on acceptance criterion for efficient successive errors and erasures decoding of reed solomon and bch codes we describe an efficient algorithm for successive errors and erasures decoding of bch codes the decoding algorithm consists of finding all necessary error locator polynomials and errata evaluator polynomials choosing the most appropriate error locator polynomial and errata evaluator polynomial using these two polynomials to compute a candidate codeword for the decoder output and testing the candidate for optimality via an originally developed acceptance criterion even in the most stringent case possible the acceptance criterion is only a little more stringent than forney s 1966 criterion for generalised minimum distance gmd decoding we present simulation results on the error performance of our decoding algorithm for binary antipodal signals over an awgn channel and a rayleigh fading channel the number of calculations of elements in a finite field that are required by our algorithm is only slightly greater than that required by hard decision decoding while the error performance is almost as good as that achieved with gmd decoding the presented algorithm is also applicable to efficient decoding of product rs codes

a unified method for evaluating the error correction radius of reliability based soft decision algorithms for linear block codes this paper presents a unified method for evaluating the error correction radii of many reliability based soft decision decoding algorithms for binary linear block codes based on this unified method these decoding algorithms as well as their potential improvements can be compared directly the error correction radius for each of these decoding algorithms is determined by finding the closest point on the boundary of the decision region of the soft decision decoder to the transmitted signal sequence it is shown that this problem can be formulated as a constrained optimization problem although no general closed form expression is possible a simple algorithm that always converges to the optimum solution of this optimization problem is presented based on these results the error correction radii of some well known reliability based soft decision decoding algorithms are revisited and compared

cooling schedules for optimal annealing a monte carlo optimization technique called simulated annealing is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima the level of randomization is determined by a control parameter t called temperature which tends to zero according to a deterministic cooling schedule we give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states in the special case that the cooling schedule has parametric form tt c log1 t the condition for convergence is that c be greater than or equal to the depth suitably defined of the deepest local minimum which is not a global minimum state

soft decision decoding using ordered recodings on the most reliable basis this correspondence investigates soft decision decoding of binary linear block codes using ordered recodings of test error patterns on the so called most reliable basis the analysis demonstrates the optimality of the most reliable basis by showing that among all possible bases the most reliable basis minimizes the list error probability for a very general and well defined class of orderings for recoding operations the correspondence then proposes a suboptimal algorithm which utilizes reprocessing ordering and incorporates two techniques that render it computationally very efficient 1 an iterative reference recoding technique which simplifies the recoding operation required for each test error pattern and 2 an adaptive skipping rule which significantly reduces the average number of recodings simulation results with codes of relatively large length show that the proposed algorithm is computationally very efficient in comparison to existing algorithms in the literature

logic applied to integer programming and integer programming applied to logic the many connections between the methods of computational logic and integer programming ip are surveyed it is shown how computational problems arising in formal logic can be solved by ip also it is shown how the methods of logic are applicable both to modelling and solving ip models it is shown how fourier motzkin elimination for linear programming when specialised to 0 1 ip models gives rise to the logic method of resolution finally conventional ip methods are applied to solving logical inference problems

construction of rule based assignment models abstract assignment refers to the problem of assigning objects or alternatives described on multiple dimensions into predefined categories most assignment models use analytical mechanisms to aggregate multiple dimensions in order to select a category for each candidate object we investigate another approach based on the use of simple if then rules we propose a general approach for a progressive construction of a rule based assignment model the process consists of testing iteratively the consistency of the rule base to transform it progressively into a consistent assignment model consistency tests are based on a correspondence between the logical representation of rules and an equivalent algebraic representation this allows us to express rules by linear constraints and then to test the consistency of rule based assignment models by solving a series of linear programs

a new generic maximum likelihood metric expression for space time block codes with applications to decoding the metric expression for a generic linear space time block code stbc is studied using a different approach to vectorization and a new representation of the metric the new representation lends itself to a simple measure of reliability based on the sum of inner products and provides a quantifiable definition for minimum distance of a stbc this provides the framework for a new family of near maximum likelihood ml and ml decoding algorithms it also has applications in the development of optimality test criteria for stbcs as well as in the design of stbcs with low decoding complexity

