permuter fsp and demonstrate the minimal delay property of this canonical form for any given permutation we present a procedure for deriving the canonical fsp engine we address the issue of implementation of the fsp and propose a very simple structure for the fsp next using the structural property of the fsp engine we develop a systematic iterative technique for construction of interleavers with a complexity that is polynomial in the interleaver size subsequently we develop a cost function that coupled with the iterative interleaver growth procedure can be used to design optimized interleavers for pcccs we provide examples of application of the interleaver design technique and compare the designed interleavers with some of the interleavers of comparable size found in the literature

the serial concatenation of rate 1 codes through uniform random interleavers until the analysis of repeat accumulate codes by divsalar et al 1998 few people would have guessed that simple rate 1 codes could play a crucial role in the construction of good binary codes we construct good binary linear block codes at any rate r 1 by serially concatenating an arbitrary outer code of rate r with a large number of rate 1 inner codes through uniform random interleavers we derive the average output weight enumerator we for this ensemble in the limit as the number of inner codes goes to infinity using a probabilistic upper bound on the minimum distance we prove that long codes from this ensemble will achieve the gilbert varshamov 1952 bound with high probability numerical evaluation of the minimum distance shows that the asymptotic bound can be achieved with a small number of inner codes in essence this construction produces codes with good distance properties which are also compatible with iterative turbo style decoding for selected codes we also present bounds on the probability of maximum likelihood decoding mld error and simulation results for the probability of iterative decoding error

the minimum distance of turbo like codes worst case upper bounds are derived on the minimum distance of parallel concatenated turbo codes serially concatenated convolutional codes repeat accumulate codes repeat convolute codes and generalizations of these codes obtained by allowing nonlinear and large memory constituent codes it is shown that parallel concatenated turbo codes and repeat convolute codes with sub linear memory are asymptotically bad it is also shown that depth two serially concatenated codes with constant memory outer codes and sublinear memory inner codes are asymptotically bad most of these upper bounds hold even when the convolutional encoders are replaced by general finite state automata encoders in contrast it is proven that depth three serially concatenated codes obtained by concatenating a repetition code with two accumulator codes through random permutations can be asymptotically good

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

on quadratic inverses for quadratic permutation polynomials over integer rings an interleaver is a critical component for the channel coding performance of turbo codes algebraic constructions are of particular interest because they admit analytical designs and simple practical hardware implementation sun and takeshita have recently shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes in this correspondence a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial for a quadratic permutation polynomial over an integer ring further a simple construction is given for the quadratic inverse all but one of the quadratic interleavers proposed earlier by sun and takeshita are found to admit a quadratic inverse although none were explicitly designed to do so an explanation is argued for the observation that restriction to a quadratic inverse polynomial does not narrow the pool of good quadratic interleavers for turbo codes

purity of the stratification by newton polygons in this paper we prove four theorems one on surface singularities two on fcrystals and one on moduli of p divisible groups the reason we put together these results in one paper is that the proofs as given here show how these theorems are related let us first describe our results let s 0 be a normal surface singularity over an algebraically closed field of characteristic p let s s be a resolution of singularities our first result is theorem 3 2 1 any qp cohomology class on the link of the singularity extends to the resolution more precisely

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

an analysis of the block error probability performance of iterative decoding asymptotic iterative decoding performance is analyzed for several classes of iteratively decodable codes when the block length of the codes n and the number of iterations i go to infinity three classes of codes are considered these are gallager s regular low density parity check ldpc codes tanner s generalized ldpc gldpc codes and the turbo codes due to berrou et al it is proved that there exist codes in these classes and iterative decoding algorithms for these codes for which not only the bit error probability p sub b but also the block frame error probability p sub b goes to zero as n and i go to infinity

upper bound on the minimum distance of turbo codes an upper bound on the minimum distance of turbo codes is derived which depends only on the interleaver length and the component scramblers employed the derivation of this bound considers exclusively turbo encoder input words of weight 2 the bound does not only hold for a particular interleaver but for all possible interleavers including the best it is shown that in contrast to general linear binary codes the minimum distance of turbo codes cannot grow stronger than the square root of the block length this implies that turbo codes are asymptotically bad a rigorous proof for the bound is provided which is based on a geometric approach

