Topic
Pseudorandom binary sequence
About: Pseudorandom binary sequence is a research topic. Over the lifetime, 2992 publications have been published within this topic receiving 39130 citations. The topic is also known as: Pseudorandomness binary sequence & PRBS.
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TL;DR: It is shown here that time-domain probing of a multipath channel with a random binary sequence, along with utilization of CS reconstruction techniques, can provide significant improvements in estimation accuracy compared to traditional least-squares based linear channel estimation strategies.
Abstract: Compressed sensing (CS) has recently emerged as a powerful signal acquisition paradigm. In essence, CS enables the recovery of high-dimensional sparse signals from relatively few linear observations in the form of projections onto a collection of test vectors. Existing results show that if the entries of the test vectors are independent realizations of certain zero-mean random variables, then with high probability the unknown signals can be recovered by solving a tractable convex optimization. This work extends CS theory to settings where the entries of the test vectors exhibit structured statistical dependencies. It follows that CS can be effectively utilized in linear, time-invariant system identification problems provided the impulse response of the system is (approximately or exactly) sparse. An immediate application is in wireless multipath channel estimation. It is shown here that time-domain probing of a multipath channel with a random binary sequence, along with utilization of CS reconstruction techniques, can provide significant improvements in estimation accuracy compared to traditional least-squares based linear channel estimation strategies. Abstract extensions of the main results are also discussed, where the theory of equitable graph coloring is employed to establish the utility of CS in settings where the test vectors exhibit more general statistical dependencies.
452 citations
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01 Jan 1999TL;DR: The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and it is described many of its apparently unrelated occurrences.
Abstract: We discuss a well-known binary sequence called the Thue-Morse sequence, or the Prouhet-Thue-Morse sequence This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921 However, it was already implicit in an 1851 paper of Prouhet The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences
444 citations
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TL;DR: In this article, the use of chaotic sequences as spectral spreading sequences in direct-sequence spread-spectrum (DS/SS) communication systems is proposed and the error probabilities of such systems are investigated and shown to be identical to the conventional DS/SS systems which use binary signature sequences.
Abstract: The use of chaotic sequences as spectral spreading sequences in direct-sequence spread-spectrum (DS/SS) communication systems is proposed. The error probabilities of such systems are investigated and shown to be, for all practical purposes, identical to the conventional DS/SS systems which use binary signature sequences. Among the advantages of the use of chaotic sequences in DS/SS are the availability of a great number of them, the ease of their generation, as well as their inherent improvement in the security of transmission. >
443 citations
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TL;DR: An efficient prediction procedure based on the incremental parsing procedure of the Lempel-Ziv data compression algorithm is shown to achieve asymptotically the finite-state predictability of an infinite sequence.
Abstract: The problem of predicting the next outcome of an individual binary sequence using finite memory is considered. The finite-state predictability of an infinite sequence is defined as the minimum fraction of prediction errors that can be made by any finite-state (FS) predictor. It is proven that this FS predictability can be achieved by universal sequential prediction schemes. An efficient prediction procedure based on the incremental parsing procedure of the Lempel-Ziv data compression algorithm is shown to achieve asymptotically the FS predictability. Some relations between compressibility and predictability are discussed, and the predictability is proposed as an additional measure of the complexity of a sequence. >
391 citations
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TL;DR: An attempt is made to carry out a program for defining the concept of a random or patternless, finite binary sequence, and for subsequently defining arandom or patterned, infinite binary sequence to be a sequence whose initial segments are all random orpatternless finite binary sequences.
Abstract: An attempt is made to carry out a program (outlined in a previous paper) for defining the concept of a random or patternless, finite binary sequence, and for subsequently defining a random or patternless, infinite binary sequence to be a sequence whose initial segments are all random or patternless finite binary sequences. A definition based on the bounded-transfer Turing machine is given detailed study, but insufficient understanding of this computing machine precludes a complete treatment. A computing machine is introduced which avoids these difficulties.
350 citations