reliability based code search algorithms for maximum likelihood decoding of block codes efficient code search maximum likelihood decoding algorithms based on reliability information are presented for binary linear block codes the codewords examined are obtained via encoding the information set utilized for encoding comprises the positions of those columns of a generator matrix g of the code which for a given received sequence constitute the most reliable basis for the column space of g substantially reduced computational complexity of decoding is achieved by exploiting the ordering of the positions within this information set the search procedures do not require memory the codeword to be examined is constructed from the previously examined codeword according to a fixed rule consequently the search algorithms are applicable to codes of relatively large size they are also conveniently modifiable to achieve efficient nearly optimum decoding of particularly large codes

reliability based syndrome decoding of linear block codes in this correspondence various aspects of reliability based syndrome decoding of binary codes are investigated first it is shown that the least reliable basis lrb and the most reliable basis mrb are dual of each other by exploiting this duality an algorithm performing maximum likelihood ml soft decision syndrome decoding based on the lrb is presented contrarily to previous lrb based ml syndrome decoding algorithms this algorithm is more conveniently implementable for codes whose codimension is not small new sufficient conditions for optimality are derived these conditions exploit both the ordering associated with the lrb and the structure of the code considered with respect to mrr based sufficient conditions they present the advantage of requiring no soft information and thus can be preprocessed and stored based on these conditions low complexity soft decision syndrome decoding algorithms for particular classes of codes are proposed finally a simple algorithm is analyzed after the construction of the lrb this algorithm computes the syndrome of smallest hamming weight among o k sup i candidates where k is the dimension of the code for an order i of reprocessing at practical bit error rates for codes of length n spl les 128 this algorithm always outperforms any algebraic decoding algorithm capable of correcting up to t 1 errors with an order of reprocessing of at most 2 where t is the error correcting capability of the code considered

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

computationally efficient soft decision decoding of linear block codes based on ordered statistics soft decision decoding of a linear block code using the most reliable basis corresponding to each received word is investigated based either on probabilistic properties or on the structure of the code considered three improvements to the algorithm devised by fossorier and lin see ibid vol 41 no 9 p 1379 1396 1995 are presented these modifications allow large computation savings or significant decoding speedup with little error performance degradation first a reduced probabilistic list of codeword candidates is associated with order i reprocessing of a given code it results in a large reduction of the maximum number of computations with a very small degradation in performance then a probabilistic stopping criterion is introduced for order 0 reprocessing this new test significantly decreases the average number of computations when appropriately implemented finally the application of the algorithm to coset decoding is considered for u u v constructed codes in addition to the conventional coset decoding a new adaptive practically optimum coset decoding method is presented where at each reprocessing stage the number of surviving cosets decreases suboptimum closest coset decoding is also investigated it is shown that two stage decoding with the algorithm of fossorier and lin offers a large variety of choices since the reprocessing order of each stage can be determined independently

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

the complexity of information set decoding information set decoding is an algorithm for decoding any linear code expressions for the complexity of the procedure that are logarithmically exact for virtually all codes are presented the expressions cover the cases of complete minimum distance decoding and bounded hard decision decoding as well as the important case of bounded soft decision decoding it is demonstrated that these results are vastly better than those for the trivial algorithms of searching through all codewords or through all syndromes and are significantly better than those for any other general algorithm currently known for codes over large symbol fields the procedure tends towards a complexity that is subexponential in the symbol size

nonstationary markov chains and convergence of the annealing algorithm we study the asymptotic behavior as timet of certain nonstationary markov chains and prove the convergence of the annealing algorithm in monte carlo simulations we find that in the limitt a nonstationary markov chain may exhibit phase transitions nonstationary markov chains in general and the annealing algorithm in particular lead to biased estimators for the expectation values of the process we compute the leading terms in the bias and the variance of the sample means estimator we find that the annealing algorithm converges if the temperaturet t goes to zero no faster thanc log t t0 ast with a computable constantc andt0 the initial time the bias and the variance of the sample means estimator in the annealing algorithm go to zero likeo t 1 e for some 0 e 1 with e 0 only in very special circumstances our results concerning the convergence of the annealing algorithm and the rate of convergence to zero of the bias and the variance of the sample means estimator provide a rigorous procedure for choosing the optimal annealing schedule this optimal choice reflects the competition between two physical effects a the adiabatic effect whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state and b the super cooling effect whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state s but may do so extremely slowly

