transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

toward a practical scheme for binary broadcast channels with varying channel quality using dirty paper coding we consider practical schemes for binary dirty paper channels and broadcast channels bcs with two receivers and varying channel quality with the bc application in mind this paper proposes a new design for binary dirty paper coding dpc by exploiting the concept of coset binning the complexity of the system is greatly reduced when compared to the existing works some design challenges of the coset binning approach are identified and addressed the proposed binary dpc system achieves similar performance to the state of the art superposition coding based system while demonstrating significant advantages in terms of complexity and flexibility of system design for binary bcs achieving the capacity generally requires the superposition of a normal channel code and a carefully designed channel code with non uniform bit distribution the non uniform bit distribution is chosen according to the channel conditions therefore to achieve the capacity for binary bcs with varying channel quality it is necessary to use quantization codes of different rates which significantly increases the implementation complexity in this paper we also propose a broadcast scheme that generalizes the concept of binary dpc which we term soft dpc by combining soft dpc with time sharing we achieve a large percentage of the capacity for a wide range of channel quality with little complexity overhead our scheme uses only one fixed pair of codes for users 1 and 2 and a single quantization code which possesses many practical advantages over traditional time sharing and superposition coding solutions and provides strictly better performance

broadcast in mimo systems based on a generalized qr decomposition signaling and performance analysis a simple signaling method for broadcast channels with multiple transmit multiple receive antennas is proposed in this method for each user the direction in which the user has the maximum gain is determined the best user in terms of the largest gain is selected the corresponding direction is used as the modulation vector mv for the data stream transmitted to the selected user the algorithm proceeds in a recursive manner where in each step the search for the best direction is performed in the null space of the previously selected mvs it is demonstrated that with the proposed method each selected mv has no interference on the previously selected mvs dirty paper coding is used to cancel the remaining interference for the case that each receiver has one antenna the presented scheme coincides with the known scheme based on gram schmidt orthogonalization qr decomposition to analyze the performance of the scheme an upper bound on the cumulative distribution function cdf of each subchannel is derived which is used to establish the diversity order and the asymptotic sum rate of the scheme it is shown that using fixed rate codebooks the diversity order of the jth data stream 1 les j les m is equal to n m j 1 k j 1 where m n and k indicate the number of transmit antennas the number of receive antennas and the number of users respectively furthermore it is proven that the throughput of this scheme scales as m log log k and asymptotically k rarr infin tends to the sum capacity of the multiple input multiple output mimo broadcast channel the simulation results indicate that the achieved sum rate is close to the sum capacity of the underlying broadcast channel

nonequiprobable signaling on the gaussian channel signaling schemes for the gaussian channel based on finite dimensional lattices are considered the signal constellation consists of all lattice points within a region r and the shape of this region determines the average signal power spherical signal constellations minimize average signal power and in the limit as n to infinity the shape gain of the n sphere over the n cube approaches pi e 6 approximately 1 53 db a nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension a signal constellation omega is partitioned into t subconstellations omega sub 0 omega sub tau 1 of equal size by scaling a basic region r signal points in the same subconstellation are used equiprobably and a shaping code selects the subconstellation omega sub i with frequency f sub i shaping codes make it possible to achieve any desired fractional bit rate the schemes presented are compared with equiprobable signaling schemes based on voronoi regions of multidimensional lattices for comparable shape gain and constellation expansion ratio the peak to average power ratio of the schemes presented is superior furthermore a simple table lookup is all that is required to address points in the constellations it is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

