distance spectra and upper bounds on error probability for trellis codes the problem of estimating error probability for trellis codes is considered the set of all squared euclidean distances between code sequences is presented as a countable set this representation is used for calculating the generating functions for upper bounding error probability and bit error probability for trellis codes satisfying some symmetry conditions the generating functions of squared euclidean distances distance spectra are obtained by inversion of a matrix of order 2 sup spl nu it is shown that the generating functions are defined in terms of one formal variable for qam and uniform am and in terms of q 4 formal variables for q ary psk q 2 sup m where m spl ges 2 is an integer for small spl nu the generating functions may be found in closed form for larger spl nu a numerical technique for obtaining some initial terms of the power series expansion is proposed this algorithm is based on the recurrent matrix equations and the chinese remainder theorem

stable bundles and integrable systems on considere la geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur une surface de riemann on montre que ce sont des systemes dynamiques hamiltoniens algebriquement completement integrables

fast tcm decoding phase quantization and integer weighting tcm combining modulation and coding achieves coding gains over conventional uncoded multilevel modulation without the attendant bandwidth expansion since tcm was proposed ungerboeck 1982 1987 substantial work has done in this area a large portion of the tcm work has been in the area of high speed data transmission over voice grade modems using quadrature amplitude modulation qam qam not having a constant envelope is unattractive for employing a twt with its nonlinear behavior as the power stage additional work has been done in utilizing m ary psk with tcm simulations by taylor and chan 1981 utilizing a 4 state convolutional code demonstrated the coding gain of a rate 2 3 coded 8 psk modulation scheme wilson et al 1984 obtained results for 16 psk tcm using codes with 4 to 32 states and achieved coding gains of 3 5 to 4 8 db respectively over 8 psk and demonstrated that small memory codes achieved good gains with simple design procedures

symmetric trellis coded vector quantization we present here design techniques for trellis coded vector quantizers with symmetric codebooks that facilitate low complexity quantization as well as partitioning into equiprobable sets for trellis coding the quantization performance of this coder on the independently identically distributed i i d laplacian source matches the performance of trellis based scalar vector quantization tb svq but requires less computational complexity

a lower bound on the minimum euclidean distance of trellis coded modulation schemes a lower bound on the minimum free euclidean distance of trellis coded modulation tcm is derived that guarantees the existence of good tcm codes of any complexity the bound is used to compare trellis codes combined with phase shift keying pulse amplitude modulation and quadratic amplitude shift keying modulation this random coding bound is the first lower bound on the free distance of trellis codes is tighter than any upper bound for large constraint lengths and predicts the asymptotic performance of tcm when the complexity of the code becomes large the bound can be used with any code rate and any modulation scheme and shows that the free distance increases linearly with the constraint length for large values of the constraint length

endoproperties of modules and local duality abstract let r be any ring and n i i n i be a direct sum of finitely presented left r modules n i suppose that d n and d n i are the local duals of n and n i for each i i we prove that the lattice of endosubmodules of n is anti isomorphic to the lattices of matrix subgroups of d n and of m i i d n i as consequences n is endoartinian if and only if m or d n is endonoetherian and n is endonoetherian if and only if m or d n is pure injective we obtain in particular that if r is a krull schmidt ring and m is an indecomposable pure injective endonoetherian right r module which is the source of a left almost split morphism in mod r then m is endofinite as an application a ring r is of finite representation type if and only if every pure injective right r module is endonoetherian

on polarizations in invariant theory abstract given a reductive algebraic group g and a finite dimensional algebraic g module v we study how close is the algebra of g invariant polynomials on v n to the subalgebra generated by polarizations of g invariant polynomials on v we address this problem in a more general setting of g actions on arbitrary affine varieties

structure optimization and realization of ffsk trellis codes the structure of combinations of l k binary trellis encoders and fast frequency shift keying ffsk modulation is studied a novel method for the optimization of these combinations is proposed it is concluded that regardless of the particular realization the best combinations can always be obtained by using a so called matched convolutional code optimum ffsk codes of rates 1 2 and 2 3 for up to 64 and 32 states respectively are reported it is shown that the best matched encoders for ffsk modulation are also matched and best for any ffsk type scheme where the pulse shape is required to satisfy nyquist s third criterion

