Efficient Generation of Statistically Good Pseudonoise by Linearly Interconnected Shift Registers

Hurd, W. J.

doi:10.1109/t-c.1974.223877

Cited by 28 publications

(15 citation statements)

References 2 publications

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“…For example, for k = 11 there are only 240,064 de Bruijn sequences that can be generated by an LFSR. In addition, LFSRgenerated sequences have uniform properties (Hurd, 1974), which are counter-productive to the problem at hand, since it requires local properties of unstructuredness. Thus, de Bruijn graphs provide a much more flexible mechanism than LFSRs to generate sets of sequences with specific properties covering all k-mers.…”

Section: Resultsmentioning

confidence: 99%

Efficient Design of Compact Unstructured RNA Libraries Covering All k-mers

Orenstein

Berger

2015

Lecture Notes in Computer Science

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Current microarray technologies to determine RNA structure or measure protein-RNA interactions rely on single-stranded, unstructured RNA probes on a chip covering together all k-mers. Since space on the array is limited, the problem is to efficiently design a compact library of unstructured [-long RNA probes, where each k-mer is covered at least p times. Ray et al. designed such a library for specific values of k, [, and p using ad-hoc rules. To our knowledge, there is no general method to date to solve this problem. Here, we address the problem of finding a minimum-size covering of all k-mers by [-long sequences with the desired properties for any value of k, [, and p. As we prove that the problem is NP-hard, we give two solutions: the first is a greedy algorithm with a logarithmic approximation ratio; the second, a heuristic greedy approach based on random walks in de Bruijn graphs. The heuristic algorithm works well in practice and produces a library of unstructured RNA probes that is only *1.1-times greater in size compared to the theoretical lower bound. We present results for typical values of k and probe lengths [ and show that our algorithm generates a library that is significantly smaller than the library of Ray et al.; moreover, we show that our algorithm outperforms naive methods. Our approach can be generalized and extended to generate RNA or DNA oligo libraries with other desired properties. The software is freely available online.

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Section: Resultsmentioning

confidence: 99%

Efficient Design of Compact Unstructured RNA Libraries Covering All k-mers

Orenstein

Berger

2015

Lecture Notes in Computer Science

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“…2. Generator with a cyclic arrangement of shiftregisters as considered in [13]- [15] The sequences obtained from such a network are solutions of the following system of linear recurrence equations Due to the cyclic nature of this system, they are also solutions of…”

Section: Parallel Feedback Generatorsmentioning

confidence: 99%

“…1.b). Warlick and Hershey have based their approach to the latter class of generators on a windmill-like arrangement of LFSR's [13]. For this reason such generators are sometimes called windmill generators.…”

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confidence: 99%

Parallel Generation of Recurring Sequences

Günther¹

1990

Lecture Notes in Computer Science

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“…The work of Tausworthe [8], Whittlesey [11], and Tootill et al [9,10] has established the criteria to be achieved for generating pseudorandom numbers from linear shift register sequences based upon primitive trinomtals (PT's) over GF (2), D p + D q + 1. These criteria refer to the correlation performance as well as the distribution and runs properties.…”

Section: Introductionmentioning

confidence: 99%

Partitioning the Period of a Class of m -Sequences and Application to Pseudorandom Number Generation

Arvillias

Maritsas

1978

J. ACM

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A criterion Is derived for the "q-equipartmon" of the period of m-sequences based on pnmmve trmomlals (PT's), 1 + D q + D" It is shown that the class of PT's with q = 2 t, where t is an integer, can be implemented efficiently so as to produce m parallel q phase-shifted versions of the same m-sequence with relative delays analytically evaluated.These implementations lead to the construction ofeffioent algontlmas for the generation of q-bit pseudorandom number sequences equivalent m correlation performance to the Tausworthe-type generators. The algonthrns are of the GFSR type introduced by Lewis and Payne. The advantage of utthzmg the specific class of PT's is that the mmahzauon procedure is not reqmred. The corresponding linear recurrences threctly yield coding for the generators which delwer q-bit number sequences uncorrelated over a length approximately equal to (2 p -l)/q.It is important that three members of this class, of degreesp = 127, 175, 521, respectively, are Merserm¢ prime

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Efficient Generation of Statistically Good Pseudonoise by Linearly Interconnected Shift Registers

Cited by 28 publications

References 2 publications

Efficient Design of Compact Unstructured RNA Libraries Covering All k-mers

Efficient Design of Compact Unstructured RNA Libraries Covering All k-mers

Parallel Generation of Recurring Sequences

Partitioning the Period of a Class of m -Sequences and Application to Pseudorandom Number Generation

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