subblock constrained codes for real time simultaneous energy and information transfer consider an energy harvesting receiver that uses the same received signal both for decoding information and for harvesting energy which is employed to power its circuitry in the scenario where the receiver has limited battery size a signal with bursty energy content may cause power outage at the receiver since the battery will drain during intervals with low signal energy in this paper we analyze subblock energy constrained codes seccs which ensure that sufficient energy is carried within every subblock duration we consider discrete memoryless channels and characterize the secc capacity and the secc error exponent and provide useful bounds for these values we also study constant subblock composition codes csccs which are a subclass of seccs where all the subblocks in every codeword have the same fixed composition and this subblock composition is chosen to maximize the rate of information transfer while meeting the energy requirement compared with constant composition codes cccs we show that csccs incur a rate loss and that the error exponent for csccs is also related to the error exponent for cccs by the same rate loss term we exploit the symmetry in csccs to obtain a necessary and sufficient condition on the subblock length for avoiding power outage at the receiver furthermore for cscc sequences we present a tight lower bound on the average energy per symbol within a sliding time window we provide numerical examples highlighting the tradeoff between the delivery of sufficient energy to the receiver and achieving high information transfer rates it is observed that the ability to use energy in real time imposes less of penalty compared with the ability to use information in real time

an improvement to the bit stuffing algorithm the bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence this approach was previously introduced and applied to d k constrained codes results show that the maximum average rate of the bit stuffing code achieves capacity when k d 1 or k spl infin while it is suboptimal for all other d k pairs furthermore this technique was generalized to produce codes with an average rate that achieves capacity for all d k pairs however this extension results in a more complicated scheme this correspondence proposes a modification to the bit stuffing algorithm that maintains its simplicity we show analytically that the proposed algorithm achieves improved average rates over bit stuffing for most d k constraints we further determine all constraints for which this scheme produces codes with an average rate equal to the shannon capacity

constraint gain in digital storage systems where the input to the noisy channel is required to satisfy a modulation constraint the constrained code and error control code ecc are typically designed and decoded independently the achievable rate for this situation is evaluated as the rate of average intersection of the constraint and the ecc the gap from the capacity of the noisy constrained channel is called the constraint gain which represents the potential improvement in combining the design and decoding of the constrained code and the ecc the constraint gain is computed for various constraints over the binary input additive white gaussian noise awgn channel biawgnc as well as over intersymbol interference isi channels finally it is shown that an infinite cascade of reverse concatenation with independent decoding of constraint and ecc has a capacity equal to the rate of average intersection

variable length state splitting with applications to average runlength constrained arc codes a new class of constrained systems average runlength constraints arcs is defined by requiring that the sum of n consecutive run lengths be bounded above by a linear function of n in particular the running average runlength of every sequence in the system is bounded above by a constant a general result is given on the capacity of arc systems the state splitting algorithm is then improved for variable length graphs this is then applied to obtain high fixed rate codes from the free binary source to arc systems as an example a rate 1 2 d k

on the power spectral density of constrained sequences this paper derives a simple closed form expression for computing the power spectral density psd of constrained sequences whose constraints are characterized by a function of an ergodic markov process specified in terms of a mealy machine a suitable matrix description of the stochastic behavior of the constrained sequence is used to express its autocorrelation sequence in a compact matrix form that simplifies the calculation of the psd examples of the application of this technique in cases of practical interest are provided including differentially encoded binary sequences source driven binary huffman codes maximum entropy d k codes and convolutional or block encoded sequences a unified treatment to several widely used constrained sequences is provided

on the capacity of a direct detection photon channel with intertransition constrained binary input the classical directed detection photon channel is modeled by an output nu sub t observed signal describing the photon arrival poisson count process with intensity rate lambda sub t lambda sub 0 where lambda sub t photons s is the channel input information carrying intensity and lambda sub 0 photons s is the dark current intensity upper and lower bounds on the capacity of this channel are presented for two level binary inputs taking on the extreme value lambda sub t in 0 a where a denotes the peak power satisfying an average power constraint e lambda sub t

subset source coding this paper studies the fundamental limits of storage for structured data where statistics and structure are both critical to the application accordingly a framework is proposed for optimal lossless and lossy compression of subsets of the possible realizations of a discrete memoryless source dms for the lossless subset compression problem it turns out that the optimal source code may not index the conventional source typical sequences but rather index certain subset typical sequences consistent with the subset of interest building upon an achievability and a strong converse an analytic expression is given based on the shannon entropy relative entropy and subset entropy which identifies such subset typical sequences for a broad class of subsets of a dms intuitively subset typical sequences belong to those typical sets which highly intersect the subset of interest but are still closest to the source distribution in the sense of relative entropy for the lossy subset compression problem an upper bound is derived on the subset rate distortion function in terms of the subset mutual information optimized over the set of conditional distributions that satisfy the expected distortion constraint with respect to the subset typical distribution and over a set of certain auxiliary subsets by proving a strong converse result this upper bound is shown to be tight for a class of symmetric subsets as shown in our numerical examples more often than not one achieves a gain in the fundamental limits in that the optimal compression rate for the subset in both the lossless and lossy settings can be strictly smaller than the source entropy and the source rate distortion function respectively although exceptions are also possible