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

on higher order permutors for serially concatenated convolutional codes a new parameter set for designing permutors is introduced it is called the set of higher order separations and can be considered as a generalization of the well known symbol separation spreading factor the respective permutor is called a higher order permutor and we show how such a permutor can be constructed for a second order permutor in a serially concatenated convolutional encoding scheme we give a lower bound on the minimum distance of the resulting overall code the integers that determine the sufficiently large separations i e the smallest separations for which the distance properties can be guaranteed are derived from the active distances of the convolutional component encoders additionally a growth rate of the minimum distance like o dfree o lfloorrho 2rfloor 1 is proved for serially concatenated convolutional encoders with permutors having large separations of order rho

a mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense abstract let x be a uniformly convex banach space such that its dual x has the kadec klee property c a bounded closed convex subset of x and t t t t 0 a one parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense we show that every continuous almost orbit of t is weakly almost convergent to a common fixed point of t a discrete version of our main result is also included

spectra and minimum distances of repeat multiple accumulate codes in this paper the ensembles of repeat multiple accumulate codes ram which are obtained by interconnecting a repeater with a cascade of m accumulate codes through uniform random interleavers are analyzed it is proved that the average spectral shapes of these code ensembles are equal to 0 below a threshold distance epsivm and moreover they form a nonincreasing sequence in m converging uniformly to the maximum between the average spectral shape of the linear random ensemble and 0 consequently the sequence epsivm converges to the gilbert varshamov gv distance a further analysis allows to conclude that if m ges 2 the ram are asymptotically good and that epsivm is the typical normalized minimum distance when the interleaver length goes to infinity combining the two results it is possible to conclude that the typical distance of the ensembles ram converges to the gilbert varshamov bound

variance of the turbo code performance bound over the interleavers we evaluate the variance of the union performance bound for a rate 1 3 turbo code over all possible interleavers of length n under the assumption of a maximum likelihood ml decoder theoretical and simulation results for turbo codes with two memory component codes indicate that the coefficient of variation of the bound increases with the signal to noise ratio and decreases with the interleaver length theoretical analysis for large interleaver lengths shows that the coefficient of variation asymptotically approaches a constant value the results also demonstrate that the majority of the interleavers have performance bounds very close to the average value of the bound this phenomenon is more palpable for larger interleaver lengths

performance analysis of 3 d turbo codes in this work we consider the minimum distance properties and convergence thresholds of 3 d turbo codes 3d tcs recently introduced by berrou here we consider binary 3d tcs while the original work of berrou considered double binary codes in the first part of the paper the minimum distance properties are analyzed from an ensemble perspective both in the finite length regime and in the asymptotic case of large block lengths in particular we analyze the asymptotic weight distribution of 3d tcs and show numerically that their typical minimum distance dmin may depending on the specific parameters asymptotically grow linearly with the block length i e the 3d tc ensemble is asymptotically good for some parameters in the second part of the paper we derive some useful upper bounds on the dmin when using quadratic permutation polynomial qpp interleavers with a quadratic inverse furthermore we give examples of interleaver lengths where an upper bound appears to be tight the best codes in terms of estimated dmin obtained by randomly searching for good pairs of qpps for use in the 3d tc are compared to a probabilistic lower bound on the dmin when selecting codes from the 3d tc ensemble uniformly at random this comparison shows that the use of designed qpp interleavers can improve the dmin significantly for instance we have found a 6144 2040 3d tc with an estimated dmin of 147 while the probabilistic lower bound is 69 higher rates are obtained by puncturing nonsystematic bits and optimized periodic puncturing patterns for rates 1 2 2 3 and 4 5 are found by computer search finally we give iterative decoding thresholds computed from an extrinsic information transfer chart analysis and present simulation results on the additive white gaussian noise channel to compare the error rate performance to that of conventional turbo codes

integral motives and special values of zeta functions for each field k we define a category of rationally decomposed mixed motives with z coefficients when k is finite we show that the category is tannakian and we prove formulas relating the behaviour of zeta functions near integers to certain ext groups