analysis of multidimensional trellis coded mpsk in rice lognormal fading channels the paper addresses the analysis of multidimensional trellis coded m ary phase shift keying mpsk modulation over a rice lognormal fading channel model applicable to a variety of environments and to both terrestrial and satellite mobile communications bounds to the bit error probability are derived and applied to the analysis of a few selected trellis coded modulation tcm schemes the results confirmed by simulation show that on the rice channel there exists a threshold in bit energy to noise density ratio above which the effective code length is the dominant parameter while the free distance is dominating below however the influence of both parameters is mitigated when shadowing is present

fibration de hitchin et endoscopie we propose a geometric interpretation of the theory of elliptic endoscopy due to langlands and kottwitz in terms of the hitchin fibration as applications we prove a global analog of a purity conjecture due to goresky kottwitz and macpherson for unitary groups this global purity statement has been used in a joint work with g laumon to prove the fundamental lemma over a local fields of equal characteristics

power bandwidth performance of smoothed phase modulation codes constant envelope phase varying sinusoids of the form sqrt 2e t cos omega c t phi t are studied in which the phase function phi t follows some coded pattern in response to data power and bandwidth performance are studied for such patterns the patterns depend on a phase shaping function a modulation index h and a sequence of m ary underlying changes in phase which are chosen at random a cutoff rate like parameter r 0 is computed which guarantees existence of codes at all rates r bits t interval whose error performance varies as exp n r 0 r where n is the code word length in t intervals plots of r 0 are given as a function of interval energy e the shaping function h and m extensive spectral calculations give the spectra of these phased sinusoids and their performance is plotted in the power bandwidth plane the results give strong evidence that phase codes can approximate any power bandwidth combination consistent with shannon s gaussian channel capacity and that linear channels are not required for narrow band transmission

geometrically uniform tcm codes over groups based on l spl times mpsk constellations the theory of geometrically uniform signal sets and codes over groups is applied to the case of l spl times mpsk constellations conditions for rotational invariance of group codes are discussed the tables of geometrically uniform partitions found in benedetto et al 1993 are used to construct good geometrically uniform trellis codes over nonbinary abelian groups the present authors consider l spl times 4psk and l spl times 8psk constellations used to transmit information rates of 1 and 2 bit two dimensions respectively and present tables of good codes over generating groups z4 sup l and z8 sup l for l ranging from 1 to 4 in most cases they improve the tables of codes known so far moreover the geometrical uniformity of codes allows a very easy performance evaluation so that the authors also present a complete set of curves of error event probability for the obtained codes

bounds for codes over the unit circle let c be a code of length n and rate r over the alphabet a q exp 2 pi ir q r o 1 cdots q 1 and let d c be the minimum euclidean distance of c for large n the lower and upper bounds are obtained in parametric form on the achievable pairs r delta where delta d 2 c n holds to obtain these bounds the arguments leading to the gilbert bound and the elias bound respectively are applied to the alphabet a q for q rightarrow infty they are shown to be expressible in terms of the modified bessel function of the first kind the elias type bound is compared with the kabatyanskii levenshtein k l bound that holds for less restrictive alphabets it turns out that our upper bound improves the k l bound for delta leq 0 93

minimal transmitter complexity design of analytically described trellis codes g ungerboeck s 1982 design rules for a class of bandlimited codes called trellis codes are reviewed his design of the trellis is based on a set partitioning of the signal constellation and he realized these trellis codes by a convolutional encoder followed by a mapping rule from the coder output to modulation symbols r calderbank and j e mazo 1984 showed how to realize trellis codes for one dimensional signal sets in a single step easily derived nonlinear transformation with memory on a sliding block of source symbols the design rules that give a signal state specification in a trellis that yields the calderbank mazo transformation with the smallest number of terms are presented this gives a minimal transmitter complexity design it is shown how to realize the ungerboeck from the calderbank mazo form and as a result a step by step search free design procedure for trellis codes is presented two additional design rules are presented and applied to two examples by analytically designing two trellis codes a simple procedure for converting an analytic code expression to a convolutional encoder realization is discussed the analytic designs of a 4 d code and a 2 d code are presented

on the minimum length error event of minimum euclidean weight let eta denote the length of the shortest error event achieving the minimum detection distance of maximum likelihood signal detection for an impulse response having memory v a family of impulse responses where eta is of order v sup 2 is exhibited this in turn shows that some difficulty can arise in computing the minimum detection distance

