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

convergence theorems for strongly pseudo contractive and strongly accretive maps supposeeis an arbitrary real banach space andkis a nonempty closed convex and bounded subset ofe supposet k kis a uniformly continuous strong pseudo contraction with constantk 0 1 suppose an bn cn a n b n and c n are sequences in 0 1 satisfying the following conditions i an bn cn 1 a n b n c n integersn 0 ii lim bn lim b n lim c n 0 iii bn iv cn for arbitraryx0 u0 v0 k define the sequence xn n 0iteratively byxn 1 anxn bntyn cnun yn a nxn b ntxn c nvn n 0 where un vn are arbitrary sequences ink then xn converges strongly to the unique fixed point oft related results deal with the iterative solutions of nonlinear equations involving set valued strongly accretive operators

a double sequence iteration process for fixed points of continuous pseudocontractions abstract let c be a bounded closed convex nonempty subset of a real hilbert space h the idea of a double sequence iteration is introduced and it is proved that a mann type double sequence iteration process converges strongly to a fixed point of a continuous pseudocontractive map t which maps c into c related results deal with the strong convergence of the iteration process to fixed points of nonexpansive maps

picard iterations for solution of nonlinear equations in certain banach spaces abstract let e be a real uniformly smooth banach space and let a d a e e be locally lipschitzian and strongly quasi accretive it is proved that a picard recursion process converges strongly to the unique solution of the equation ax f f r a with the convergence being at least as fast as a geometric progression related results deal with the convergence of picard iterations to the fixed point of locally lipschitzian strong hemicontractions t and to the solutions of nonlinear equations of the forms x ax f and x ax f where a is an accretive type map

convergence of iterative processes with errors for set valued pseudocontractive and accretive type mappings in banach spaces abstract in this paper some new results on convergence of iterative processes with errors for set valued pseudocontractive and accretive mappings in banach spaces are obtained our results extend and improve a number of the recent results

strong convergence of an iterative algorithm for pseudocontractive mapping in banach spaces abstract let c be a nonempty closed convex subset of a real uniformly smooth banach space x t c c a pseudocontractive mapping let n n and n be three real sequences in 0 1 satisfying appropriate conditions then for fixed u c and arbitrary x 0 c the sequence x n generated by x n n u n x n 1 n t x n n 1 converges strongly to a fixed point of t

a generalized steepest descent approximation for the zeros of m accretive operators a necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of m accretive operators related results deal with the convergence of the scheme to fixed points of pseudocontractive maps

iterative solution of nonlinear equations involving set valued uniformly accretive operators abstract let e be a real normed linear space and let a e 2 e be a uniformly continuous and uniformly quasi accretive multivalued map with nonempty closed values such that the range of i a is bounded and the inclusion f ax has a solution x e it is proved that ishikawa and mann type iteration processes converge strongly to x further if t e 2 e is a uniformly continuous and uniformly hemicontractive set valued map with bounded range and a fixed point x e it is proved that both the mann and ishikawa type iteration processes converge strongly to x the strong convergence of these iteration processes with errors is also proved

bounds on the information rate of intertransition time restricted binary signaling over an awgn channel upper and lower bounds on the capacity of a continuous time additive white gaussian noise awgn channel with bilevel spl plusmn spl radic p input signals subjected to a minimum inter transition time t sub min constraint are derived the channel model and input constraints reflect basic features of certain magnetic recording systems the upper bounds are based on duncan s relation between the average mutual information in an awgn regime and the mean square error mse of an optimal causal estimator evaluation or upper bounding the mse of suboptimal causal estimators yields the desired upper bounds the lower bound is found by invoking the extended mrs gerber s lemma and asymptotic properties of the entropy of max entropic bipolar d k codes asymptotic results indicate that at low snr pt sub min n sub 0 with n sub 0 designating the noise one sided power spectral density the capacity tends to p n sub 0 nats per second nats s i e it equals the capacity in the simplest average power limited case at high snr the capacity in the simplest average power limited case at high snr the capacity behaves asymptotically as t sub min sup 1 ln snr ln snr nats s demonstrating the degradation relatively to t sub avg sup 1 lnsnr which is the asymptotic known behavior of the capacity with a bilevel average intertransition time t sub avg restricted channel input additional lower bounds are obtained by considering specific signaling formats such as pulsewidth modulation the effect of mild channel filtering on the lower bounds on capacity is also addressed and novel techniques to lower bound the capacity in this case are introduced