performance of parallel concatenated coding schemes in this paper ensembles of parallel concatenated codes are studied and rigorous results on their asymptotic performance under the assumption of maximum likelihood ml decoding are presented in particular it is proven that in any parallel concatenation scheme with k branches where all k encoders are recursive and the bhattacharyya parameter of the channel is sufficiently small the bit error rate ber and the word error rate go to 0 exactly like n 1 k and n 2 k respectively different types of ensembles by changing the subgroup of permutations used to interconnect the various encoders are considered

a new cycle based joint permutor design for multiple turbo codes in this letter a permutor design parameter called the weight of a cycle through j 1 permutation matrices for multiple turbo codes is introduced analogously to the single permutor case of conventional turbo codes we show the connection of the new parameter to the minimum distance of special classes of multiple turbo codes in addition simulation results are presented for multiple turbo codes based on the new design

permutation polynomial interleavers an algebraic geometric perspective an interleaver is a critical component for the channel coding performance of turbo codes algebraic constructions are important because they admit analytical designs and simple practical hardware implementation the spread factor of an interleaver is a common measure for turbo coding applications maximum spread interleavers are interleavers whose spread factors achieve the upper bound an infinite sequence of quadratic pps over integer rings that generate maximum spread interleavers is presented new properties of pp interleavers are investigated from an algebraic geometric perspective resulting in a new non linearity metric for interleavers a new interleaver metric that is a function of both the nonlinearity metric and the spread factor is proposed it is numerically demonstrated that the spread factor has a diminishing importance with the block length a table of good interleavers for a variety of interleaver lengths according to the new metric is listed extensive computer simulation results with impressive frame error rates confirm the efficacy of the new metric further when tail biting constituent codes are used the resulting turbo codes are quasi cyclic

rapid carrier acquisition from baud rate samples maximum likelihood estimation of phase and frequency offset involves the maximization of a nonlinear likelihood function we develop an estimator for carrier acquisition by linearizing the likelihood function and show that its performance is close to the cramer rao bound crb the estimator is then extended to blind frequency acquisition and combined with testing to eliminate unlikely hypotheses with proper modeling of the likelihood resulting from the blind search simulations show that the algorithm quickly rejects all but the correct frequency hypothesis

interleavers for turbo codes using permutation polynomials over integer rings a class of deterministic interleavers for turbo codes tcs based on permutation polynomials over spl zopf sub n is introduced the main characteristic of this class of interleavers is that they can be algebraically designed to fit a given component code moreover since the interleaver can be generated by a few simple computations storage of the interleaver tables can be avoided by using the permutation polynomial based interleavers the design of the interleavers reduces to the selection of the coefficients of the polynomials it is observed that the performance of the tcs using these permutation polynomial based interleavers is usually dominated by a subset of input weight 2m error events the minimum distance and its multiplicity or the first few spectrum lines of this subset are used as design criterion to select good permutation polynomials a simple method to enumerate these error events for small m is presented searches for good interleavers are performed the decoding performance of these interleavers is close to s random interleavers for long frame sizes for short frame sizes the new interleavers outperform s random interleavers

the iwasawa mu invariant of p adic hecke l functions for an odd prime p we compute the invariant of the anticyclotomic katz p adic l function of a p ordinary cm field if the conductor of the branch character is a product of primes split over the maximal real subfield except for rare cases where the root number of the p adic functional equation is congruent to 1 modulo p the invariant vanishes

period spaces for hodge structures in equal characteristic we develop the analog in equal positive characteristic of fontaine s theory for crystalline galois representations of a p adic eld in particular we describe the analog of fontaine s functor which assigns to a crystalline galois representation an isocrystal with a hodge ltration in equal characteristic the role of isocrystals and hodge ltrations is played by z isocrystals and hodge pink structures the latter were invented by pink our rst main result in this article is the analog of the colmez fontaine theorem that weakly admissible implies admissible next we construct period spaces for hodge pink structures on a xed z isocrystal these period spaces are analogs of the rapoport zink period spaces for fontaine s ltered isocrystals in mixed characteristic and likewise are rigid analytic spaces for our period spaces we prove the analog of a conjecture of rapoport and zink stating the existence of a universal local system on a berkovich open subspace of the period space as a consequence of weakly admissible implies admissible this berkovich open subspace contains every classical rigid analytic point of the period space as the principal tool to demonstrate these results we use the analog of kedlaya s slope filtration theorem which we also formulate and prove here

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