a geometric construction procedure for geometrically uniform trellis codes the problem of maximizing the minimum free squared euclidean distance of a trellis code is developed from a geometric point of view this approach provides a new way of constructing constellations for trellis coding a decomposition of the trellis topology leads to a systematic construction of signal sets and generators for geometrically uniform trellis codes an algorithm is proposed to construct geometrically uniform trellis codes and examples show how to obtain large free distance trellis codes this approach unifies the construction of convolutional codes over the binary field and trellis codes over the real field

design of multilayer coded modulation for nonergodic block fading channels multilayer coded modulation mlyc in single antenna and multiple antenna wireless fading channels is investigated while the mlyc has been known to achieve ergodic fading channel capacity the problem of interest here is to design practical and efficient mlyc for nonergodic block fading channels we develop a design methodology which maximizes the information rate of mlyc subject to an upper bound on the decoding error probability moreover we show that the mlyc performs closer to channel capacity when the overall diversity order of the channel is higher and proper spatial interleaving is employed the relationship between the mlyc scheme and other transmission techniques such as multilevel coded modulation and bit interleaved coded modulation bicm is also discussed it is shown through simulation examples that in realistic block fading channels the mlyc with practical coded modulation outperforms the bicm without turbo receiver iteration we propose the mlyc as a promising alternative to bicm especially when turbo iterative processing is not desired e g for progressive layered media transmission

channel coding with quadrature quadrature phase shift keying q sup 2 psk signals channel coding due to trellis modulation has been proved to be useful for bandlimited channels however these modulations mostly designed with n use of 2d signals are primarily aimed at coding gain only it is pointed out that utilization of all available signal dimensions which is limited by the time bandwidth product may improve the bandwidth efficiency and simultaneously bring an additional coding gain trellis coding with a spectrally efficient 4d signal set based on q sup 2 psk is addressed without any expansion of the q sup 2 psk signal set a simple hand designed 16 state trellis code provides a coding gain of 6 02 db with the same number of states in g ungergoeck s 1982 8 psk trellis the gain is 4 1 db in low intersymbol interference situations the bandwidth efficiency of this coded q sup 2 psk is twice that of coded 8 psk if both operate at 2 b s hz and p sub b e 10 sup 5 the coded q sup 2 psk provides a saving of about 4 db over the coded 8 psk some fully connected trellises with an expanded signal due to 2 use of q sup 2 psk signals are also presented two such codes ar rate 7 8 achieve a gain of 5 45 db with only eight states

impact of diversity reception on fading channels with coded modulation ii differential block detection for pt i see ibid vol 45 no 6 p 563 572 1997 we study coded modulation with block differential detection in an arbitrarily correlated rician fading channel with space diversity coded differential q psk is included in our analysis as a special case a metric is chosen that is optimum for perfect interleaving slow fading and independent diversity branches for slow fading we compare the the cutoff rates of the channels resulting from different choices of block length n and diversity index m specifically we show that block detection with diversity may or may not generate a better coding channel than usual differential detection according to the code selected and the combination of values of m and n in particular for low diversity orders m 1 2 and for low to medium code rates differential detection is still an optimal or near optimal solution while for high diversity orders m spl ges 2 and medium to high code rates up to uncoded modulation block detection with n 2 can provide a significant gain an error floor always exists when fading is fast it decreases exponentially with the product of code diversity and space diversity so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading performance examples based on actual coding schemes are also shown

multidimensional modulation and coding for band limited digital channels a class of multidimensional signals based on generalized group alphabets is introduced and its basic properties are derived the combination of generalized group alphabets and coding is also examined two coding schemes are considered g ungerboeck s scheme 1982 for combination with convolutional codes and v v ginzburg s 1984 scheme for combination with block codes it is concluded that the performance of these schemes makes them attractive for transmission over band limited digital channels

decomposition properties of strict mittag leffler modules we show that a not necessarily unitary ring with enough idempotents is left perfect if and only if there exists a cardinal number such that every flat strict mittag leffler module is a direct sum of generated modules several applications are given to the decomposition properties of modules into direct summands

