Symbol Alphabet Size Research Articles

Neural Probabilistic Forecasting of Symbolic Sequences With Long Short-Term Memory

This paper makes use of long short-term memory (LSTM) neural networks for forecasting probability distributions of time series in terms of discrete symbols that are quantized from real-valued data. The developed framework formulates the forecasting problem into a probabilistic paradigm as hΘ: X × Y → [0, 1] such that ∑y∈YhΘ(x,y)=1, where X is the finite-dimensional state space, Y is the symbol alphabet, and Θ is the set of model parameters. The proposed method is different from standard formulations (e.g., autoregressive moving average (ARMA)) of time series modeling. The main advantage of formulating the problem in the symbolic setting is that density predictions are obtained without any significantly restrictive assumptions (e.g., second-order statistics). The efficacy of the proposed method has been demonstrated by forecasting probability distributions on chaotic time series data collected from a laboratory-scale experimental apparatus. Three neural architectures are compared, each with 100 different combinations of symbol-alphabet size and forecast length, resulting in a comprehensive evaluation of their relative performances.

Low-complexity iterative channel estimation for serially concatenated systems over frequency-nonselective Rayleigh fading channels

A low-complexity iterative maximum a posteriori (MAP) channel estimator is proposed whose complexity increases linearly with the symbol alphabet size 'M. Prediction-based MAP channel estimation is not appropriate with a high-order prediction filter or a large modulation alphabet size, since the computational complexity increases with ML , where L is the predictor order. In contrast, the proposed channel estimator has a constant number of trellis states regardless of the prediction filter order, and is shown to provide comparable error performance to the prediction-based MAP estimator

Hermitian codes for frequency-hop spread-spectrum packet radio networks

Hermitian codes are an attractive alternative to Reed-Solomon codes for use in frequency-hop spread-spectrum packet radio networks. For a given alphabet size, a Hermitian code has a much longer block length than a Reed-Solomon code. This and other considerations suggest that Hermitian codes may be superior for certain applications. Analytical results are developed for the evaluation of the packet error probability for frequency-hop transmissions using Hermitian coding. We find there are several situations for which Hermitian codes provide much lower packet error probabilities than can be obtained with Reed-Solomon codes. In general, as the code rate decreases or the symbol alphabet size increases, the relative performance of Hermitian codes improves with respect to Reed-Solomon codes. Performance evaluations are presented for an additive white Gaussian noise channel and for certain partial-band interference channels, and the packet error probability is evaluated for both errors-only and errors-and-erasures decoding.

Accurate evaluation for MDPSK with noncoherent diversity

The error probability analysis of M-ary differential phase-shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases. The difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal, and this often leads to a mathematically intractable issue. In this paper, we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output. We further derive fast convergent techniques for two-dimensional (2-D) inverse Laplace transform enabling us to accurately evaluate the phase distribution. The error probability formulas thus obtained involve a twofold integral, which can be efficiently evaluated by using our algorithms developed on the basis of the 2-D trapezoidal summation and Gauss-Chebyshev quadrature. The new technique is very general, taking into account the effects of arbitrary diversity order, symbol alphabet size M, and arbitrary diversity branches correlation. Numerical results are also presented for illustration.