With the development of communication technology, modern communication networks
need to achieve ultra-high reliability to meet practical demands. Forward error correction
coding has been widely used in real-world communication systems for providing reliable
data transmission over noisy channels. In this thesis, we investigate the efficient performance
evaluation methods for block codes over memoryless channels. Performance bounds
are powerful tools to provide insights on the error performance of the coded systems. In
many practical scenarios where performance bounds are not applicable (e.g., due to the
unavailability of the relevant coding parameters under a given decoder), the Monte Carlo
simulation is still popular despite its inefficiency, especially in the low error probability
regi...[
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With the development of communication technology, modern communication networks
need to achieve ultra-high reliability to meet practical demands. Forward error correction
coding has been widely used in real-world communication systems for providing reliable
data transmission over noisy channels. In this thesis, we investigate the efficient performance
evaluation methods for block codes over memoryless channels. Performance bounds
are powerful tools to provide insights on the error performance of the coded systems. In
many practical scenarios where performance bounds are not applicable (e.g., due to the
unavailability of the relevant coding parameters under a given decoder), the Monte Carlo
simulation is still popular despite its inefficiency, especially in the low error probability
regime. As a variance-reduction technique, importance sampling (IS) can significantly
reduce the sample size needed for reliable estimation.
We firstly examine the problem of efficient performance evaluation of linear block
codes over binary symmetric channels (BSCs). Contrary to the conventional wisdom, we
prove that for BSCs, all bounds based on Gallager’s first bounding technique, including
the famous union bound, are not asymptotically tight for all possible choices of the Gallager
region. By proposing the so-called input demodulated-output weight enumerating
function (IDWEF) of a code, asymptotically tight maximum-likelihood decoding upper
and lower bounds for BSCs are derived. For the cases that coding parameters are absent
or suboptimal decoders are applied, we propose an efficient IS estimator by deriving the optimal IS distribution of the Hamming weight of the error vector. In addition, the
asymptotic percentage saving of the proposed IS estimator over the state-of-the-art IS
estimator is characterized in terms of the sample size. Its accuracy in predicting the
efficiency of the proposed IS estimator is verified by extensive computer simulation.
We further examine the IS estimator design and efficiency analysis problems for the
additive white generalized Gaussian noise (AWGGN) channel. The generalized Gaussian
distribution is an effective model to describe real-world systems with impulsive noise. It
can be specialized to the Laplace and Gaussian distributions depending on the choices
of the decay rates of the heavy tail. By deriving the optimal IS distribution on the one-dimensional
space mapped from the observation space, we present a general framework
for designing IS estimators for linear block codes over a memoryless continuous channel.
We apply the framework to the AWGGN channel and propose a noise-magnitude-domain
IS (NM-IS) estimator. As an efficiency measure, the asymptotic IS gain of the proposed
estimator is derived in a multiple integral as the signal-to-noise ratio (SNR) tends to
infinity. Specifically, we reduce the gains of both Laplace and Gaussian noise cases to
a one-dimensional integral. In addition, by limiting the use of the union bound to an
L
1-norm sphere with an optimized radius, we derive the sphere bound for the additive
white Laplace noise channel. Simulation results show the efficiency of the proposed IS
estimator in terms of the sample size and verify the accuracy of the prediction of the
derived IS gain.
Besides, we specialize the proposed framework to further improve the efficiency of the
IS simulation based on the side information of the modulation. For the AWGGN channel
with binary phase-shift keying (BPSK) modulation, we propose an enhanced NM-IS
estimator, which outperforms the NM-IS estimator in efficiency. For the additive white
Gaussian noise channel with M-PSK modulation, we propose an angular domain IS estimator
and provide its efficiency analysis in terms of the asymptotic IS gain. Furthermore,
in the performance evaluation of communication systems, it is often seen that researchers
are more interested in the required SNR at a target error probability P
e than the other way
around. The conventional solution to this P
e-targeted SNR estimation problem involves
interpolation of simulated error probabilities at multiple handpicked SNRs for estimating
the required SNR at the target error probability. We propose a P
e-targeted iterative IS
estimator that solves the problem algorithmically. The proposed method can achieve the
same efficiency (in terms of sample size) as estimating the error probability at the required SNR and allow the confidence interval of the SNR estimate to be obtained.
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