robust lattice alignment for k user mimo interference channels with imperfect channel knowledge in this paper we consider a robust lattice alignment design for k user quasi static multiple input multiple output mimo interference channels with imperfect channel knowledge with random gaussian inputs the conventional interference alignment ia method has the feasibility problem when the channel is quasi static on the other hand structured lattices can create structured interference as opposed to the random interference caused by random gaussian symbols the structured interference space can be exploited to transmit the desired signals over the gaps however the existing alignment methods on the lattice codes for quasi static channels either require infinite signal to noise ratio snr or symmetric interference channel coefficients furthermore perfect channel state information csi is required for these alignment methods which is difficult to achieve in practice in this paper we propose a robust lattice alignment method for quasi static mimo interference channels with imperfect csi at all snr regimes and a two stage decoding algorithm to decode the desired signal from the structured interference space we derive the achievable data rate based on the proposed robust lattice alignment method where the design of the precoders decorrelators scaling coefficients and interference quantization coefficients is jointly formulated as a mixed integer and continuous optimization problem the effect of imperfect csi is also accommodated in the optimization formulation and hence the derived solution is robust to imperfect csi we also design a low complex iterative optimization algorithm for our robust lattice alignment method by using the existing iterative ia algorithm that was designed for the conventional ia method numerical results verify the advantages of the proposed robust lattice alignment method compared with the time division multiple access tdma two stage maximum likelihood ml decoding generalized han kobayashi hk distributive ia and conventional ia methods in the literature

error exponents of modulo additive noise channels with side information at the transmitter consider the optimum strategy for using channel state side information in transmission over a modulo additive noise channel with state dependent noise where the receiver does not have access to the side information si previous work showed that capacity wise the optimum transmitter shifts each code letter by a prediction of the noise sample based on the si we show that this structure achieves also the random coding error exponent and therefore is optimum at some range of rates below capacity specifically the optimum transmitter predictor minimizes the renyi entropy of the prediction error the renyi order depends on the rate and goes to one corresponding to shannon entropy for rates close to capacity in contrast it is shown that this prediction strategy may not be optimal at low transmission rates

abelian group codes for channel coding and source coding in this paper we study the asymptotic performance of abelian group codes for the channel coding problem for arbitrary discrete finite alphabet memoryless channels as well as the lossy source coding problem for arbitrary discrete finite alphabet memoryless sources for the channel coding problem we find the capacity characterized in a single letter information theoretic form this simplifies to the symmetric capacity of the channel when the underlying group is a field for the source coding problem we derive the achievable rate distortion function that is characterized in a single letter information theoretic form when the underlying group is a field it simplifies to the symmetric rate distortion function we give several illustrative examples due to the nonsymmetric nature of the sources and channels considered our analysis uses a synergy of information theoretic and group theoretic tools

practical dirty paper coding with sum codes in this paper we present a practical method to construct dirty paper coding dpc schemes using sum codes unlike the commonly used approach to dpc where the coding scheme involves concatenation of a channel code and a quantization code the proposed method embodies a unified approach that emulates the binning method used in the proof of the dpc result auxiliary bits are used to create the desired number of code vectors in each bin sum codes are obtained when information sequences augmented with auxiliary bits are encoded using linear block codes sum code based dpc schemes can be implemented using any linear block code and entail a relatively small increase in decoder complexity when compared to standard communication schemes they can also lead to significant reduction in transmit power in comparison to standard schemes

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

rate gains in block coded modulation systems with interblock memory this paper examines the performance gains achievable by adding interblock memory to and altering the mapping of coded bits to symbols in block coded modulation systems the channel noise considered is additive gaussian and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors in the case of the additive white gaussian noise channel these goals translate into the design of block codes of a given weighted or normalized distance whose rate is as high as possible and whose number of codewords at minimum normalized distance is low the effect of designing codes for normalized distance rather than hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest and many such best codes are given

filter and nested lattice code design for mimo fading channels with side information linear assignment gel fand pinsker coding la gpc is a coding technique for channels with interference known only at the transmitter where the known interference is treated as side information si as a special case of the la gpc dirty paper coding has been shown to be able to achieve the optimal interference free rate for si channels with perfect channel state information at the transmitter csit in the cases where only the channel distribution information at the transmitter cdit is available la gpc also has good sometimes optimal performance in a variety of fast and slow fading si channels in this letter we design filters in the nested lattice based coding to make it achieve the same rate performance as the la gpc in multiple input multiple output mimo channels compared with the random gaussian codebooks used in previous works our resultant coding schemes have algebraic structures and can be implemented in practical systems simulations in slow fading channels are provided and near interference free error performance is obtained the proposed coding schemes can serve as the fundamental building blocks to achieve the promised rate performance of mimo gaussian broadcast channels with cdit or perfect csit