trellis coding with asymmetric modulations traditionally symmetric signal constellations i e those with uniformly spaced signal points have been used for both uncoded and coded systems although symmetric signal constellations are optimum with no coding the same is not necessarily true for coded systems this paper shows that by designing the signal constellations to be asymmetric one can in many instances obtain a performance gain over the traditional symmetric constellations combined with trellis coding in particular we consider the joint design of n n 1 trellis codes and asymmetric 2 n 1 point signal constellations which has no bandwidth expansion relative to an uncoded 2n point symmetric signal set the asymptotic performance gains due to coding and asymmetry are evaluated in terms of the minimum free euclidean distance d free of the trellis a comparison of the maximum value of this performance measure to the minimum distance d min of the uncoded system is an indication of the maxiamm reduction in required e b n 0 that can be achieved for arbitrarily small system bit error rates bit error probability analysis is carried out for general cases a few examples are given to show the performance gain due to the asymmetry of the signal set it is to be emphasized that the introduction of asymmetry into the signal set does not affect the bandwidth or power requirements of the system hence the abovementioned improvements in performance come at little or no cost asymmetric signal sets in coded systems first appear in the work of divsalar and yuen 1 2 here we expand upon these results by considering various types of asymmetric signal sets combined with the optimum in the sense of maximum d free trellis code having 2 4 8 and 16 states the numerical results obtained will clearly demonstrate the tradeoff between the additional savings in required e b n 0 and the additional complexity more trellis states needed to achieve it

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

error probability for digital transmission over nonlinear channels with application to tcm the computation of upper and lower bounds to error probability in digital transmission over nonlinear channels with a finite memory is considered by using orthogonal volterra series the authors derive a canonical representation for discrete nonlinear systems based on a linear convolutional code and a memoryless mapper this representation shows that finite memory discrete nonlinear systems can be analyzed in much the same way as tcm trellis coded modulation schemes in particular tcm over nonlinear channels can be analyzed a technique is derived that expresses an upper bound to error probability based on the computation of the transfer of a state diagram with n branches and whose branch labels are matrices rather than scalars some examples of its application are given in particular error bounds are derived for nonlinear tcm schemes and for tcm schemes operating on nonlinear channels

on joint source and channel coding using trellis coded cpm analytical bounds on the channel distortion joint source and channel coding jscc using trellis coded quantization tcq in conjunction with trellis coded continuous phase modulation cpm is studied the channel is assumed to be the additive white gaussian noise awgn channel analytical bounds on the channel distortion for the investigated systems with maximum likelihood sequence detection mlsd are developed the bounds are based on the transfer function technique which was modified and generalized to include continuous amplitude discrete time signals for a memoryless uniform source the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal to noise ratio snr values for a memoryless nonuniform source the constructed bounds are not as tight as the one for the uniform source however it still can be used as an indication to how the system performs it is concluded that the minimum euclidean distance of the system alone is not enough to evaluate the performance of the considered systems the number of error events having minimum euclidean distance and the total distortion caused by those error events also affect the asymptotic performance this work provides an analysis tool for the investigated systems the analysis method is very general it may be applied to any trellis based jscc schemes

adaptive trellis coded multiple phase shift keying for rayleigh fading channels an adaptive scheme for trellis coded modulation of mpsk signals called adaptive trellis coded multiple phaseshift keying atcmpsk is proposed for slowly rayleigh fading channels the adaptive scheme employs a slightly modified rate 1 2 convolutional encoder and the corresponding viterbi decoder to realize a family of codes of different rates which are employed according to channel conditions during poor channel conditions trellis coded qpsk tcqpsk together with repetition schemes are employed as channel conditions improve higher rate schemes such as trellis coded 16 psk are used an interleaving deinterleaving method suitable for the adaptive scheme is proposed theoretical bounds for the error performance and an exact expression for the throughput of the proposed adaptive scheme are derived and are compared against simulation results simulations have been performed to measure the performance of the scheme for different parameters and some nonideal conditions it is shown that atcmpsk results in considerable improvement in bit error rate ber performance of mpsk signals under ideal conditions gains in the range of 3 20 db are achieved over conventional fixed rate pragmatic trellis coded schemes

superposition coding for side information channels we present simple practical codes designed for the binary and gaussian dirty paper channels we show that the dirty paper decoding problem can be transformed into an equivalent multiple access decoding problem for which we apply superposition coding our concept is a generalization of the nested lattices approach of zamir shamai and erez in a theoretical setting our constructions are capable of achieving capacity using random component codes and maximum likelihood decoding we also present practical implementations of the constructions and simulation results for both dirty paper channels our results for the gaussian dirty paper channel are on par with the best known results for nested lattices we discuss the binary dirty tape channel for which we present a simple effective coding technique finally we propose a framework for extending our approach to general gel fand pinsker channels