spectral analysis of maximum entropy multitrack modulation codes the problem of calculating the power spectral density of a constrained maxentropic vector sequence a sup n a sup n a sub i sup n sub 0 spl les i spl les n 1 is considered the constraints of the constituent sequences a sub i sup n are defined by the sofic systems s sub i presented by the directed graphs g sub i 0 spl les i spl les n 1 but the vector sequence itself is constrained additionally and given by a function spl phi of constituent graphs g spl phi g sub 0 spl middot spl middot spl middot g sub n 1 this class of vector constraints is met in parallel multitrack recording the general case of a simultaneous recording on n tracks is considered assuming that the common vector constraint is track invariant

optimal block codes for m ary runlength constrained channels in this work we consider the analysis and design of optimal block decodable m ary runlength limited rll codes we present two general construction methods one based on permutation codes due to datta and mclaughlin 1999 and the other a nonbinary generalization of the binary enumeration methods of patrovics and immink 1996 and gu and fuja 1994 the construction based on permutation codes is simple and asymptotically in block length optimal while the other construction is optimal in the sense that the resulting codes have the highest rate among all block decodable codes for any block length in the process we shall also extend a result due to zehavi and wolf 1988 on the capacity of binary d k constraints to m ary channels finally we present examples of template codes remarkably low complexity m d k block codes which achieve the optimal rate without the use of enumeration

the feedback capacity of the binary erasure channel with a no consecutive ones input constraint the input constrained erasure channel with feedback is considered where the binary input sequence contains no consecutive ones i e it satisfies the 1 infty rll constraint we derive the capacity for this setting which can be expressed as c epsilon max 0 leq p leq 0 5 frac 1 epsilon h b p 1 1 epsilon p where epsilon is the erasure probability and h b cdot is the binary entropy function moreover we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity the feedback capacity was calculated using an equivalent dynamic programming dp formulation with an optimal average reward that is equal to the capacity furthermore we obtained an optimal encoding procedure from the solution of the dp leading to a capacity achieving zero error coding scheme for our setting dp is thus shown to be a tool not only for solving optimization problems such as capacity calculation but also for constructing optimal coding schemes the derived capacity expression also serves as the only non trivial upper bound known on the capacity of the input constrained erasure channel without feedback a problem that is still open

achievable performance over the correlated rician channel the correlated rician channel is a useful model for a slowly fading channel in which the complex fading process is composed of two quadrature gaussian processes with a given autocorrelation function for slow fading the correlation between adjacent symbols is relatively high the authors investigate the achievable error probabilities over the channel employing coherent detection and ideal side information on the realization of the fading processes at the receiver an underlying decoding delay constraint which precludes the use of ideal interleaving is assumed coded bpsk performance is addressed both with and without the piecewise constant approximation according to which the fading value remains constant during the symbol duration for the latter case that is no piecewise constant approximation the analysis relies on the fredholm determinant associated with the fading process autocorrelation function the authors focus on the exponentially correlated channel the worst case pairs of codewords are identified the exponential behavior of the error probability with random coding and i i d gaussian inputs is analyzed and the behavior of the cut off rate and capacity is addressed the results enhance the insight to the effect of the basic parameters governing the performance and these are examined in view of previous works and compared to relevant performance results for the block fading channel model

a multiple insertion deletion correcting code for run length limited sequences a code construction is proposed to add a multiple insertion deletion error correcting capability to a run length limited sequence the codewords of this code are themselves run length limited the insertion deletion correcting capability is achieved by requiring several weighted sums of run lengths in the codewords to satisfy certain congruences modulo primes the construction is similar to the number theoretic code proposed by dolecek and anantharam which can correct multiple repetition errors or equivalently multiple insertions of zeros it is shown that if the codewords in this code are run length limited then the code is capable of correcting both insertions and deletions of zeros and ones an algorithm is proposed for decoding over a multiple insertion deletion channel following the work of dolecek and anantharam a systematic encoding method is also proposed for the codes furthermore it is shown that the proposed construction has a higher rate asymptotically than the helberg code which is unconstrained in terms of run lengths even though our construction has the additional run length constraints the need for run length limited codes that can correct insertion deletion errors is motivated by bit patterned media for magnetic recording

