  The common approach of designing a communication device is to maximize a
well-defined objective function, e.g., the channel capacity and the cut-off
rate. We propose easy-to-implement solutions for Gaussian channels that
approximate the optimal results for these maximization problems. Three topics
are addressed. First, we consider the case where the channel output is
quantized, and we find the quantization thresholds that maximize the mutual
information. The approximation derived from the asymptotic solution has a
negligible loss on the entire range of SNR when 2-PAM modulation is used, and
its quantization thresholds linearly depend on the standard deviation of noise.
We also derive a simple estimator of the relative capacity loss due to
quantization, based on the high-rate limit. Then we consider the integer
constraint on the decoding metric, and maximize the mismatched channel
capacity. We study the asymptotic solution of the optimal metric assignment and
show that the same approximation we derived in the matched decoding case still
holds for the mismatched decoder. Finally, we consider the demodulation problem
for 8PSK bit-interleaved coded modulation(BICM). We derive the approximated
optimal demodulation metrics that maximize the general cut-off rate or the
mismatched capacity using max-log approximation . The error rate performances
of the two metrics' assignments are compared, based on
Reed-Solomon-Viterbi(RSV) code, and the mismatched capacity metric turns out to
be better. The proposed approximation can be computed using an efficient
firmware algorithm, and improves the system performance of commercial chips.