simulated annealing via sobolev inequalities we use sobolev inequalities to study the simulated annealing algorithm this approach takes advantage of the local time reversibility of the process and yields the optimal freezing schedule as well as quantitative information about the rate at which the process is tending to its ground state

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

efficient heuristic search algorithms for soft decision decoding of linear block codes efficient new algorithms are presented for maximum likelihood and suboptimal soft decision decoding algorithms for linear block codes the first algorithm ma improves the efficiency of the a decoding algorithm conducting the heuristic search through a code tree while exploiting code specific properties the second algorithm h reduces search space by successively estimating the cost of the minimum cost codeword with a fixed value at each of the most reliable and linearly independent components of the received message the third algorithm directed search finds the codeword closest to the received vector by exploring a continuous search space the strengths of these three algorithms are combined in a hybrid algorithm applied to the 128 64 the 256 131 and the 256 139 binary extended bose chaudhuri hocquenghem bch codes simulation results show that this hybrid algorithm can efficiently decode the 128 64 code for any signal to noise ratio with near optimal performance previously no practical decoder could have decoded this code with such a performance for all ranges of signal to noise ratio

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

tools for reformulating logical forms into zero one mixed integer programs abstract a systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an integer linear programming ilp formulation or a mixed integer programming mip formulation is presented a reformulation procedure which uses the extended reverse polish notation to represent a compound logical form is then described the syntax of an lp modelling language is extended to incorporate statements in propositional logic forms with linear algebraic forms whereby 0 1 mip models can be automatically formulated a prototype user interface by which logical forms can be reformulated and the corresponding mip constructed and analysed within an existing mathematical programming modelling system is illustrated finally the steps to formulate a discrete optimisation model in this way are illustrated by means of an example

a new adaptive two stage maximum likelihood decoding algorithm for linear block codes in this paper we propose a new two stage ts structure for computationally efficient maximum likelihood decoding mld of linear block codes with this structure near optimal mld performance can be achieved at low complexity through ts processing the first stage of processing estimates a minimum sufficient set mss of candidate codewords that contains the optimal codeword while the second stage performs optimal or suboptimal decoding search within the estimated mss of small size based on the new structure we propose a decoding algorithm that systematically trades off between the decoding complexity and the bounded block error rate performance a low complexity complementary decoding algorithm is developed to estimate the mss followed by an ordered algebraic decoding oad algorithm to achieve flexible system design since the size of the mss changes with the signal to noise ratio the overall decoding complexity adaptively scales with the quality of the communication link theoretical analysis is provided to evaluate the potential complexity reduction enabled by the proposed decoding structure

a new reed solomon code decoding algorithm based on newton s interpolation a reed solomon code decoding algorithm based on newton s interpolation is presented this algorithm has as main application fast generalized minimum distance decoding of reed solomon codes it uses a modified berlekamp massey algorithm to perform all necessary generalized minimum distance decoding steps in only one run with a time domain form of the new decoder the overall asymptotic generalized minimum distance decoding complexity becomes o dn with n the length and d the distance of the code including the calculation of all error locations and values this asymptotic complexity is optimal other applications are the possibility of fast decoding of reed solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay

a modified belief propagation algorithm for code word quantization modern coding advances including dirty paper coding and information hiding require quantizing a given binary word to a code word a good solution would approach the rate distortion bound in lossy source compression here we propose a simple variant on belief propagation which is observed to converge to a solution giving respectable rate distortion performance comparisons with other recently proposed source quantization methods reveal that the proposed algorithm holds particular interest in short block length applications as encountered in packet based communication systems

