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In a recent work, Bernardini and Rinaldo generalize and attempt to improve upon Elias method to obtain unbiased random bits from a geometric distribution resulted from a Poisson process. As a response, we analyse the output rates of their method and compare with the original binary Elias method applied on a Bernoulli process resulted from the same Poisson process, which turns out to be much simpler to implement and to have a higher output rate. [ABSTRACT FROM AUTHOR]

We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is conjectured to exhibit a sharp information-theoretic threshold, below which the signal is too weak for any algorithm to detect. We derive upper and lower bounds on these thresholds by applying the first and second moment methods to the likelihood ratio between these “planted models” and null models where the signal matrix is zero. For sparse PCA and submatrix localization, we determine this threshold exactly in the limit where the number of blocks is large or the signal matrix is very sparse; for the clustering problem, our bounds differ by a factor of $\sqrt {2}$ when the number of clusters is large. Moreover, our upper bounds show that for each of these problems there is a significant regime where reliable detection is information-theoretically possible but where known algorithms such as PCA fail completely, since the spectrum of the observed matrix is uninformative. This regime is analogous to the conjectured “hard but detectable” regime for community detection in sparse graphs. [ABSTRACT FROM AUTHOR]

For non-binary codes the Elias bound is a good upper bound for the asymptotic information rate at low-relative minimum distance, whereas the Plotkin bound is better at high-relative minimum distance. In this paper, we obtain a hybrid of these bounds, which improves both. This in turn is based on the anticode bound, which is a hybrid of the Hamming and Singleton bounds and improves both bounds. The question of convexity of the asymptotic rate function is an important open question. We conjecture a much weaker form of the convexity, and we show that our bounds follow immediately if we assume the conjecture. [ABSTRACT FROM AUTHOR]

The problem of generating a sequence of true random bits (suitable for cryptographic applications) from random discrete or analog sources is considered. A generalized version, including vector quantization, of the classical approach by Elias for the generation of truly random bits is introduced, and its performance is analyzed, both in the finite case and asymptotically. The theory allows us to provide an alternative proof of the optimality of the original Elias' scheme. We also consider the problem of deriving random bits from measurements of a Poisson process and from vectors of iid Gaussian variables. The comparison with the scheme of Elias, applied to geometric-like non-binary vectors, originally based on the iso-probability property of permutations of iid variables, confirms the potential of the generalized scheme proposed in our work. [ABSTRACT FROM AUTHOR]

Next-generation sequencing (NGS) technologies permit the rapid production of vast amounts of data at low cost. Economical data storage and transmission hence becomes an increasingly important challenge for NGS experiments. In this paper, we introduce a new non-reference based read sequence compression tool called SRComp. It works by first employing a fast string-sorting algorithm called burstsort to sort read sequences in lexicographical order and then Elias omega-based integer coding to encode the sorted read sequences. SRComp has been benchmarked on four large NGS datasets, where experimental results show that it can run 5–35 times faster than current state-of-the-art read sequence compression tools such as BEETL and SCALCE, while retaining comparable compression efficiency for large collections of short read sequences. SRComp is a read sequence compression tool that is particularly valuable in certain applications where compression time is of major concern. [ABSTRACT FROM AUTHOR]

Our physical environment is a natural storage where we can store and share information. For instance, a stop sign is a piece of information implanted in a particular location. In this paper, we propose a storage underlay platform called “ELIAS” (Every Location Is A Storage) for a mobile peer-to-peer system. ELIAS enables user applications to transparently save/retrieve data items to/from a location without concerning with low-level detailed implementation. The underlying platform chooses appropriate mobile nodes to store/retrieve data items. We discuss an efficient implementation of ELIAS, and present a detailed analytical model that is validated by simulation. Finally, we show results of sensitivity analysis on a variety of factors that impact the performance of ELIAS. [ABSTRACT FROM AUTHOR]