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

trellis coded quantization designed for noisy channels trellis coded quantization tcq of memoryless sources is developed for transmission over a binary symmetric channel the optimized tcq coder can achieve essentially the same performance as ayanoglu and gray s 1987 unconstrained trellis coding optimized for the binary symmetric channel but with a much lower implementation complexity for transmission rates above 1 b sample in most cases the optimized tcq coder also provides larger signal to noise ratio than farvardin and vaishampayan s 1991 channel optimized vector quantization algorithms are developed for the joint design of trellis coded quantization modulation tcq tcm the jointly designed tcq tcm system outperforms the straightforward cascade of separately designed tcq and tcm systems the improvement is most significant at low channel signal to noise ratio for a first order gauss markov source the predictive tcq tcm performance can exceed that of optimum pulse amplitude modulation

concatenated multilevel block coded modulation encoding and decoding schemes for concatenated multilevel block codes are presented by one of these structures a real coding gain of 5 6 7 4 db for the bit error range of 10 sup 6 to 10 sup 9 is achieved for transmission through the additive white gaussian noise channel also a rather large asymptotic coding gain is obtained the new coding schemes have very low decoding complexity and increased coding gain in comparison with the conventional block and trellis coded modulation structures a few design rules for concatenated single and multilevel block codes with large coding gain are also provided

tcm schemes with partially overlapped signal constellations in conventional tcm schemes for a rate of n bits per channel symbol a 2 sup n 1 point constellation is used it is shown that using constellations with less than 2 sup n 1 points one can achieve a considerable coding gain in comparison to the traditional 2 sup n 1 point constellation the increase in coding gain is due to a reduction in transmitted signal energy as a result of deleting some high power signals from the original constellation and reusing of some of the low power signals instead

multiple trellis coded modulation mtcm the authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation mtcm wherein more than one channel symbol per trellis branch is transmitted they have found simple two state trellis codes for symmetric mpsk multiple phase shift keying and am modulations that can achieve 3 db gain over uncoded modulation at very high signal to noise ratios without bandwidth expansion or reduction in information bit rate the gain of these codes with respect to previously reported two state trellis codes is between 1 and 2 db at very high signal to noise ratios depending on the number of bits per hertz transmitted these gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram the authors note that additional computations per branch are needed for the multiple trellis coding scheme the concept can be extended to a higher number of states and other types of modulations

a modified design of trellis coded mpsk for the fading channel it is shown that the classical additive white gaussian noise awgn channel design can be retained for the fading channel with any degree of fading if carried out with the appropriate signal set size m m sub min the size of the signal set m sub min is shown to depend upon the number of parallel transitions between a given pair of states and the throughput rate in the proposed multiple trellis coded modulation mtcm scheme with a modified design mtcm md the output bits from a rate m m 1 trellis encoder are assigned multiple signals from an m sub min psk signal set compared to the mtcm with set partitioning proposed for the fading channel spf design the mtcm md scheme provides the same signal diversity and the same or increased values of the branch distance product and always leads to increased value of d sup 2 free as a result the performance is always improved on the rician fading channel due to the increased d sup 2 free and is improved on any fading channel when an increase in branch distance produce p takes place when compared to the mtcm with the set partitioning optimum for the awgn channel spa design the mtcm md scheme under certain conditions provides the same value of d sup 2 free as the mtcm spa design and is then asymptotically optimum for both the awgn channel and the fading channels

effects of the catastrophic behavior of tcm schemes with partially overlapped signal constellations the paper shows that the catastrophic behavior of tcm codes based on partially overlapped signal constellations significantly increases both the effective error coefficient and the decoding delay of such codes resulting in a non negligible performance degradation with respect to the asymptotic coding gain

multistage decoding of multilevel block m psk modulation codes and its performance analysis multistage decoding of multilevel block multilevel phase shift keying m psk modulation codes for the additive white gaussian noise awgn channel is investigated several types of multistage decoding including a suboptimum soft decision decoding scheme are devised and analyzed upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes error probabilities of some specific multilevel block 8 psk modulation codes are evaluated and simulated the computation and simulation results for these codes show that with multistage decoding significant coding gains can be achieved with large reduction in decoding complexity in one example it is shown that the difference in performance between the proposed suboptimum multistage soft decision decoding and the single stage optimum decoding is small only a fraction of a db loss in snr at the block error probability of 10 sup 6