corrected proof of de buda s theorem lattice channel codes an error in de buda s see ieee j select areas commun vol 7 no 6 p 893 1989 proof on the asymptotic optimality of lattice channel codes is pointed out and corrected using a modification of de buda s approach comments are given on the correct interpretation and the limitations of this result

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

high snr analysis for mimo broadcast channels dirty paper coding versus linear precoding in this correspondence we compare the achievable throughput for the optimal strategy of dirty paper coding dpc to that achieved with suboptimal and lower complexity linear precoding techniques zero forcing and block diagonalization both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain but an absolute difference in terms of throughput does exist the sum rate difference between the two strategies is analytically computed at asymptotically high snr furthermore the difference is not affected by asymmetric channel behavior when each user has a different average snr weighted sum rate maximization is also considered in the process it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

near capacity dirty paper code design a source channel coding approach this paper examines near capacity dirty paper code designs based on source channel coding we first point out that the performance loss in signal to noise ratio snr in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss which is a function of the granular loss from source coding and the target dirty paper coding rate or snr we then examine practical designs by combining trellis coded quantization tcq with both systematic and nonsystematic irregular repeat accumulate ira codes like previous approaches we exploit the extrinsic information transfer exit chart technique for capacity approaching ira code design but unlike previous approaches we emphasize the role of strong source coding to achieve as much granular gain as possible using tcq instead of systematic doping we employ two relatively shifted tcq codebooks where the shift is optimized via tuning the exit charts to facilitate the ira code design our designs synergistically combine tcq with ira codes so that they work together as well as they do individually by bringing together tcq the best quantizer from the source coding community and exit chart based ira code designs the best from the channel coding community we are able to approach the theoretical limit of dirty paper coding for example at 0 25 bit per symbol b s our best code design with 2048 state tcq performs only 0 630 db away from the shannon capacity

low density graph codes that are optimal for binning and coding with side information in this paper we describe and analyze the source and channel coding properties of a class of sparse graphical codes based on compounding a low density generator matrix ldgm code with a low density parity check ldpc code our first pair of theorems establishes that there exist codes from this ensemble with all degrees remaining bounded independently of block length that are simultaneously optimal for both channel coding and source coding with binary data when encoding and decoding are performed optimally more precisely in the context of lossy compression we prove that finite degree constructions can achieve any pair r d on the rate distortion curve of the binary symmetric source in the context of channel coding we prove that the same finite degree codes can achieve any pair c p on the capacity noise curve of the binary symmetric channel bsc next we show that our compound construction has a nested structure that can be exploited to achieve the wyner ziv bound for source coding with side information scsi as well as the gelfand pinsker bound for channel coding with side information ccsi although the results described here are based on optimal encoding and decoding the proposed graphical codes have sparse structure and high girth that renders them well suited to message passing and other efficient decoding procedures

vector precoding for gaussian mimo broadcast channels impact of replica symmetry breaking the replica method of statistical physics is employed for the large system analysis of vector precoding for the gaussian multiple input multiple output broadcast channel the transmitter comprises a linear front end combined with nonlinear precoding minimizing transmit energy by means of input alphabet relaxation for the common discrete lattice based relaxation the problem violates replica symmetry and a replica symmetry breaking rsb ansatz is taken the limiting empirical distribution of the precoder s output and the limiting transmit energy are derived for one step rsb particularizing to a zero forcing zf linear front end a decoupling result is derived for discrete lattice based relaxations the impact of rsb is demonstrated for the transmit energy the spectral efficiencies of the aforementioned precoding methods are compared to linear zf and tomlinson harashima precoding thp focusing on quaternary phase shift keying qpsk significant performance gains of both lattice and convex relaxations are revealed for medium to high signal to noise ratios snrs when compared to linear zf precoding thp is shown to be outperformed as well comparing certain lattice based relaxations for qpsk against a convex counterpart the latter is found to be superior for low and high snrs but slightly inferior for medium snrs in terms of spectral efficiency

