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Recently, Gallager's bounding techniques have been used to derive tight performance bounds for coded systems in fading channels. Most works in this field have thus far dealt with coherent decoding. This paper develops Gallager bounds for noncoherent systems in fading channels. Unlike coherent decoding, the exact error probability of a noncoherent decoder/detector conditioned on the fading coefficients does not admit a closed-form expression. This difficulty is overcome in this paper by employing the Chernoff technique. Although it weakens the bounds to some extent, the Chernoff technique enables the derivations of the limit-before-average (LBA) bound and Gallager bounds in closed form for noncoherent fading channels. Numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound. [ABSTRACT FROM AUTHOR]

Tight frames, also known as general Welch-bound-equality sequences, generalize orthonormal systems. Numerous applications-including communications, coding, and sparse approximation-require finite-dimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems (IEPs), which includes the frame design problem. To apply this method, one needs only to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is the fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate that alternating projection is an effective tool for frame design, the paper studies some important structural properties in detail. First, it addresses the most basic design problem: constructing tight frames with prescribed vector norms. Then, it discusses equiangular tight frames, which are natural dictionaries for sparse approximation. Finally, it examines tight frames whose individual vectors have low peak-to-average-power ratio (PAR), which is a valuable property for code-division multiple-access (CDMA) applications. Numerical experiments show that the proposed algorithm succeeds in each of these three cases. The appendices investigate the convergence properties of the algorithm. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) decoding algorithms can efficiently recover an N-dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = O(k log N/k) measurements y = Φx. If the sparsity or approximate sparsity level of x were known, then this theoretical guarantee would imply quality assurance of the resulting estimate. However, because the underlying sparsity of the signal x is unknown, the quality of a CS estimate ... using m measurements is not assured. It is nevertheless shown in this paper that sharp bounds on the error ||x - ...||𝓁N2 can be achieved with no effort. More precisely, suppose that a maximum number measurements m is preimposed. One can reserve 10 log p of these m measurements and compute a sequence of possible estimates (...j)pj=1 to x from the m - 10 log p remaining measurements; errors ||x - ...j||𝓁N2 for j = 1,..., p can then be bounded high probability. As a consequence, numerical upper and lower bounds on the error between x and the best k-term approximation to x can be estimated for p values of k with almost no cost. observation has applications outside CS as well. [ABSTRACT FROM AUTHOR]

The d-ary Sidel'nikov sequence S = s0, s1 … of period q - 1 for a prime power q = pm is a frequently analyzed sequence in the literature. Recently, it turned out that the linear complexity over Fp of the d-ary Sidel'nikov sequence is considerably smaller than the period if the sequence element s( q - 1) /2 mod (q - 1) is chosen adequately. In this paper this work is continued and tight lower bounds on the linear complexity over Fp of the d-ary Sidel'nikov sequence are given. For certain cases exact values are provided. Finally, results on the k-error linear complexity over Fp of the d-ary Sidel'nikov sequence are presented. [ABSTRACT FROM AUTHOR]

The central issue in this paper is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this purpose, we incorporate redundancy by mapping a given initial quantum state to a messenger state on a larger dimensional Hilbert space via a C* -algebra embedding. Our noise model for the transmission is a phase damping channel which admits a noiseless subsystem or decoherence-free subspace. More precisely, the transmission channel is obtained from convex combinations of a set of lowest rank yes/no measurements that leave a component of the messenger state unchanged. The objective of our encoding is to distribute quantum information optimally across the noise-susceptible component of the transmission when the noiseless component is not large enough to contain all the quantum information to be transmitted. We derive simple geometric conditions for optimal encoding and construct examples of such encodings. [ABSTRACT FROM AUTHOR]

