Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0707.0479

Precoding for the AWGN Channel with Discrete Interference

Hamidreza Farmanbar·Amir K. Khandani
View original source ↗Read source document ↗Export metadata ↓

Abstract

For a state-dependent DMC with input alphabet $\mathcal{X}$ and state alphabet $\mathcal{S}$ where the i.i.d. state sequence is known causally at the transmitter, it is shown that by using at most $|\mathcal{X}||\mathcal{S}|-|\mathcal{S}|+1$ out of $|\mathcal{X}|^{|\mathcal{S}|}$ input symbols of the Shannon's \emph{associated} channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter, $M$-ary signal transmission over AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. For the special case where the Gaussian noise power is zero, a sufficient condition, which is independent of interference, is given for the capacity to be $\log_2 M$ bits per channel use. The problem of maximization of the transmission rate under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet is investigated. For this setting, the general structure of a communication system with optimal precoding is proposed.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hamidreza Farmanbar, Amir K. Khandani. 2007-07-03. Precoding for the AWGN Channel with Discrete Interference. https://arxiv.org/abs/0707.0479

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bistatic Target Detection by Exploiting Both Deterministic Pilots and Unknown Random Data Payloads

Integrated sensing and communication (ISAC) plays a crucial role in 6G, enabling innovative applications such as drone surveillance, urban air mobility, and low-altitude logistics. However, the hybrid ISAC signal, which comprises deterministic pilot and random data payload components, poses challenges for target detection due to two reasons: 1) these two components cause coupled shifts in both the mean and variance of the received signal, and 2) the random data payloads are typically unknown to the sensing receiver in the bistatic setting. Unfortunately, these challenges could not be tackled by existing target detection algorithms. In this paper, a generalized likelihood ratio test (GLRT)-based detector is derived by leveraging the known deterministic pilots and the statistical characteristics of the unknown random data payloads. Due to the analytical intractability of exact performance characterization, we perform an asymptotic analysis for the false alarm probability and detection probability of the proposed detector. The results reveal a deterministic-random trade-off: the deterministic pilots enhance detection through a target-induced mean shift, while the random data payloads provide an additional covariance-domain target signature but simultaneously introduce statistical uncertainty due to their unknown realizations. Simulations validate the theoretical findings and demonstrate the effectiveness of the proposed detector, which highlights the necessity of designing a dedicated detector to fully exploit the signaling resources assigned to random data payloads.

cs.IT↗
arXiv2026

Second-Order Schalkwijk-Kailath Coding for Autoregressive Gaussian Channels

We study noiseless-feedback communication over Gaussian channels with stationary autoregressive (AR) noise of arbitrary finite order. We introduce a class of Gaussian linear-feedback coding schemes based on the celebrated Schalkwijk--Kailath (SK) coding scheme, called SK(2), whose message process follows a second-order deterministic recursion, and derive a closed-form characterization of its maximal achievable rate under average power constraint $P$. As a first-order benchmark, we formulate SK(1) as a sign-consistent, branch-complete version of the real constant signed-ratio specialization of Butman's linear-feedback construction. For stationary AR($p$) Gaussian channels, optimizing over recursions with both characteristic roots outside the unit circle gives the same rate supremum as optimizing over all SK(2) recursions and yields a rate no smaller than the maximal SK(1) rate. The SK(2) scheme achieves feedback capacity for the AWGN channel, stationary AR(1) Gaussian channels, and a subclass of stationary AR(2) Gaussian channels obtained by interleaving two independent AR(1) noise processes. For the interleaved subclass, we show that a genuine SK(2) scheme strictly outperforms SK(1). Numerical comparisons illustrate further strict rate gains over a broader range of AR(2) parameters. These results show that the SK(1) scheme is not universally optimal beyond AR(1) noise and disprove a corrected form of Butman's conjecture.

cs.IT↗
arXiv2026

Computing the entropy rate of a quantized stationary Gaussian process

The entropy rate of a uniformly quantized stationary Gaussian process is the fundamental limit on its lossless compression. It has no closed form, and the classical high-resolution approximation breaks down whenever the spectral density is small on part of the band, as routine smoothing and filtering produce. Here we present two methods for computing the rate. The first is an analytical approximation, obtained from an exact dithering identity and the Kolmogorov-Szegő formula, in which the quantization noise power acts as a floor on the spectral density. The second is a Monte Carlo estimate of the exact rate: a minimum-phase moving-average representation makes the quantized sequence a hidden Markov process whose optimal particle filter is available in closed form, and the filter's log-likelihood on one long sequence gives the rate. The approximation agrees with the estimate to within a few millibits per sample over most of the parameter range for quantization steps up to the signal standard deviation, including processes on which the classical formula fails; for coarser steps the estimate should be used instead. At a step of a quarter of the standard deviation, linear predictive coding comes within 2 to 4 percent of the rate, FLAC within 3 to 32 percent, and general-purpose compressors remain 12 to 89 percent above it.

cs.IT↗