constrained designs for maximum likelihood soft decoding of rm 2 m and the extended golay codes we present algorithms for maximum likelihood soft decoding of the second order reed muller codes rm 2 m and the extended 24 12 8 golay code the decoding procedures are based on a concise representation of appropriately selected cosets of a subcode of the code considered such representation enables application of certain elimination rules a structure called constrained design is established to support the elimination procedures remarkably efficient algorithms are obtainable by this approach the method of elimination is applicable also in combination with existing coset decoding schemes

on decoding of the 89 45 17 quadratic residue code in this paper three decoding methods of the 89 45 17 binary quadratic residue qr code to be presented are hard soft and linear programming decoding algorithms firstly a new hybrid algebraic decoding algorithm for the 89 45 17 qr code is proposed it uses the laplace formula to obtain the primary unknown syndromes as done in lin et al s algorithm when the number of errors v is less than or equal to 5 whereas gaussian elimination is adopted to compute the unknown syndromes when v 6 secondly an appropriate modification to the algorithm developed by chase is also given in this paper therefore combining the proposed algebraic decoding algorithm with the modified chase ii algorithm called a new soft decision decoding algorithm becomes a complete soft decoding of qr codes thirdly in order to further improve the error correcting performance of the code linear programming lp is utilized to decode the 89 45 17 qr code simulation results show that the proposed algebraic decoding algorithm reduces the decoding time when compared with lin et al s hard decoding algorithm and thus significantly reduces the decoding complexity of soft decoding while maintaining the same bit error rate ber performance moreover the lp based decoding improves the error rate performance almost without increasing the decoding complexity when compared with the new soft decision decoding algorithm it provides a coding gain of 0 2 db at ber 2 x 10 6

reduced gmd decoding a framework is presented for generalized minimum distance gmd decoding with a limited number of decoding trials and a restricted set of reliability values in gmd decoding symbols received from the channel may be erased before being fed into an algebraic error erasure decoder for error correction in subsequent or simultaneous trials with different erasing patterns the decision whether or not to erase a symbol in a certain trial is taken by an erasure choosing algorithm which takes into account reliability information from the channel the final gmd decoder output is a codeword which results from a decoding trial and satisfies a certain distance criterion for various erasing strategies and reliability sets the guaranteed error correction radius and the unsuccessful decoding probability of this technique are studied both known and new results with applications to concatenated coding follow from the unified approach presented in this correspondence

algebraic unimodular counting we study algebraic algorithms for expressing the number of non negative integer solutions to a unimodular system of linear equations as a function of the right hand side our methods include todd classes of toric varieties via grobner bases and rational generating functions as in barvinok s algorithm we report polyhedral and computational results for two special cases counting contingency tables and kostant s partition function

an improvement to generalized minimum distance decoding a novel acceptance criterion that is less stringent than previous criteria is developed the criterion accepts the codeword that is closest to the received vector for many cases where previous criteria fail to accept any codeword as a result the performance of generalized minimum distance gmd decoding is better if the new criterion is used for m ary signaling the weights used in gmd decoding are generalized to permit each of the possible m symbol values to have a different weight

structured set partitions and multilevel concatenated coding for partial response channels we present a systematic way to construct multilevel concatenated codes for partial response pr channels using 1 a structured set partition ssp of multiple channel output sets and 2 a set of conventional block codes with different error correcting capabilities a lower bound on the minimum squared euclidean distance of the constructed codes is given this bound is based on the interset minimal euclidean distances of the ssp and the minimum hamming distances of the used block codes an example of ssp for the extended class 4 partial response channel epr4 is presented iterative suboptimal decoding which combines viterbi detection on the trellis of the pr channel with algebraic error detection correction can be applied to the constructed concatenated codes truncated versions of the iterative decoding scheme are simulated and compared with each other

decoding linear block codes using a priority first search performance analysis and suboptimal version an efficient maximum likelihood soft decision decoding algorithm for linear block codes using a generalized dijkstra s algorithm was proposed by han hartmann and chen 1993 we prove that this algorithm is efficient for most practical communication systems where the probability of error is less than 10 sup 3 by finding an upper bound of the computational effort of the algorithm a suboptimal decoding algorithm is also proposed the performance of this suboptimal decoding algorithm is within 0 25 db of the performance of an optimal decoding algorithm for the 104 52 binary extended quadratic residue code and within 0 5 db of the optimal performance for the 128 64 binary bch code respectively