state amplification we consider the problem of transmitting data at rate over a state dependent channel with state information available at the sender and at the same time conveying the information about the channel state itself to the receiver the amount of state information that can be learned at the receiver is captured by the mutual information between the state sequence and the channel output the optimal tradeoff is characterized between the information transmission rate and the state uncertainty reduction rate when the state information is either causally or noncausally available at the sender in particular when state transmission is the only goal the maximum uncertainty reduction rate is given by this result is closely related and in a sense dual to a recent study by merhav and shamai which solves the problem of masking the state information from the receiver rather than conveying it

improved linear transmit processing for single user and multi user mimo communications systems in this paper we propose a novel linear transmit precoding strategy for multiple input multiple output mimo systems employing improper signal constellations in particular improved zero forcing zf and minimum mean square error mmse precoders are derived based on modified cost functions and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders the superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results the novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi user channels in both cases the improved precoding schemes yield significant performance gain compared to the conventional counterparts

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

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

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

capacity and lattice strategies for canceling known interference we consider the generalized dirty paper channel y x s n e x sup 2 spl les p sub x where n is not necessarily gaussian and the interference s is known causally or noncausally to the transmitter we derive worst case capacity formulas and strategies for strong or arbitrarily varying interference in the causal side information si case we develop a capacity formula based on minimum noise entropy strategies we then show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity at high signal to noise ratio snr conditions i e if n is weak relative to the power constraint p sub x these bounds coincide the optimum strategies take the form of scalar lattice quantizers and the capacity loss due to not having s at the receiver is shown to be exactly the shaping gain 1 2log 2 spl pi e 12 spl ap 0 254 bit we extend the schemes to obtain achievable rates at any snr and to noncausal si by incorporating minimum mean squared error mmse scaling and by using k dimensional lattices for gaussian n the capacity loss of this scheme is upper bounded by 1 2log2 spl pi eg spl lambda where g spl lambda is the normalized second moment of the lattice with a proper choice of lattice the loss goes to zero as the dimension k goes to infinity in agreement with the results of costa these results provide an information theoretic framework for the study of common communication problems such as precoding for intersymbol interference isi channels and broadcast 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

a robust multi level design for dirty paper coding we propose a robust close to capacity dirty paper coding dpc design framework in which multi level low density parity check ldpc codes and trellis coded quantization tcq are employed as the channel and source coding components respectively the proposed design framework is robust in the sense that it yields close to capacity solutions in the high medium and low rate regimes this is in contrast to existing practical dpc schemes that perform well only in one or two of these regimes but not all three we design codes for transmission rates of 0 5 1 0 1 5 and 2 0 bits sample b s using one two three and four ldpc levels at a block length of 2 105 the codes perform 0 95 0 58 0 55 and 0 54 db from the corresponding information theoretic limits respectively we also propose a low complexity decoding scheme that does not involve iterative message passing between the source and channel decoders the low complexity scheme performs only 1 08 0 85 and 0 79 db away from the theoretical limits at transmission rates of 1 0 1 5 and 2 0 b s respectively

rate 5 6 trellis coded 8 psk some new short constraint length codes are described for satellite channels which are constant envelope and which have spectral and energy efficiencies intermediate to other recent coded techniques namely r 2 3 coded 8 psk and r 3 4 coded 16 psk we use two intervals of 8 psk transmission to form a modulation base for r 5 6 trellis codes a particularly attractive design is an eight state code producing 6 2 db gain on the gaussian channel over uncoded 8 psk yet sacrificing only 16 percent in spectral efficiency

tenth degree number fields with quintic fields having one real place in this paper we enumerate all number fields of degree 10 of discriminant smaller than 10 11 in absolute value containing a quintic field having one real place for each one of the 21509 resp 18167 found fields of signature 0 5 resp 2 4 the field discriminant the quintic field discriminant a polynomial defining the relative quadratic extension the corresponding relative diseriminant the corresponding polynomial over q and the galois group of the galois closure are given in a supplementary section we give the first coincidence of discriminant of 19 resp 20 nonisomorphic fields of signature 0 5 resp 2 4

