3 research outputs found
Easily Computed Lower Bounds on the Information Rate of Intersymbol Interference Channels
Provable lower bounds are presented for the information rate I(X; X+S+N)
where X is the symbol drawn independently and uniformly from a finite-size
alphabet, S is a discrete-valued random variable (RV) and N is a Gaussian RV.
It is well known that with S representing the precursor intersymbol
interference (ISI) at the decision feedback equalizer (DFE) output, I(X; X+S+N)
serves as a tight lower bound for the symmetric information rate (SIR) as well
as capacity of the ISI channel corrupted by Gaussian noise. When evaluated on a
number of well-known finite-ISI channels, these new bounds provide a very
similar level of tightness against the SIR to the conjectured lower bound by
Shamai and Laroia at all signal-to-noise ratio (SNR) ranges, while being
actually tighter when viewed closed up at high SNRs. The new lower bounds are
obtained in two steps: First, a "mismatched" mutual information function is
introduced which can be proved as a lower bound to I(X; X+S+N). Secondly, this
function is further bounded from below by an expression that can be computed
easily via a few single-dimensional integrations with a small computational
load.Comment: 14 pages, 14 figures including subfigures. arXiv admin note:
substantial text overlap with arXiv:1001.391
Lower Bounds and Approximations for the Information Rate of the ISI Channel
We consider the discrete-time intersymbol interference (ISI) channel model,
with additive Gaussian noise and fixed i.i.d. inputs. In this setting, we
investigate the expression put forth by Shamai and Laroia as a conjectured
lower bound for the input-output mutual information after application of a
MMSE-DFE receiver. A low-SNR expansion is used to prove that the conjectured
bound does not hold under general conditions, and to characterize inputs for
which it is particularly ill-suited. One such input is used to construct a
counterexample, indicating that the Shamai-Laroia expression does not always
bound even the achievable rate of the channel, thus excluding a natural
relaxation of the original conjectured bound. However, this relaxed bound is
then shown to hold for any finite entropy input and ISI channel, when the SNR
is sufficiently high. Finally, new simple bounds for the achievable rate are
proven, and compared to other known bounds. Information-Estimation relations
and estimation-theoretic bounds play a key role in establishing our results.Comment: 21 pages, 4 figure
Comparison of the Achievable Rates in OFDM and Single Carrier Modulation with I.I.D. Inputs
We compare the maximum achievable rates in single-carrier and OFDM modulation
schemes, under the practical assumptions of i.i.d. finite alphabet inputs and
linear ISI with additive Gaussian noise. We show that the Shamai-Laroia
approximation serves as a bridge between the two rates: while it is well known
that this approximation is often a lower bound on the single-carrier achievable
rate, it is revealed to also essentially upper bound the OFDM achievable rate.
We apply Information-Estimation relations in order to rigorously establish this
result for both general input distributions and to sharpen it for commonly used
PAM and QAM constellations. To this end, novel bounds on MMSE estimation of PAM
inputs to a scalar Gaussian channel are derived, which may be of general
interest. Our results show that, under reasonable assumptions, optimal
single-carrier schemes may offer spectral efficiency significantly superior to
that of OFDM, motivating further research of such systems.Comment: Revised version of IEEE IT submission. Includes new results on
uniform input