0000000000190265
AUTHOR
Matteo Campanella
On the ∗-cocharacter sequence of 3×3 matrices
Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…
Relation Between the State of a System as Isolated and as Open
We discuss the differences in considering the description of a system as isolated or as a subsystem of a wider isolated system. In the latter case, a description in terms of a density operator directly arises without involving probability concepts, but as an orbit invariant. The non-probabilistic physical interpretation of the density operator is mathematically discussed.
Simple method for limiting delay of optimized interleavers for turbo-codes
An iterative interleaver growth algorithm is extended to allow the delay and required memory of designed interleavers to be halved with negligible performance loss. The original algorithm is efficient for two-component parallel concatenated turbo-codes with given constituent encoders that are optimum with regard to a cost function satisfying some mild conditions. However, it is only actually optimum if the selected set of patterns is representative of low-weight turbo-codewords. The new interleaver uses all terminating error patterns having an input weight not greater than a fixed IWX and single-coder output weight not greater than WX is proposed.
The Probability Law for Generic Density Operators
In this chapter, the probability law of the non-null eigenstates of a generic density operator—studied in the previous chapter—is determined, by showing that given the composite system and the subsystem being considered, a mapping arises which associates a universal probability distribution to the non-null eigenstates of the generic density operator. We thus recover the Born statistical interpretation without having assumed it as a postulate.
Statistical analysis of RaptorQ failure probability applied to a data recovery software
In this work, we have implemented a data recovery software integrating the most recent rateless codes, i.e., RaptorQ codes. Thanks to the above-mentioned software, it is possible to recover data loss occurring on several kinds of network conditions. We have performed a statistical analysis of failure probabilities at several configurations of RaptorQ parameters. We have found a good agreement with the theoretical values of a random linear fountain code over Galois Field GF(256). Moreover, we have shown that the probability of having a certain number of failed decoded source blocks - when sending a fixed size file - follows a Poisson distribution.
The State of a Quantum System as a Subsystem of a Composite System
The notion of state in quantum systems is analized, a non-probabilistic definition of state provided, the Zurek’s concept of envariance is mathematically formulated, and the characterization of a state through its properties is discussed.
A simple joint estimation-detection technique for OFDM systems
In this work a simple approach for the joint estimation-detection in a frequency selective severe fading environment of OFDM signals adopting PSK constellations is presented. A linear predictor of suitable order is adopted for the channel estimation in the frequency domain. The predictor coefficients are estimated on the basis of a sample estimation of the autocorrelation of the channel frequency response, aided by a preliminary differential decoding, in a blockwise manner. The detection technique proposed here is based on a simple tree search where a small number of best survivor paths are maintained at each step. Despite the simplicity of above detection approach, the simulation results s…
Fading mitigation coding techniques for space to ground free space optical communications (Euro Med Telco 2014)
In this manuscript, a Geostationary satellite-toground Free Space Optics (FSO) downlink channel model has been implemented, which is able to predict temporal irradiance fluctuations caused by scintillation at a wide range of turbulence conditions and for different values of the zenith angle. In order to mitigate fading events that occur in FSO communications, we have also tested the performance of three different families of Rateless Codes (Luby Transform, Raptor and RaptorQ) into our model and found that RaptorQ is the best candidate to mitigate errors in FSO links.
A study on spectral optimisation in partial response CPM signals
An optimisation technique for the minimisation of the effective bandwidth in partial response CPM signals is described. The minimum Euclidean distance is used as optimisation constraint because the bit error probability is a function of this parameter for high values of signal to noise ratio. The procedure has been implemented for a correlation length corresponding to two signalling intervals. The optimisation problem leads to a system of two nonlinear differential equations for the pulse shape, together with some boundary conditions. Numerical solution of the differential equations has been performed; initial conditions have been adjusted, to satisfy the boundary conditions using an iterat…
The structure of the state representation of shift invariant controllable and observable group codes
AbstractIn this paper an investigation on the structure of the canonical trellis section of shift invariant, l-controllable and m-observable group codes is carried out. Necessary and sufficient conditions for a set of group homomorphisms in order that they represent the trellis section of this class of codes are established.
Fading mitigation coding techniques for space to ground free space optical communications
In this manuscript, a Geostationary satellite-toground Free Space Optics (FSO) downlink channel model has been implemented, which is able to predict temporal irradiance fluctuations caused by scintillation at a wide range of turbulence conditions and for different values of the zenith angle. In order to mitigate fading events that occur in FSO communications, we have also tested the performance of three different families of Rateless Codes (Luby Transform, Raptor and RaptorQ) into our model and found that RaptorQ is the best candidate to mitigate errors in FSO links. Keywords— Optical Wireless Communications; Space-toGround FSO links, time-series, rateless codes; fading mitigation
Design of efficient codes for the AWGN channel based on decomposable binary lattices
This work is concerned with the use of binary decomposable lattice codes over the QAM Gaussian channel. First, we investigate the structure of such class of lattices: we derive consistency conditions for the binary codes appearing in their decomposition and express their nominal coding gain and some bounds for their error coefficient in terms of the parameters of the component codes. Then we describe a general multistage bounded‐distance decoding algorithm with low complexity and we evaluate its performance. Finally, we develop a design example and report the corresponding simulation results; as a reference some comparisons with standard TCM codes are also presented.