Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are suggested.Comment: submitte

Secure quantum key distribution using squeezed states

We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor e^r=1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel.Comment: 19 pages, 3 figures, RevTeX and epsf, new section on channel losse

Pseudo noise code and data transmission method and apparatus

Pseudo noise ranging codes, having a predetermined chipping rate, and a pair of binary data sources, each having a bit rate no greater than one tenth the chipping rate, quadriphase, digitally modulate a suppressed carrier wave having a first frequency are examined. Two additional binary data sources, each having a bit rate that is not restricted by the chipping rate of the first carrier, quadriphase, digitally modulate a suppressed carrier wave having a second frequency. The first and second frequencies are only slightly displaced so that there is overlap in the frequency bands which modulate the two carriers. The two suppressed carrier waves are linearly combined and transmitted from a first station to a second station so that the amplitude of the transmitted first wave is controlled so as not to degrade the detectability of the second wave at the second station

Pseudo-random number generators for Monte Carlo simulations on Graphics Processing Units

Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX and Mersenne Twister (MT19937)) on CPU and GPU are discussed. The obtained speed-up factor is hundreds of times in comparison with CPU. RANLUX generator is found to be the most appropriate for using on GPU in Monte Carlo simulations. The brief review of the pseudo-random number generators used in modern software packages for Monte Carlo simulations in high-energy physics is present.Comment: 31 pages, 9 figures, 3 table

Luby Transform Coding Aided Bit-Interleaved Coded Modulation for the Wireless Internet

Bit-Interleaved Coded Modulation using Iterative Decoding (BICM-ID) is amalgamated with Luby Transform (LT) coding. The resultant joint design of the physical and data link layer substantially improves the attainable Bit Error Rate (BER) performance. A Cyclic Redundancy Check (CRC) combined with a novel Log-Likelihood Ratio (LLR) based packet reliability estimation method is proposed for the sake of detecting and disposing of erroneous packets. Subsequently, bit-by-bit LT decoding is proposed, which facilitates a further BER improvement at a lower number of BICM-ID iterations. Finally, we revisit the pseudo random generator function used for designing the LT generator matrix

On the Combinatorial Version of the Slepian-Wolf Problem

We study the following combinatorial version of the Slepian-Wolf coding scheme. Two isolated Senders are given binary strings $X$ and $Y$ respectively; the length of each string is equal to $n$, and the Hamming distance between the strings is at most $\alpha n$. The Senders compress their strings and communicate the results to the Receiver. Then the Receiver must reconstruct both strings $X$ and $Y$. The aim is to minimise the lengths of the transmitted messages. For an asymmetric variant of this problem (where one of the Senders transmits the input string to the Receiver without compression) with deterministic encoding a nontrivial lower bound was found by A.Orlitsky and K.Viswanathany. In our paper we prove a new lower bound for the schemes with syndrome coding, where at least one of the Senders uses linear encoding of the input string. For the combinatorial Slepian-Wolf problem with randomized encoding the theoretical optimum of communication complexity was recently found by the first author, though effective protocols with optimal lengths of messages remained unknown. We close this gap and present a polynomial time randomized protocol that achieves the optimal communication complexity.Comment: 20 pages, 14 figures. Accepted to IEEE Transactions on Information Theory (June 2018