on the capacity of binary and gaussian channels with run length limited inputs bounds on the capacity of binary symmetric channels and additive gaussian channels with run length limited two level binary bipolar inputs are presented and their tightness is demonstrated for some cases stationary input sequences which do not degrade capacity are considered when deriving the bounds lower bounds on the magnetic recording density for a simple continuous time recording model incorporating a minimal intertransition constraint are evaluated for soft and hard decisions a superiority of about 1 5 db in signal to noise ratio is observed for the soft decision scheme

on runlength codes several results on binary d k codes are given first a novel derivation for the capacity of these codes based on information theoretic principles is given based on this result the spectrum of a d k code is computed finally the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the d k constraint is considered lower bounds on the capacity of such a channel are derived

the fleet assignment problem solving a large scale integer program given a flight schedule and set of aircraft the fleet assignment problem is to determine which type of aircraft should fly each flight segment this paper describes a basic daily domestic fleet assignment problem and then presents chronologically the steps taken to solve it efficiently our model of the fleet assignment problem is a large multi commodity flow problem with side constraints defined on a time expanded network these problems are often severely degenerate which leads to poor performance of standard linear programming techniques also the large number of integer variables can make finding optimal integer solutions difficult and time consuming the methods used to attack this problem include an interior point algorithm dual steepest edge simplex cost perturbation model aggregation branching on set partitioning constraints and prioritizing the order of branching the computational results show that the algorithm finds solutions with a maximum optimality gap of 0 02 and is more than two orders of magnitude faster than using default options of a standard lp based branch and bound code

concavity of the mutual information rate for input restricted memoryless channels at high snr we consider a memoryless channel with an input markov process supported on a mixing finite type constraint we continue the development of asymptotics for the entropy rate of the output hidden markov chain and deduce that at high signal to noise ratio the mutual information rate of such a channel is concave with respect to almost all input markov chains of a given order

asymptotics of input constrained erasure channel capacity in this paper we examine an input constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low more specifically for a general memoryless erasure channel with its input supported on an irreducible finite type constraint we derive partial asymptotics of its capacity using some series expansion type formula of its mutual information rate and for a binary erasure channel with its first order markovian input supported on the 1 infty rll constraint based on the concavity of its mutual information rate with respect to some parameterization of the input we numerically evaluate its first order markov capacity and further derive its full asymptotics the asymptotics obtained in this paper when compared with the recently derived feedback capacity for a binary erasure channel with the same input constraint enable us to draw the conclusion that feedback may increase the capacity of an input constrained channel even if the channel is memoryless

constant weight and constant charge binary run length limited codes constant weight and constant charge binary sequences with constrained run length of zeros are introduced the weight and charge distribution for these sequences are found next recurrent and direct formulas for calculating the number of these sequences are obtained by considering these numbers of constant weight and constant charge run length limited rll sequences as coefficients of convergent power series generating functions are derived the fact that generating function for enumerating constant charge rll sequences does not have a closed form is proved subsequently implementation of encoding and decoding procedures using cover s enumerative scheme is shown based on the obtained results some examples such as enumeration of running digital sum rds constrained rll sequences or peak shifts control capability are also provided

noisy constrained capacity for bsc channels we study the classical problem of noisy constrained capacity in the case of the binary symmetric channel bsc namely the capacity of a bsc whose input is a sequence from a constrained set as stated by fan while calculation of the noise free capacity of constrained sequences is well known the computation of the capacity of a constraint in the presence of noise has been an unsolved problem in the half century since shannon s landmark paper we first express the constrained capacity of a binary symmetric channel with d k constrained input as a limit of the top lyapunov exponents of certain matrix random processes then we compute asymptotic approximations of the noisy constrained capacity for cases where the noise parameter e is small in particular we show that when k 2d the error term excess of capacity beyond the noise free capacity is o e whereas it is o eloge when k 2d in both cases we compute the coefficient of the error term in the course of establishing these findings we also extend our previous results on the entropy of a hidden markov process to higher order finite memory processes these conclusions are proved by a combination of analytic and combinatorial methods

shannon capacity of m ary redundant multitrack runlength limited codes we consider multiamplitude multitrack runlength limited d k constrained channels with and without clock redundancy we calculate the shannon capacities of these channels and present some simple 100 efficient codes to compute capacity a constraint graph equivalent to the usual runlength limited constraint graph is used the introduced graph model has the vertex labeling independent of number of tracks to be written on in parallel which provides computational savings when the number of tracks is large we show that increasing the number of tracks written on in parallel provides significant increase of per track capacity for the more restrictive clocking constraint case i e when k d but it does not have much influence on the channel capacity when k spl ges d