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

wyner ziv coding based on tcq and ldpc codes this paper considers trellis coded quantization tcq and low density parity check ldpc codes for the quadratic gaussian wyner ziv coding problem after tcq of the source x ldpc codes are used to implement slepian wolf coding of the quantized source q x with side information y at the decoder assuming 256 state tcq and ideal slepian wolf coding in the sense of achieving the theoretical limit h q x y we experimentally show that slepian wolf coded tcq performs 0 2 db away from the wyner ziv distortion rate function dwz r at high rate this result mirrors that of entropy constrained tcq in classic source coding of gaussian sources furthermore using 8 192 state tcq and assuming ideal slepian wolf coding our simulations show that slepian wolf coded tcq performs only 0 1 db away from dwz r at high rate these results establish the practical performance limit of slepian wolf coded tcq for quadratic gaussian wyner ziv coding practical designs give performance very close to the theoretical limit for example with 8 192 state tcq irregular ldpc codes for slepian wolf coding and optimal non linear estimation at the decoder our performance gap to dwz r is 0 20 db 0 22 db 0 30 db and 0 93 db at 3 83 bit per sample b s 1 83 b s 1 53 b s and 1 05 b s respectively when 256 state 4 d trellis coded vector quantization instead of tcq is employed the performance gap to dwz r is 0 51 db 0 51 db 0 54 db and 0 80 db at 2 04 b s 1 38 b s 1 0 b s and 0 5 b s respectively

on computing isomorphisms of equation orders a number geometric method for computing isomorphisms of algebraic number fields respectively z orders of such fields is developed its main advantage is its easy implementation and moderate computation time

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

polar codes are optimal for lossy source coding we consider lossy source compression of a binary symmetric source using polar codes and a low complexity successive encoding algorithm it was recently shown by arikan that polar codes achieve the capacity of arbitrary symmetric binary input discrete memoryless channels under a successive decoding strategy we show the equivalent result for lossy source compression i e we show that this combination achieves the rate distortion bound for a binary symmetric source we further show the optimality of polar codes for various multiterminal problems including the binary wyner ziv and the binary gelfand pinsker problems our results extend to general versions of these problems

on block coded modulation with interblock memory block coded modulation with interblock memory bcmim is a variation of block coded modulation bcm which is designed for multilevel coding by providing interblock memory between adjacent blocks the coding rate of a bcmim scheme can be increased without decreasing the minimum squared euclidean distance msed as compared to the original bcm in an early version of bcmim interblock coding is provided only between the first two coding levels of adjacent blocks in this paper we design bcmim with a more general form for which interblock coding can be introduced among many coding levels in this way we can further increase the coding rate of bcmim without decreasing the msed we provide many examples to show the advantages of bcmim with the general form most of the examples are designed based on multidimensional signal sets since a multidimensional signal set can provide more coding levels than a two dimensional 2 d signal set

lattice precoding and pre distorted constellation in degraded broadcast channel with finite input alphabets in this letter we propose a novel transmission scheme based on lattice precoding and pre distorted constellation for the two user awgn degraded broadcast channel in the proposed scheme the lattice precoding is used for the weaker user to cancel the interference from the stronger user the predistorted constellation is also proposed for the stronger user to overcome the nonlinear distortion due to the lattice precoding numerical results show that the achievable rate of the proposed transmission scheme is beyond the achievable rate region of the superposition coding and successive interference cancelation with finite input alphabets