In this paper, we consider a graph-based framework for transmission of correlated sources over multiple-access channels. It is well known that the separation approach is not optimal for this multiuser communication. Our objective in this work is to reintroduce modularity in this problem using a graph-based discrete interface and to minimize the performance loss as compared to the optimal joint source-channel coding scheme. The proposed framework envisages a transmission systems with two modules: a source-coding module and a channel-coding module. In the former module, the correlated sources are encoded distributively into correlated messages whose correlation structure can be associated with a bipartite graph. These correlated messages are then encoded by using correlated codewords and are reliably transmitted over the multiple-access channel -in the latter module. This leads to performance gains in terms of enlarging the class of correlated sources that can be reliably transmitted over a multiple-access channel as compared to the conventional separation approach. We provide an information-theoretic characterization of 1) the rate of exponential growth (as a function of the number of channel uses) of the size of the bipartite graphs whose edges can be reliably transmitted over a multiuser channel and 2) the rate of exponential growth (as a function of the number of source samples) of the size of the bipartite graphs which can reliably represent a pair of correlated sources to be transmitted over a multiuser channel. [ABSTRACT FROM AUTHOR]

The filter generator is an important building block in many stream ciphers. The generator consists of a linear feedback shift register of length n that generates an m-sequence of period 2′ - 1 filtered through a Boolean function of degree d that combines bits from the shift register and creates an output bit zt at any time t. The previous best attacks aimed at reconstructing the initial state from an observed keystream, have essentially reduced the problem to solving a nonlinear system of D = (Multiple line equation(s) cannot be represented in ASCII text) (i) equations in n unknowns using techniques based on linear algebra. This attack needs about D bits of keystream and the system can be solved in complexity O (Dω), where ω can be taken to be Strassen's reduction exponent ω = log2 (7) ≈ 2.807. This paper describes a new algorithm that recovers the initial state of most filter generators after observing O(D) keystream bits with complexity O((D - n)/2) ≈ O(D), after a pre-computation with complexity O(D(log2 D)³). [ABSTRACT FROM AUTHOR]

This paper presents models, algorithms and analysis for measurement-based admission control in network applications in which there is high uncertainty concerning source statistics. In the process it extends and unifies several recent approaches to admission control. A new class of algorithms is introduced based on results concerning Markov's canonical distributions. In addition, a new model is developed for the evolution of the number of flows in the admission control system. Performance evaluation is done through both analysis and simulation. Results show that the proposed algorithms minimize buffer-overflow probability among the class of all moment-consistent algorithms. [ABSTRACT FROM AUTHOR]

This paper deals with the linear-programming-based decoding algorithm of Feldman and Karger for repeat-accumulate "turbo-like" codes. We present a new structural characterization that captures the event that decoding fails. Based on this structural characterization, we develop polynomial algorithms that, given an RA (2) code, compute upper and lower bounds on the word error probability Pw for the binary-symmetric and the additive white Gaussian noise (AWGN) channels. Our experiments with an implementation of these algorithms for bounding Pw demonstrate in many interesting cases an improvement in the upper bound on the word error probability by a factor of over 1000 compared to the bounds by Feldman et al.. The experiments also indicate that the improvement in upper bound increases as the codeword length increase and the channel noise decrease. The computed lower bounds on the word error probability in our experiments are roughly ten times smaller than the upper bound. [ABSTRACT FROM AUTHOR]

Without additional resources, it is often impossible to transform one entangled quantum state into another with local quantum operations and classical communication. Jonathan and Plenio (Phys. Rev. Left., vol. 83, p. 3566, 1999) presented an interesting example showing that the presence of another state, called a catalyst, enables such a transformation without changing the catalyst. They also pointed out that in general it is very hard to find an analytical condition under which a catalyst exists. In this paper, we study the existence of catalysts for two incomparable quantum states. For the simplest case of 2 × 2 catalysts for transformations from one 4 × 4 state to another, a necessary and sufficient condition for existence is found. For the general case, we give an efficient polynomial time algorithm to decide whether a k × k catalyst exists for two n × n incomparable states, where k is treated as a constant. [ABSTRACT FROM AUTHOR]