signal shaping for bicm at low snr the generalized mutual information gmi of bit interleaved coded modulation bicm systems sometimes called the bicm capacity is investigated at low signal to noise ratio snr the combinations of input alphabet input distribution and binary labeling that achieve the shannon limit 1 59 db are completely characterized the main conclusion is that a bicm system with probabilistic shaping achieves the shannon limit at low snr if and only if it can be represented as a zero mean linear projection of a hypercube hence probabilistic shaping offers no extra degrees of freedom to optimize the low snr bicm gmi in addition to what is provided by geometrical shaping the analytical conclusions are confirmed by numerical results which also show that for a fixed input alphabet probabilistic shaping can improve the bicm gmi in the low and medium snr range

binary multilevel coset codes based on reed muller codes we study the construction and decoding of binary multilevel coset codes this construction originally introduced by blokh and zyablov in 1974 and by zinov ev in 1976 shows remarkable analogies with most recent schemes of coded modulations basic elements of the construction are an inner code head of a partition chain having suitable distance properties and a set of outer codes generally nonbinary for each partition level there is an outer code whose alphabet has the same order of the partition in this way it is possible to associate every partition subset to a code symbol it is well known that these codes can be efficiently decoded by the so called multistage decoding we show that good codes in terms of performance complexity can be constructed using reed muller rm codes as inner codes to this aim rm codes are revisited in the framework of the above construction and decoding techniques in particular we describe a family of decoders for rm codes which include forney s 1988 and hemmati s 1989 decoders as special cases finally we present some examples of efficient binary codes based on rm codes and assess their performance via computer simulation

a new description of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of real or complex numbers that are input to a noisy transmission channel ungerboeck has constructed simple trellis codes that provide the same noise immunity as is given by increasing the power of uncoded transmission by factors ranging from two to four his method is to specify an underlying convolutional code and a rule mapping by set partitioning that maps the output of this code onto a fixed signal constallation a new description of a trellis code is given that combines these two steps into one the new description is analytic rather than graphical many practical codes can be described very simply and strict bounds on performance can be obtained a method for differential encoding trellis codes is presented that was suggested by the authors representation

optimization of trellis codes with multilevel amplitude modulation with respect to an error probability criterion an easily computed upper bound on the error probability of a data communications system with combined trellis coding and multilevel phase modulation is derived assuming an additive white gaussian noise channel and maximum likelihood decoding this bound is used to search for codes obtained by set partitioning that minimize the bound for a fixed number of trellis states only amplitude modulated signals typically used in voiceband modem applications are considered the signal levels that minimize the error probability bound subject to an average power constraint are presented for some specific codes

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

on information transfer by envelope constrained signals over the awgn channel using t e duncan s theorem 1970 on the relation between mutual information and the mean square error of the optimum causal estimator of a random signal in additive white gaussian noise awgn the maximum achievable information transfer over the awgn channel is derived with the random telegraph wave input the information transfer is bounded and symptotically determined for the wiener phase modulated process input at large signal to noise ratio snr both results are compared to the information transfer for the capacity achieving gauss markov input process for both the wiener phase modulated and the gauss markov processes the information transfer increases asymptotically as the square root of snr but for the random telegraph wave it increases only as its logarithm

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

error performance analysis of quadrature partial response trellis coded modulation qpr tcm in fading mobile satellite channels in order to improve the bandwidth efficiency and error performance partial response signaling prs and trellis coded modulation tcm are combined together this method is named qpr tcm whereas previous contributions have considered the performance of tcm transmitted over an additive white gaussian noise awgn channel the emphasis in this paper is on the performance of trellis coded m ary qam combined with prs in the fading environment we only consider the case where interleaving deinterleaving is employed to further combat the fading and assume that the ideal channel state information csi is available analytical upper bounds are derived using the well known transfer function bounding technique the bandwidth efficiencies are computed and the numerical results for several practical schemes are compared to each other one interesting result is that when the combined system is used on a rician fading channel the bit error probability upper bounds of the proposed 6qpr tcm and 9qpr tcm systems are better than their counterparts the 4qam tcm systems with 2 and 4 states respectively for snr values greater than a threshold which have the best error performances in the literature