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

trellis coding with multidimensional qam signal sets trellis coding using multidimensional quadrature amplitude modulation qam signal sets is investigated finite size 2d signal sets are presented that have minimum average energy are 90 degrees rotationally symmetric and have from 16 to 1024 points the best trellis codes using the finite 16 qam signal set with two four six and eight dimensions are found by computer search the multidimensional multi d signal set is constructed from the 2 d signal set the best moderate complexity trellis codes for infinite lattices with two four six and eight dimensions are also found the minimum free squared euclidean distance and number of nearest neighbors for these codes were used as the selection criteria many of the multi d codes are fully rotationally invariant and give asymptotic coding gains up to 6 0 db from the infinite lattice codes the best codes for transmitting j j 1 4 j 1 3 j 1 2 j 2 3 and j 3 4 b sym j an integer are presented

a targeted martinet search constructing number fields with prescribed ramification is an important problem in computational number theory in this paper we consider the problem of computing all imprimitive number fields of a given degree which are unramified outside of a given finite set of primes s by combining the techniques of targeted hunter searches with martinet s relative version of hunter s theorem we then carry out this algorithm to generate complete tables of imprimitive number fields for degrees 4 through 10 and certain sets s of small primes

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

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

on multilevel block modulation codes the multilevel technique for combining block coding and modulation is investigated a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures a specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed given a multilevel block modulation code c with no interdependency among the binary component codes the proposed method gives a multilevel block modulation code c that has the same rate as c a minimum squared euclidean distance not less than that of c a trellis diagram with the same number of states as that of c and a smaller number of nearest neighbor codewords than that of c finally a technique is presented for analyzing the error performance of block modulation codes for an additive white gaussian noise awgn channel based on soft decision maximum likelihood decoding error probabilities of some specific codes are evaluated by simulation and upper bounds based on their euclidean weight distributions

a close to capacity dirty paper coding scheme the writing on dirty paper channel model offers an information theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter it indicates that lossless precoding is theoretically possible at any signal to noise ratio snr and thus dirty paper coding may serve as a basic building block in both single user and multiuser communication systems we design an end to end coding realization of a system materializing a significant portion of the promised gains we employ multidimensional quantization based on trellis shaping at the transmitter coset decoding is implemented at the receiver using virtual bits combined with iterative decoding of capacity approaching codes we achieve an improvement of 2db over the best scalar quantization scheme code design is done using the exit chart technique

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

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

trellis shaping the author discusses trellis shaping a method of selecting a minimum weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code c sub s shaping gains on the order of 1 db may be obtained with simple four state shaping codes and with moderate constellation expansion the shaping gains obtained with more complicated codes approach the ultimate shaping gain of 1 53 db with a feedback free syndrome former for c sub s transmitted data can be recovered without catastrophic error propagation constellation expansion and peak to average energy ratio may be effectively limited by peak constraints with lattice theoretic constellations the shaping operation may be characterized as a decoding of an initial sequence in a channel trellis code by a minimum distance decoder for a shaping trellis code based on the shaping convolutional code and the set of possible transmitted sequences is then the set of code sequences in the channel trellis code that lie in the voronoi region of the trellis shaping code

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

a coded modulation scheme with interblock memory proposes a coded modulation scheme with interblock memory the proposed scheme has a multi stage coding structure however at some coding stage the coding designs for every two adjacent blocks are related compared to coded modulation schemes for which each block is independent of the others the introduction of interblock coding provides additional flexibility in the design in this way for the proposed scheme one can achieve a large minimum euclidean distance while the number of nearest neighbors is not too large the authors also design a multi stage decoding algorithm which is optimum in each stage and has low decoding complexity three specific examples are provided to demonstrate the advantages of the proposed scheme

