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A novel construction of polar codes with dynamic frozen symbols and twisted encoding scheme is proposed. It enables one to reduce the error probability and average complexity of the directed search successive cancellation decoding algorithm.
In this research paper, the problem of efficient computation of transient probability distribution of a Continuous Time Markov chain (CTMC) is addressed and a signal processing based approach is proposed. Also CTMCs whose generator matrix is a structured matrix (Toeplitz, Toeplitz-type) are considered and two efficient algorithms for the computation of transient probability distribution are proposed...
The multivariate Gaussian distribution is used to model random processes with distinct pair-wise correlations, such as stock prices that tend to rise and fall together. Multivariate Gaussian vectors with length are usually produced by first generating a vector of independent Gaussian samples, then multiplying with a correlation inducing matrix requiring multiplications. This paper presents...
In this paper, we design a precoding codebook generator with an angular channel model using eigen beamforming. We consider a codebook generator which is constructed by an eigen beamforming with a channel state rotation matrix. The transmission signals are rotated by a real (θ) and a complex (φ) phase angle in the channel. Complex phase rotation (φ) depends on real phase angle (θ) and it has a free...
We consider the problem of designing H2 and H∞ linear estimators for time-varying spatially interconnected systems distributed in one spatial dimension. In general, numerical implementation of the algebraic Riccati equation (ARE) solution for such systems is a complex and computationally expensive operation. However, the spatially interconnected systems can be described by state-space models whose...
From our earlier works, we know that in the case of analog codes, a Turbo-like iterative decoding can be nicely illustrated as iterative projections onto super codes that correspond to parts of the parity check matrix. So-called LCD (linear code with complementary dual) codes are recognized as a counterpart in finite fields for the orthogonal case, where two iterative projections lead to the final...
In Fall 2009, the final step of the factorization of rsa768 was carried out on several clusters of the Grid'5000 platform, leading to a new record in integer factorization. This step involves solving a huge sparse linear system defined over the binary field GF(2). This article aims at describing the algorithm used, the difficulties encountered, and the methodology which led to success. In particular,...
We develop fast parallel solutions to a number of basic problems involving solvable and nilpotent permutation groups. Testing solvability is in NC, and RNC includes, for solvable groups, finding order, testing membership, finding the derived series and finding a composition series. Additionally, for nilpotent groups, one can, in RNC, find the center, a central composition series, and point-wise stabilizers...
A new simple algorithm for the decomposition of the state space of a dynamical system into the minimal number of cyclic subspaces is proposed. This algorithm allows to perform the transformation to the Jordan form using the same fast techniques already known for systems with a cyclic dynamical matrix. The proposed algorithm does not introduce any assumption on the considered system and gives also,...
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