coded phase frequency modulation channel coding combined with expanded signal sets has been shown 1 to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals in this paper new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented the new schemes combine fsk and psk modulation and make use of trellis coding and viterbi decoding to improve error performance over uncoded modulation the free euclidean distance is calculated for several classes of codes and upper bounds and simulation results are also presented for some simple codes the spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two dimensional modulation formats differential encoding and various extensions of the basic scheme are also discussed

uniform distance and error probability properties of tcm schemes the class of uniform trellis coded modulation tcm techniques is defined and simple explicit conditions for uniformity are derived uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning as well as on the assignment of binary labels to channel symbols the uniform distance property and uniform error property which are both derived from uniformity but are not equivalent are discussed the derived concepts are extended to encompass transmission over a not necessarily gaussian memoryless channel in which the metric used for detection may not be maximum likelihood an appropriate distance measure is defined that generalizes the euclidean distance it is proved that uniformity of a tcm scheme can also be defined under this new distance the results obtained are shown to hold for channels with phase offset or independent amplitude only fading examples are included to illustrate the applicability of the results

on the hamming distance properties of group codes under certain mild conditions the minimum hamming distance d of an n k d group code c over a non abelian group g is bounded by d n 2 consequently there exists no n k n k 1 group code c over an non abelian group g if 1

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

exact calculation of the union bound on performance of trellis coded modulation in fading channels this paper presents a method for the exact calculation of the union bound on the error performance of trellis coded modulation tcm in fading channels previous analyses have approximated the error expression to allow the use of the transfer function or restricted their attention to the most common error events or both in contrast we combine the transfer function which counts all error events with exact calculation of event probabilities and produce an exact expression for the union bound although computationally intensive the technique produces the tightest bound yet published in addition it is very general and is applicable to coherent differential and pilot based detection and to phase shift keying psk and quadrature amplitude modulation qam types of constellations

binary convolutional codes with application to magnetic recording calderbank heegard and ozarow 1 have suggested a method of designing codes for channels with intersymbol interference such as the magnetic recording channel these codes are designed to exploit intersymbol interference the standard method is to minimize intersymbol interference by constraining the input to the channel using run length limited sequences calderbank heegard and ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function 1 d n 2 where the channel inputs are constrained to be pm 1 this problem is considered here channel inputs are generated using a nontrivial coset of a binary convolutional code the coset is chosen to limit the zero run length of the output of the channel and so maintain clock synchronization the minimum squared euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code an interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic

robust source coding of images for very noisy channels robust source coding provides the compression and noise mitigation necessary for image transmission over noisy channels two methods are compared differential pulse code modulation dpcm and predictive trellis coded quantisation ptcq incorporating linear and nonlinear filters findings show that although ptcq has better rate distortion properties dpcm provides better performance in noise additionally the nonlinear filter yields better images

asymptotic upper bounds on the minimum distance of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of signal points in rn when a trellis code is used to encode data at the rate of k bits channel symbol each channel input depends not only on the most recent block of k bits to enter the encoder but will also depend on a set of bits preceding this block the bits determine the state of the encoder and the most recent block of k bits generates the channel symbol conditional on the encoder state the performance of a trellis code depends on a suitably defined minimum distance property of that code this paper obtains upper bounds on this minimum distance that are better than any previously known

baer and mittag leffler modules over tame hereditary algebras we develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras the baer modules and the mittag leffler ones a right r module m is called baer if rm ext 1 r m t 0 for all torsion modules t and m is mittag leffler in case the canonical map m otimes r prod i in i q i to prod i in i m otimes rq i is injective where q i i in i are arbitrary left r modules we show that a module m is baer iff m is p filtered where p is the preprojective component of the tame hereditary algebra r we apply this to prove that the universal localization of a baer module is projective in case we localize with respect to a complete tube using infinite dimensional tilting theory we then obtain a structure result showing that baer modules are more complex then the infinite dimensional preprojective modules in the final section we give a complete classification of the mittag leffler modules