on the equivalence of the convergence criteria between modified mann ishikawa and multi step iterations with errors for successively strongly pseudo contractive operators abstract in this paper the equivalence of the convergence between the modified mann ishikawa and multi step noor iterations with errors is proven for the successively strongly pseudo contractive operators without lipschitzian assumption our results generalize the recent results of the paper b e rhoades s m soltuz the equivalence between mann ishikawa iterations and multi step iteration nonlinear anal 58 2004 219 228 b e rhoades s m soltuz the equivalence between the convergences of ishikawa and mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudo contractive maps j math anal appl 289 2004 266 278 by extending to the more generalized multi step iterations with errors and hence improve the corresponding results of all the references in bibliography by providing the equivalences of convergence between all of these up to date iteration schemes

bounds on information combining when the same data sequence is transmitted over two independent channels or when a data sequence is transmitted twice but independently over the same channel the independent observations can be combined at the receiver side from an information theory point of view the overall mutual information between the data sequence and the received sequences represents a combination of the mutual information of the two channels this concept is termed information combining a lower bound and an upper bound on the combined information is presented and it is proved that these bounds are tight furthermore this principle is extended to the computation of extrinsic information on single code bits for a repetition code and for a single parity check code of length three respectively for illustration of the concept and the bounds on information combining two applications are considered first bounds on the information processing characteristic ipc of a parallel concatenated code are derived from its extrinsic information transfer exit chart second bounds on the exit chart for an outer repetition code and for an outer single parity check code of a serially concatenated coding scheme are computed

extremes of information combining extreme densities for information combining are found for two important channel models the binary input symmetric parallel broadcast channel and the parity constrained input symmetric parallel channels following upper and lower mutual information thresholds are stated for per bit maximum a posteriori probability map decoding and low density parity check ldpc code ensembles

the efficiency of investment information we investigate how the description of a correlated information v improves the investment in the stock market x the objective is to maximize the growth rate of wealth in repeated investments we find a single letter characterization of the incremental growth rate spl delta r the maximum increase in growth rate when v is described to the investor at rate r the incremental growth rate specialized to the horse race market is related to source coding with side information of wyner and ahlswede kormer we provide two horse race examples jointly binary and jointly gaussian the initial efficiency spl delta 0 is the maximum possible increase in the growth rate per bit of description we show that the initial efficiency is related to the dependency between v and the market in particular for the horse race market the initial efficiency is the square of the hirschfeld gebelein renyi maximal correlation between v and x this provides a connection with the hypercontraction of the markov operator of ahlswede and gacs for the general market the initial efficiency is 1 when the side information v is equal to the stock market outcome x

iteration processes for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p 1 p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l satisfying p p 1 l 2 p 2 p 1 1 k define s x x by sx tx x for arbitrary x 0 x the sequence x n n 1 is defined by x n 1 1 n x n n sy n y n 1 n x n n sx n n 0 where n n 1 n n 1 are two real sequences satisfying i 0 n 2 1 p 2 p 1 1 k k n l 2 n p 2 p l 2 1 w n w l 2 1 2 n p 2 p 1 1 k k n l 2 n p 1 2 l 2 1 w n w l 2 1 2 n 1 1 for each n ii 0 n min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 for each n iii n n where w p 2 p 1 1 k p 2 p l 2 then x n 1 converges strongly to the unique solution of tx moreover if n 2 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 and n for each n and some 0 min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 then x n 1 q p n 2 x 1 q where q denotes the solution of tx and 1 4 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 0 1 a related result details with the iterative approximation of lipschitz strongly pseudocontractive maps in x

the solution by iteration of nonlinear equations of hammerstein type let e be a real uniformly smooth banach space suppose n is a set valued locally accretive map with open domain d n c e k is a single valued map with domain d k c e such that im n c d k and k exists and is locally strongly accretive on im k if the equation f e x knx has a solution x e d n the strong convergence of iteration methods of the ishikawa and mann types to this solution is established related theorems deal with the iterative solution of nonlinear equations of the form f g x tx for the case where t is accretive explicit convergence rates are established miramare trieste november 1996 permanent address department of mathematics and computer science nnamdi azikiwe university p m b 5025 awka anambra state nigeria

