Memory truncation and crosstalk cancellation in transmultiplexers

This article addresses the design of linear networks that reduce intersymbol interference and crosstalk in transmultiplexers. The proposed filter design method is based on the maximization of the signal-to-noise ratio at the detector input, defined for channel memories being truncated to arbitrarily short lengths. Thus, low-complexity Viterbi (1986) detectors working independently for all data channels can be used. The design of minimum mean-square error equalizer networks is included in the framework     

Orthogonal transmultiplexers in communication: a review

This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics     

Design of multichannel nonuniform transmultiplexers using generalbuilding blocks

The paper considers design of multichannel, nonuniform-band transmultiplexers. It is well known that using traditional building blocks-up and downsamplers and linear time-invariant (LTI), causal filters-nonuniform transmultiplexers typically do not achieve perfect reconstruction. To alleviate this, we propose to build nonuniform transmultiplexers using general dual-rate structures that provide more design freedom, and hence, perfect reconstruction can be achieved. Such general transmultiplexers have a new source of error called aliasing distortion in addition to the traditional cross-talk, magnitude, and phase distortions. We propose a composite error criterion that captures all four distortions in one. Using this error criterion as reconstruction performance measure. We develop an optimal design procedure and apply it to a three-channel nonuniform example, yielding an FIR transmultiplexer that has good frequency-limiting properties in the synthesis end and is very close to perfect reconstruction     

Equalizers for transmultiplexers in orthogonal multiple carrier data transmission

Orthogonal multiple carrier data transmission systems are efficiently realized using modified dft transmultiplexer filter banks. In data transmission applications, a non-ideal transmission channel causes distortions such as intersymbol interference and crosstalk between the subrate bands of the transmultiplexer. Hence, in order to equalize these distortions, subband equalizers, which affect the intersymbol interference and crosstalk behavior, are considered for implementation. The special structure of modified dft transmultiplexers requires a discussion concerning the various possibilities of placing the subband equalizers at the receiver. Wiener solutions and lms adaptive algorithms for various new subband equalizer structures are derived and compared by means of simulation results.     

Some problems in the asymptotic theory of diffraction

The paper is a review of asymptotic methods in the theory of diffraction and emphasizes Soviet contributions. Without going into mathematical details it presents a survey of a number of applications of ray techniques and their generalizations to problems of diffraction.     

Some counterexamples in the theory of Weyl-Heisenberg frames

We present an example of a positive function g with a positive Fourier transform gˆ and reasonable smoothness and decay properties such that (-1)^nmexp(πitm)g(t-n), n, m∈Z does not constitute a frame for L²(R). We also give counterexamples for the statement that one can tell (in)definiteness of a Weyl-Heisenberg frame operator from (in)definiteness of its Weyl symbol     

Design of high-resolution cosine-modulated transmultiplexers with sharp transition band

Due to the growing importance of multichannel modulation, there has been great interest in the design of high-performance transmultiplex systems. In this paper, a new cosine-modulated transmultiplex structure is proposed based on a prototype filter designed with the frequency-response masking (FRM) approach. This new structure leads to substantial reduction in the computational complexity (number of multiplications per output sample) of the prototype filters having sharp transition band and equivalently small roll-off values. The relation between the interpolation factor used in the FRM prototype filter and the decimation factor in the subbands leads to distinct structures. Examples included indicate that the reduction in computational complexity can be higher than 50% of the current state-of-art designs, whereas the reduction on the number of distinct coefficients of the prototype filter can be reduced even further (over 75%). As a result, the proposed approach allows the design of very selective subfilters for transmultiplexes with a very large number of subchannels.     

New results in the theory of identification via channels

The identification capacity is the maximal iterated logarithm of the number of messages divided by the blocklength that can be reliably transmitted when the receiver is only interested in deciding whether a specific message was transmitted or not. The identification coding theorem of R. Ahlswede and G. Dueck (1989) for single-user discrete memoryless channels states that the identification capacity is equal to the Shannon capacity. A novel method to prove the converse to the identification coding theorem is shown to achieve the strong version of the result. Identification plus transmission (IT) coding, a variant of the original problem of identification via channels, is proposed in the context of a common problem in point-to-multipoint communication, where a central station wishes to transmit information reliably to one of N terminals, whose identity is not predetermined. The authors show that as long as log log N is smaller than the number of bits to be transmitted, IT codes allow information transmission at channel capacity     

On the design of high-complexity cosine-modulated transmultiplexers based on the frequency-response masking approach

Two efficient techniques exploiting the frequency-response masking (FRM) approach are proposed in order to make it feasible to design prototype filters for highly selective nearly perfect-reconstruction cosine-modulated transmultiplexers and filter banks (CMTs and CMFBs) having a very large number of channels. In these design schemes, the number of unknowns is drastically reduced when compared with the corresponding techniques for designing direct-form prototype filters. Furthermore, in the proposed techniques, the main figures of merits, that is, the intersymbol interference and the interchannel interference for CMTs and the overall and aliasing distortions for CMFBs are taken into account in a controlled manner. In order to speed up the convergence of these two optimization techniques, simplifications for computing the resulting nonlinear constraints and the corresponding gradient vectors are proposed. They differ from each other in the sense that the first and second ones utilize the frequency-domain and time-domain constraints for controlling the figures of merit, respectively. Combining these two techniques results in numerically efficient algorithms for designing optimized CMTs (or CMFBs) with a reduced computational complexity (number of arithmetic operations per output sample), particularly when both branches of the FRM structure are required. Design examples are included illustrating the efficiency of the design methods and the high performance of the resulting CMT structures.     