generating functions and lower bounds on rates for limited error correcting codes runlength limited rll and digital sum limited dsl codes are considered for these codes the finite and asymptotic lower bounds on achievable rates for the given minimum hamming distance are derived using generating functions and trellis diagram techniques the authors prove the existence of rll and dsl codes of rate r and minimum distance d delta n such that r or 2 log lambda sub 1 0 min log lambda sub 1 z delta log z 0

perfect d k codes capable of correcting single peak shifts codes for the multibit peak shift recording channel called d k codes of reduced length n are considered arbitrary d k and perfect d k codes capable of correcting single peak shifts of given size t are defined for the construction of perfect codes a general combinatorial method connected with finding good weight sequences in abelian groups is used and the concept of perfect t shift n designs is introduced explicit constructions of such designs for t 1 t 2 and t p 1 2 are given where p is a prime this construction is universal in that it does not depend on the d k constraints it also allows automatic correction of those peak shifts that violate d k constraints the construction is extended to d k codes of fixed binary length and allows the beginning of the next codeword to be determined the question whether the designed codes can be represented as systematic codes with minimal redundancy is considered as well

an enumerative method for runlength limited codes permutation codes permutation codes introduced by slepian 1965 were shown to perform well on an additive white gaussian noise awgn channel unfortunately these codes required large lookup tables making them quite complex to implement even though the maximum likelihood decoder is very simple in this correspondence we present an enumeration scheme which encodes and decodes permutation codes with low complexity we concentrate on the use of permutation codes for constructing high rate codes that satisfy runlength limited constraints wolf 1990 showed that permutation codes can be used for runlength constraints and that they have rate that asymptotically achieves the capacity of a noiseless runlength limited constrained channel wolf however gave no efficient encoders decoder our code construction is enumerative but unlike other enumerative codes has storage requirements that are a function of the runlength parameters d and k instead of the block length n in addition these codes have error detection and correction capabilities finally we use this approach to construct 0 g i codes whereby all odd numbered occurrences of double adjacent errors are detected as an example a 99 2 efficient rate 498 528 0 6 3 code is presented

a randomized algorithm for the capacity of finite state channels inspired by ideas from the field of stochastic approximation we propose a randomized algorithm to compute the capacity of a finite state channel with a markovian input when the mutual information rate of the channel is concave with respect to the chosen parameterization the proposed algorithm proves to be convergent to the capacity of the channel almost surely with the derived convergence rate we also discuss the convergence behavior of the algorithm without the concavity assumption

the power spectrum of run length limited codes a novel method is developed for computing formulas for power spectra associated with run length limited rll codes explicit use is made of a compact description of the run length process associated with the rll code this association simplifies the general derivation of the power spectrum the calculation of the spectra of several rll codes popular in data storage applications is presented some of the closed form expressions for the spectra of these widely used codes are new

distance spectrum formulas on the largest minimum distance of block codes a general formula for the asymptotic largest minimum distance in block length of deterministic block codes under generalized distance functions not necessarily additive symmetric and bounded is presented as revealed in the formula the largest minimum distance can be fully determined by the ultimate statistical characteristics of the normalized distance function evaluated under a properly chosen random code generating distribution interestingly the new formula has an analogous form to the general information spectrum expressions of the channel capacity and the optimistic channel capacity respectively derived by verdu and han 1994 and chen and alajaji 1998 1999 as a result a minor class of distance functions for which the largest minimum distance can be derived is characterized a general varshamov gilbert lower bound is next addressed some discussions on the tightness of the general varshamov gilbert bound are also provided finally lower bounds on the largest minimum distances for several specific block coding schemes are rederived in terms of the new formulas followed by comparisons with the known results devoted to the same codes

on the distribution of runs of ones in binary strings in this paper we derive the number of binary strings which contain for a given i k exactly i k runs of 1 s of length k in all possible binary strings of length n email protected email protected n such a knowledge about the distribution pattern of runs of 1 s in binary strings is useful in many engineering applications for example data compression bus encoding techniques to reduce crosstalk in vlsi chip design computer arithmetic using redundant binary number system and design of energy efficient communication schemes in wireless sensor networks by transformation of runs of 1 s into compressed information patterns among others we present here a generating function based approach to derive a solution to this counting problem our experimental results demonstrate that for most commonly used file formats the observed distributions of exactly i k runs of length k email protected email protected n closely follow the theoretically derived distributions for a given n for n 8 we find that the experimentally obtained values for most file formats agree within 5 of the theoretically obtained values for all i k runs of length k email protected email protected n also the root mean square rms values of these deviations across all file types studied in this paper are less than 5 for n 8 in view of these facts the results presented in this paper could be useful in various application domains like the ones mentioned above