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

ishikawa iteration process for nonlinear lipschitz strongly accretive mappings abstract let e lp p 2 and let t e e be a lipschitzian and strongly accretive mapping let s e e be defined by sx tx x it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process x0 e xn 1 1 n xn ns 1 n xn nsxn n 0 converges strongly to the unique solution of tx a related result deals with the iterative approximation of fixed points for lipschitz strongly pseudocontractive mappings in e a consequence of our result gives an affirmative answer to a problem posed by c e chidume j math anal appl 151 no 2 1990 453 461

steepest descent method for equilibrium points of nonlinear systems with accretive operators let e be a real normed linear space and let a e 2e be a bounded uniformly continuous strongly accretive multi valued map with nonempty closed values such that the inclusion 0 ax has a solution x e it is proved that both the ishikawa and the mann iteration processes are bounded and converge strongly to x related results deal with the convergence of the iteration processes to fixed points of strongly pseudocontractive maps and the iterative solution of the equation 0 x fx for an accretive map f furthermore the ishikawa and mann iteration methods with errors are discussed and proofs are sketched on how our theorems extend to these methods our method of proof is of independent interest

an iterative process for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l define s x x by sx f tx x let c n n 1 be a real sequence satisfying 1 i 0 c n k p 1 l 2 2 k 1 1 for each n 2 ii n c n then for arbitrary x 0 x the sequence x n 1 1 c n x n c n sx n n 0 converges strongly to the unique solution of tx f moreover if c n k p 1 l 2 2 k 1 1 for each n then x n 1 q n 2 x 1 q where q denotes the solution of tx f and 1 k p 1 l 2 2 k 1 1 0 1 a related result deals with the iterative approximation of lipschitz strongly pseudocontractive maps in x

on mann iteration in hilbert spaces abstract let k be a compact convex subset of a real hilbert space h t k k a hemicontractive map let n be a real sequence in 0 1 satisfying appropriate conditions then for arbitrary x 0 k the sequence x n defined iteratively by x n n x n 1 1 n t x n n 1 converges strongly to a fixed point of t

weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations abstract let h be a real hilbert space k a nonempty closed convex subset of h and t k k a lipschitz pseudocontraction with a nonempty fixed point set weak and strong convergence theorems for the iterative approximation of fixed points of t are proved furthermore if t h h is a lipschitz monotone operator and f r t where r t denotes the range of t weak and strong convergence theorems for the iterative approximation of solutions of the operator equation tx f are proved

on achieving an asymptotically error free fixed point of iterative decoding for perfect a priori information in this paper we provide necessary and sufficient conditions for constituent codes in multiple concatenated and graph based coding schemes to achieve an asymptotically error free iterative decoding fixed point if the maximum possible a priori information is available at least one constituent code in an iterative decoding scheme must satisfy these conditions in order to ensure an asymptotically vanishing bit error probability at the convergence point of the decoder our results are proved for arbitrary binary input symmetric memoryless channels bismcs and thus can be universally applied to many transmission scenarios specifically using a factor graph framework it is shown that non inner codes in a serial concatenation or check nodes in generalized ldpc codes achieve perfect extrinsic information if and only if the minimum hamming distance between codewords is two or greater for inner codes in a serial concatenation constituent codes in a parallel concatenation or variable nodes in doubly generalized ldpc codes the corresponding encoder condition for acquiring perfect extrinsic information is an infinite codeword weight for a weight one input sequence for this case we provide a general proof which holds for all linear encoders and bismcs we also show that these results can improve the performance of concatenated coding schemes

on the polynomial integrability of kirchoff s equations abstract we prove that kirchoff s equations either are completely integrable or have at most four functionally independent polynomial first integrals

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

extension of an entropy property for binary input memoryless symmetric channels the channel output entropy property introduced by a d wyner and j ziv ibid vol it 19 p 769 762 nov 1973 for a binary symmetric channel is extended to arbitrary memoryless symmetric channels with binary inputs and discrete or continuous outputs this yields lower bounds on the achievable information rates of these channels under constrained binary inputs using the interpretation of entropy as a measure of order and randomness the authors deduce that output sequences of memoryless symmetric channels induced by binary inputs are of a higher degree of randomness if the redundancy of the input binary sequence is spread in memory rather than in one dimensional asymmetry it is of interest to characterize the general class of schemes for which this interpretation holds

constrained information combining theory and applications for ldpc coded systems this paper tightens previous information combining bounds on the performance of iterative decoding of binary low density parity check ldpc codes over binary input symmetric output channels by tracking the probability of erroneous bit in conjunction with mutual information evaluation of the new bounds as well as of other known bounds on different ldpc ensembles demonstrates sensitivity of the finite dimensional iterative bounds to lambda2 the fraction of edges connected to degree 2 variable nodes