Some results on the norm of codes

Two upper bounds for the norm N(C) of a binary linear code C with minimal weight d and covering radius R are given. The second of these bounds implies that C is normal if R=3     

Some aspects of the theory of nonlinear networks

In the development of network theory over the years, the primary focus of attention has been in the area of linear systems. Several reasons for this emphasis can easily be cited, but perhaps the foremost reason is that it has long been thought that, except in certain very special cases, little progress toward a rigorous definitive theory could be expected once the hypothesis of linearity is discarded. The recent success in the use of numerical methods for computing solutions of the equations for specific nonlinear networks (the importance of which is not to be minimized) has, furthermore, resulted in a certain complacency on the part of many engineers who occasionally need to solve network problems. One senses their outlook as being, basically, that whenever a particular nonlinear problem arises, one need only then run, data in hand, to the computer. Somewhat ironically, however, the development of computer-aided network analysis techniques has also been a prime impetus for many of the recent theoretical investigations in the field of nonlinear networks, and although much remains to be done, a rather comprehensive body of knowledge in this area has begun to take form. A number of related recent contributions to the theory of non-linear networks are reviewed here. As distinct from the computational aspects of the network analysis problem, we discuss work whose primary purpose is to yield an understanding of the nature of the equations that describe the behavior of nonlinear networks, and to identify and relate certain properties of the network elements, and the manner of their interconnection, to properties of the equations and their solutions. In addition, we do frequently touch on the problem of computation since, as has already been implied, it is indeed one of the purposes of the work discussed here to provide more of a theoretical foundation on which to base the numerical analyses.     

Some results on the self-similarity property in communication networks

Due to the strong experimental evidence that packet network traffic is self-similar in nature, it is important to study the problems to see whether the superposition of self-similar processes retains the property of self-similarity, and whether the service of a server changes the self-similarity property of the input traffic. In this letter, we first discuss some definitions and superposition properties of self-similar processes. We obtain some good results about the property of merging self-similar data streams. Then we present a model of a single server with infinite buffer and prove that when the queue length has finite second-order moment, the input process, being strong asymptotically second-order self-similar (sas-s), is equivalent to the output process which also bears the sas-s property.     

Some results in fixed point error analysis of the Bruun-FTTalgorithm

Results for a fixed-point error analysis of the Bruun-fast Fourier-transform (FFT) algorithm are presented. The noise-to-signal ratio of the Bruun algorithm is evaluated theoretically as well as experimentally and is compared to that of the decimation-in-time FFT. The noise-to-signal ratio of the Bruun-FFT is found to be significantly higher if safe scaling is applied in both cases     

Some results on the invertibility of nonlinear operators

The objective of this paper is to present certain conditions guaranteeing invertibility of a nonlinear operator between normed linear spaces. The idea is to approximate the given operator by an invertible, possibly linear operator, and reduce the problem to the contraction mapping principle. Several theorems of this kind are given, which appear as generalizations of some early results by I.W. Sandberg, and estimates for an approximate inverse are established. Finally, introducing certain invertibility indices, further sufficient and necessary conditions for invertibility are given.     

Some notes on availability theory

This is an expository paper which seeks to fill some gaps in the theory of the availability of a two-state system modelled by an alternating renewal process. A discussion of point availability and average availability complements the results of Baxter, J. appl. Prob.18, 227–235, 1981. This is followed by some remarks on equilibrium alternating renewal processes, the Haynes-Davis waiting-time theorem and the correlated alternating renewal process.     

Some aspects of convexity useful in information theory

From its very beginning, information theory has been pervaded by convexity arguments. Much of the necessary background was developed on an ad hoc basis without reference to the knowledge available from the mathematical study of convex sets and functions. Yet explicit use shown by examples.     

关于Negabent函数的若干结论

利用二次不定方程的求解,研究了Negabent函数的判别和构造问题,给出了Negabent函数的一个直观判别条件和一种间接构造法,同时,证明了一类Maiorana-McFarland bent函数不是Negabent函数。     

Some results on the algebraic immunity of Boolean functions

From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity(AI) of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed.     

Some results on the covering radii of Reed-Muller codes

Let R(r,m) be the rth-order Reed-Muller code of length 2^m and let ρ(r,m ) be its covering radius. R(2,7), R(2,8), R (3,7), and R(4,8) are among those smallest Reed-Muller codes whose covering radii are not known. New bounds for the covering radii of these four codes are obtained. The results are ρ(2,7)⩾40, ρ(2,8)⩾84, 20⩽ρ(3,7)⩽23, and ρ(4,8)⩾22. Noncomputer proofs for the known results that ρ(2,6)=18 and that R(1,5) is normal are given