minimum euclidean distance and power spectrum for a class of smoothed phase modulation codes with constant envelope a class of smoothed phase modulation codes is analyzed in terms of power spectral density and error probability for large signal to noise ratios the signals have constant envelope and the information carrying phase function is of multi h partial response continuous phase type a cyclic variation of modulation index from symbol time interval to symbol time interval is introduced coherent transmission and an additive white gaussian channel are assumed both power and bandwidth efficient signals are to be found in the above class comparisons are made between fixed h and multi h systems both for the binary and multilevel cases tradeoff is performed between bandwidth and error probability performance for large signal to noise ratios it is concluded that quaternary and octal systems always seem preferable increasing the number of modulation indexes from one in the fixed h case to two in the simplest multi h case gives performance advantages at the expense of increased system complexity

joint optimization of tcq tcm systems signal set expansion and set partitioning ideas from trellis coded modulation tcm have been previously applied to develop a source coding technique known as trellis coded quantization tcq it has been also known that joint optimization of source and channel encoders decoders results in substantial performance improvement in this work we investigate the performance of joint tcq tcm systems and develop various system optimization techniques we consider channel optimized tcq levels and asymmetric tcm symbol sets and propose a simulated annealing based algorithm for joint optimization of tcq levels and tcm symbols using these techniques signal to quantization noise ratio sqnr gains of 0 5 4 db over nonoptimized systems are attained off line this in turn provides all the gain of going to a one step higher order trellis

a systematic approach to the construction of bandwidth efficient multidimensional trellis codes we present a unified approach to the construction of multidimensional trellis codes that have small constellation expansion ratio cer and small peak to average power ratio par and hence are of high bandwidth efficiency in the approach we extend wei s 1987 construction to dimensionalities other than a power of two and propose a low complexity encoder we also present a general partition technique that gives geometrically uniform partitions with a good distance profile the proposed method can generate many good codes including previously reported ungerboeck codes gallager calderbank sloane codes and wei codes with quadrature amplitude modulation signals some newly discovered six dimensional trellis codes are compared with these known codes on their cer par effective coding gain and encoder decoder complexities

error bounds for trellis coded mpsk on a fading mobile satellite channel analytical performance bounds are presented for trellis coded mpsk transmitted over a satellite based land mobile channel upper bounds are evaluated using the well known transfer function bounding technique and lower bounds are achieved through knowledge of exact pairwise error probabilities in order to analyze practical trellis codes four or more states the uniform properties displayed by a certain class of trellis codes are exploited enabling the encoder transfer function to be obtained from a modified state transition diagram having no more states than the encoder itself monte carlo simulation results are presented in confirmation of all performance bounds and indicate a general weakness in the transfer function upper bounds a new asymptotically tight upper bound is derived based on a simple modification to the standard transfer function bound and results are presented for the four and eight state trellis codes in rician and rayleigh fading

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

invariant differential operators on a reductive lie algebra and weyl group representations let v be a finite dimensional vector space and let g be a subgroup of gl v set d v equal to the algebra of differential operators on v with polynomial coefficients and d v g equal to the g invariants in d v if g is a reductive lie algebra over c then t c g is a cartan subgroup of g and if g is the adjoint group of g then w is the weyl group of g harish chandra introduced an algebra homomorphism 5 of d g g to d t w h3 a is given by the obvious restriction mapping on the subalgebra of invariant polynomials and on the invariant constant coefficient differential operators and ker is

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

a key module over pure semisimple hereditary rings abstract let r be a hereditary indecomposable left pure semisimple ring inspired by i reiten c m ringel infinite dimensional representations of canonical algebras canad j math 58 2006 180 224 we investigate the perfect cotorsion pair c d in r mod generated by the preinjective component q we show that there is a finitely generated product complete tilting and cotilting left r module w such that c cogen w and d gen w the finite subcategory w of r mod given by the indecomposable summands of w stores important information on r for example if we assume r of infinite representation type then by b zimmermann huisgen strong preinjective partitions and representation type of artinian rings proc amer math soc 109 1990 309 322 there are non preinjective indecomposable modules occurring as direct summands of products of preinjective modules and it turns out that w is precisely the class of such modules moreover we prove that r has finite representation type if and only if every module in w is source of a left almost split map in r mod finally we address the question when w is endofinite

conjugacy classes of n tuples in lie algebras and algebraic groups let g be a reductive algebraic group over an algebraically closed field f of characteristic zero and let l g be the lie algebra of g then g acts on g by inner automorphisms and it acts on l g by the adjoint representation by taking the diagonal actions we get actions of g on the spaces of n tuples g n and l g in this paper we will prove a number of geometric properties of the orbits of g on these spaces of n tuples