optimal modulation for known interference we present a symbol by symbol approach to the problem of canceling known interference at the transmitter in a communication system in the envisioned system the modulator maps an information symbol taken from a finite alphabet and an interference symbol from the complex field onto a transmitted constellation point our scheme is based on joint optimization of a modulator and demodulator subject to a constraint on the average transmit power the demodulator picks the information symbol as a function of the received symbol that minimizes the average error probability we emphasize that our focus is on transmission in a single complex dimension and hence the proposed technique is a modulation rather than a coding scheme we illustrate that the new scheme outperforms tomlinson harashima precoding which is a classical but suboptimal solution to the one dimensional known interference precoding problem in our simulations the new approach is able to perform close to the no interference bound

gradient based power minimization in mimo broadcast channels with linear precoding we study the problem of minimizing the sum transmit power in mutliple input multiple output mimo downlink channels with linear transceivers if per user quality of service qos constraints expressed in terms of rates have to be fulfilled to find a suboptimal solution of the arising non convex optimization problem we introduce new auxiliary variables representing the di vision of the per user rate constraints into per stream rate targets and we optimize these variables by means of gradient projection steps this new method is combined with alternating updates of the transmit and receive filters furthermore the proposed algorithm ensures that the mean square error mse matrices of all users are diagonal and in the course of the execution of the algorithm it is possible that inactive streams get activated if this leads to a decreased sum transmit power in numerical simulations the new algorithm turns out to be superior to the various existing methods since these methods either lead to a higher sum transmit power than the proposed scheme or have a higher computational complexity or make restrictive assumptions on the system parameters

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

precoded integer forcing universally achieves the mimo capacity to within a constant gap an open loop single user multiple input multiple output mimo communication scheme is considered where a transmitter equipped with multiple antennas encodes the data into independent streams all taken from the same linear code the coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space time code at the receiver side integer forcing equalization is applied followed by standard single stream decoding it is shown that this communication architecture achieves the capacity of any gaussian mimo channel up to a gap that depends only on the number of transmit antennas

performance of pll based optical oppm communication systems the power spectral density psd of a direct detected optical signal with overlapping pulse position modulation oppm scheme is derived it is demonstrated that this spectrum contains a strong periodic component at the signal symbol frequency thereby enabling a simple pll device to provide joint symbol and slot synchronization the variance of the timing error for a linearized pll synchronizer is shown to be mainly dominated by and is inversely proportional to the product of the pll closed loop bandwidth and symbol duration of the oppm signal the performance of a shot noise limited pll based optical oppm communication system is then assessed in terms of the overall system symbol error rate

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

quadratic extensions of totally real quintic fields in this work we establish lists for each signature of tenth degree number fields containing a totally real quintic subfield and of discriminant less than 10 13 in absolute value for each field in the list we give its discriminant the discriminant of its subfield a relative polynomial generating the field over one of its subfields the corresponding polynomial voer q and the galois group of its galois closure we have examined the existence of several non isomorphic fields with the same discriminants and also the existence of unramified extensions and cyclic extensions

non primitive number fields of degree eight and of signature 2 3 4 2 and 6 1 with small discriminant give the lists of all non primitive number fields of degree eight having two four and six real places of discriminant less than 6688609 24363884 and 92810082 respectively in absolute value for each field in the lists we give its discriminant the discriminant of its subfields a relative polynomial generating the field over one of its subfields and its discriminant the corresponding polynomial over q and the galois group of its galois closure

iterative decoding of coded thp with quantized output this paper proposes an improved receiver for the tomlinson harashima precoder thp in this paper we demonstrate that most of the capacity loss associated with conventional thp is due to the suboptimal receiver which is a simple modulo operation we then demonstrate how this loss can can be avoided with the optimization of the receiver in the suboptimal receiver the modulo operation ignores the dependency between the implicitly added sequence of symbols removed by it we then implement a thp with quantized outputs the quantized outputs enable to implement a maximum a posteriori probability map receiver that exploits the dependency between the received symbols the map receiver is named enhanced modulo operation emod and operates as an inner decoder within an iterative scheme either with outer low density parity check ldpc code or outer turbo code simulation results show considerable gains relative to coded conventional thp and also relative to the turbo equalizer te which does not use a precoder in the transmitter