DTSC - GTSA - Comunicaciones en congresos y otros eventoshttp://hdl.handle.net/10016/262092018-08-16T10:28:22Z2018-08-16T10:28:22ZOn the information dimension rate of stochastic processesGeiger, BernhardKoch, Tobias Mircohttp://hdl.handle.net/10016/262342018-07-09T12:40:52Z2017-08-15T00:00:00ZOn the information dimension rate of stochastic processes
Geiger, Bernhard; Koch, Tobias Mirco
Jalali and Poor ("Universal compressed sensing," arXiv:1406.7807v3, Jan. 2016) have recently proposed a generalization of Rényi's information dimension to stationary stochastic processes by defining the information dimension of the stochastic process as the information dimension of k samples divided by k in the limit as k →∞ to. This paper proposes an alternative definition of information dimension as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m →∞ ; to. It is demonstrated that both definitions are equivalent for stochastic processes that are ψ*-mixing, but that they may differ in general. In particular, it is shown that for Gaussian processes with essentially-bounded power spectral density (PSD), the proposed information dimension equals the Lebesgue measure of the PSD's support. This is in stark contrast to the information dimension proposed by Jalali and Poor, which is 1 if the process's PSD is positive on a set of positive Lebesgue measure, irrespective of its support size.
Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June 2017
2017-08-15T00:00:00ZA high-SNR normal approximation for single-antenna Rayleigh block-fading channelsLancho Serrano, AlejandroKoch, Tobias MircoDurisi, Giuseppehttp://hdl.handle.net/10016/262212018-07-09T12:40:53Z2017-08-15T00:00:00ZA high-SNR normal approximation for single-antenna Rayleigh block-fading channels
Lancho Serrano, Alejandro; Koch, Tobias Mirco; Durisi, Giuseppe
This paper concerns the maximal achievable rate at which data can be transmitted over a non-coherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. In particular, a high-SNR normal approximation of the maximal achievable rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate already at SNR values of 15 dB.
Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017
2017-08-15T00:00:00ZOn LDPC Code Ensembles with Generalized ConstraintsLiu, YanfangMartínez Olmos, PabloKoch, Tobias Mircohttp://hdl.handle.net/10016/262102018-07-09T12:40:53Z2017-08-15T00:00:00ZOn LDPC Code Ensembles with Generalized Constraints
Liu, Yanfang; Martínez Olmos, Pablo; Koch, Tobias Mirco
In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without having to resort on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoder (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a success probability that depends on the GC block code and its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code. We illustrate our analysis for GLDPC code ensembles using (2, 6) and (2,15) base DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity.
Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017
2017-08-15T00:00:00Z