reliability based soft decision decoding with multiple biases in this paper a new reliability based soft decision decoding algorithm is presented this algorithm repeatedly uses biased reliability values to construct the most reliable basis mrb as a result this new method makes use of multiple information sets in a stochastic way compared to previously proposed competitive approaches this new method produces a more efficient mrb reprocessing type algorithm to achieve near maximum likelihood decoding mld performance with a proper choice of the bias value it can be combined with any mrb reprocessing type algorithm and in each case a tight performance analysis can be derived

an efficient maximum likelihood decoding algorithm for linear block codes with algebraic decoder a new soft decoding algorithm for linear block codes is proposed the decoding algorithm works with any algebraic decoder and its performance is strictly the same as that of maximum likelihood decoding mld since our decoding algorithm generates sets of different candidate codewords corresponding to the received sequence its decoding complexity depends on the received sequence we compare our decoding algorithm with chase 1972 algorithm 2 and the tanaka kakigahara 1983 algorithm in which a similar method for generating candidate codewords is used computer simulation results indicate for some signal to noise ratios snr that our decoding algorithm requires less average complexity than those of the other two algorithms but the performance of ours is always superior to those of the other two

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

on algebraic soft decision decoding algorithms for bch codes three algebraic soft decision decoding algorithms are presented for binary bose chaudhuri hocquengham bch codes two of these algorithms are based on the bounded distance bd 1 generalized minimum distance gmd decoding presented by berlekamp 1984 and the other is based on chase 1972 decoding a simple algebraic algorithm is first introduced and it forms a common basis for the decoding algorithms presented next efficient bd 1 gmd and bd 2 gmd decoding algorithms are presented it is shown that for binary bch codes with odd designed minimum distance d and length n both the bd 1 gmd and the bd 2 gmd decoding algorithms can be performed with complexity o nd the error performance of these decoding algorithms is shown to be significantly superior to that of conventional gmd decoding by computer simulation finally an efficient algorithm is presented for chase decoding of binary bch codes like a one pass gmd decoding algorithm this algorithm produces all necessary error locator polynomials for chase decoding in one run

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

optimal design of truss structures by logic based branch and cut the truss design problem is to find the optimal placement and size of structural bars that can support a given load the problem is nonlinear and in the version addressed here the bars must take certain discrete sizes it is shown that a logic based method that dispenses with integer variables and branches directly on logical disjunctions can solve substantially larger problems than mixed integer programming even though the nonlinearities disappear in the mixed integer model a primary purpose of the paper is to investigate whether advantages of logic based branching that have been demonstrated elsewhere for linear problems extend to nonlinear programming

code automorphisms and permutation decoding of certain reed solomon binary images we consider primitive reed solomon rs codes over the field f2m of length n 2m 1 building on lacan s results for the case of binary extension fields we show that the binary images of certain two parity symbol rs n n 2 3 code have a code automorphism subgroup related to the general linear group gl m 2 for these codes we obtain a code automorphism subgroup of order m gl m 2 an explicit algorithm is given to compute a code automorphism if it exists that sends a particular choice of m binary positions into binary positions that correspond to a single symbol of the rs code if one such automorphism exists for a particular choice of m binary symbol positions we show that there are at least m of them computationally efficient permutation decoders are designed for the two parity symbol rs n n 2 3 codes simulation results are shown for the additive white gaussian noise awgn channel for the finite fields f23 and f24 we go on to derive subgroups of code automorphisms belonging to binary images of certain rs codes that have three parity symbols a table of code automorphism subgroup orders computed using the groups algorithms and programming gap software is tabulated for the fields f23 f24 and f25

on the reliability order based decoding algorithms for binary linear block codes in this correspondence we consider the decoding of binary block codes over the additive white gaussian noise awgn channel with binary phase shift keying bpsk signaling by a reliability order based decoding algorithm robda we mean a soft decision decoding algorithm which decodes to the best most likely codeword of the form that is the sum of the hard decision tuple and an error pattern in a set determined only by the order of the reliabilities of the hard decisions examples of robdas include many well known decoding algorithms such as the generalized minimum distance gmd decoding algorithm chase decoding algorithms and the reliability based decoding algorithms proposed by fossorier and lin it is known that the squared error correction radii of robdas can be computed from the minimal squared euclidean distances mseds between the all one sequence and the polyhedra corresponding to the error patterns for the computation of such mseds we give a new method which is more compact than the one proposed by fossorier and lin these results are further used to show that any bounded distance robda is asymptotically optimal the ratio between the probability of decoding error of a bounded distance robda and that of the maximum likelihood ml decoding approaches 1 when the signal to noise ratio snr approaches infinity provided that the minimum hamming distance of the code is greater than 2

an adaptive two stage algorithm for ml and sub ml decoding of binary linear block codes two distinct codeword searching procedures based on iterative bounded distance decoding bdd are combined to form an adaptive two stage maximum likelihood ml decoder for binary linear block codes during the first stage of the algorithm a tight upper bound on an error likelihood metric discrepancy is established iteratively for the ml codeword first stage processing requires sorting and storage adaptive switching to the second stage removes the sorting and storage requirements and allows to rule out redundant bdds efficiently second stage processing accounts for all codewords with discrepancy lower bound below the upper bound of the ml codeword and guarantees ml performance in addition the proposed two stage algorithm is inherently tunable for controlled suboptimum operation under sub ml operation the overall scheme can be interpreted as a generalization of the chase 1972 algorithm simulation studies for the 24 12 8 extended golay and the 64 30 14 and 128 64 22 extended bose chaudhuri hocquenghem bch codes illustrate and support these theoretical developments

a low weight trellis based iterative soft decision decoding algorithm for binary linear block codes this paper presents a new low weight trellis based soft decision iterative decoding algorithm for binary linear block codes the algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test the initial candidate codeword is generated by a simple decoding method the subsequent candidate codewords if needed are generated by a chain of low weight trellis searches one at a time each search is conducted through a low weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested this improvement is then used as the next candidate codeword for a test of optimality the decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low weight trellis search results in a repetition of a previously generated candidate codeword a divide and conquer technique is also presented for codes that are not spanned by their minimum weight codewords the proposed decoding algorithm has been applied to some well known codes of lengths 48 64 and 128 simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the 128 29 32 rm code with a significant reduction in computational decoding complexity

iterative soft input soft output decoding of reed solomon codes by adapting the parity check matrix an iterative algorithm is presented for soft input soft output siso decoding of reed solomon rs codes the proposed iterative algorithm uses the sum product algorithm spa in conjunction with a binary parity check matrix of the rs code the novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the spa is applied at each iteration the proposed algorithm can be geometrically interpreted as a two stage gradient descent with an adaptive potential function this adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and therefore significantly improves the performance simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding hdd and compare favorably with other popular soft decision decoding methods

generalized minimum distance decoding of euclidean space codes and lattices it is shown that multistage generalized minimum distance gmd decoding of euclidean space codes and lattices can provide an excellent tradeoff between performance and complexity we introduce a reliability metric for gaussian channels that is easily computed from an inner product and prove that a multistage gmd decoder using this metric is a bounded distance decoder up to the true packing radius the effective error coefficient of multistage gmd decoding is determined two simple modifications in the gmd decoding algorithm that drastically reduce this error coefficient are proposed it is shown that with these modifications gmd decoding achieves the error coefficient of maximum likelihood decoding for block codes and for generalized construction a lattices multistage gmd decoding of the lattices d sub 4 e sub 8 k sub 12 bw sub 16 and spl lambda sub 24 is investigated in detail for k sub 12 bw sub 16 and spl lambda sub 24 the gmd decoders have considerably lower complexity than the best known maximum likelihood or bounded distance decoding algorithms and appear to be the most practically attractive decoders available for high dimensional codes and lattices spl ges 64 dimensions maximum likelihood decoding becomes infeasible while gmd decoding algorithms remain quite practical as an example we devise a multistage gmd decoder for a 128 dimensional sphere packing with a nominal coding gain of 8 98 db that attains an effective error coefficient of 1365760 this decoder requires only about 400 real operations in addition to algebraic errors and erasures decoding of certain bch and hamming codes it therefore appears to be practically feasible to implement algebraic multistage gmd decoders for high dimensional sphere packings and thus achieve high effective coding gains

logic cuts for multilevel generalized assignment problems abstract in the multilevel generalized assignment problem mgap agents can perform tasks at more than one efficiency level important manufacturing problems such as lot sizing can be easily formulated as mgaps however the large number of variables in the related 0 1 integer program makes it hard to find optimal solutions to these problems even when using powerful commercial optimization packages the mgap includes a set of knapsack constraints one per agent that can be useful for generating simple logical constraints or logic cuts we exploit the fact that logic cuts can be generated in linear time and can be easily added to the model before solving it with classical branch and bound methodology we generate all contiguous 1 cuts for every knapsack in large mgap s problems and report the effect of adding these cuts in our experimental results

an improvement of soft decision maximum likelihood decoding algorithm using hard decision bounded distance decoding a new soft decision maximum likelihood decoding algorithm is proposed which generates a set of candidate codewords using hard decision bounded distance decoding by improving the generating method of input vectors for the bounded distance decoding due to kaneko et al see ibid vol 40 no 3 p 320 27 1994 the decoding time complexity is reduced without degradation of the performance the space complexity is dependent on the bounded distance decoding

soft decision decoding of reed solomon codes this paper presents a maximum likelihood decoding mld and a suboptimum decoding algorithm for reed solomon rs codes the proposed algorithms are based on the algebraic structure of the binary images of rs codes theoretical bounds on the performance are derived and shown to be consistent with simulation results the proposed suboptimum algorithm achieves near mld performance with significantly lower decoding complexity it is also shown that the proposed suboptimum algorithm has better performance compared with generalized minimum distance decoding while the proposed mld algorithm has significantly lower decoding complexity than the well known vardy be ery 1991 mld algorithm

a bounded distance decoding algorithm for binary linear block codes achieving the minimum effective error coefficient a new bounded distance bd decoding algorithm is presented for binary linear n k d block codes on additive white gaussian noise channels the algorithm is based on the generalized minimum distance gmd decoding algorithm of forney 1989 using the acceptance criterion of taipale and pursley gmd tp proposed in 1991 it is shown that the gmd tp decoding algorithm is a bd decoding algorithm with effective error coefficient sup n sub d it is also shown that the decision regions of gmd tp are good inner approximations of those of full gmd decoding and therefore full gmd decoding is bd and has an effective error coefficient that is well approximated by sup n sub d moreover by adding a d erasure correction step to gmd decoding the effective error coefficient can be reduced to a sub d the number of minimum weight codewords which is the same as the effective error coefficient of maximum likelihood decoding the decoding algorithm is mainly based on algebraic errors and erasures decoding and therefore has polynomial rather than exponential complexity

optimization models of discrete event system dynamics a methodology is given for modeling the dynamics of discrete event stochastic systems as optimization problems the intent is to provide a means to utilize the rich mathematical theory and algorithms of optimization in the study of this important class of systems a procedure for mapping a simulation event relationship graph into a mixed integer program is presented along with examples of queueing networks and manufacturing systems that illustrate the approach several potential applications are examined including automatic constraint generation for optimal resource scheduling representations of max plus algebra models for queueing system dynamics response gradient estimation and an unconventional technique for simulating queueing systems using virtual resources that are identified from the optimization models for these systems

decoding by local optimization corresp the maximum likelihood decoding problem for linear binary n k codes is reformulated as a continuous optimization problem in a k dimensional solid cube we obtain a near optimum solution of this problem by use of a simple gradient local optimization algorithm computer simulation results are presented for the 21 11 projective geometry code and the 47 23 quadratic residue code