On the Achievable Information Rates of Finite-State Input Two-Dimensional Channels with Memory

Ori Shental; Noam Shental; Shlomo Shamai

Home/Archive/arXiv

arXiv · cs/0502077

On the Achievable Information Rates of Finite-State Input Two-Dimensional Channels with Memory

Ori Shental·Noam Shental·Shlomo Shamai

View original source ↗Read source document ↗Export metadata ↓

Abstract

The achievable information rate of finite-state input two-dimensional (2-D) channels with memory is an open problem, which is relevant, e.g., for inter-symbol-interference (ISI) channels and cellular multiple-access channels. We propose a method for simulation-based computation of such information rates. We first draw a connection between the Shannon-theoretic information rate and the statistical mechanics notion of free energy. Since the free energy of such systems is intractable, we approximate it using the cluster variation method, implemented via generalized belief propagation. The derived, fully tractable, algorithm is shown to provide a practically accurate estimate of the information rate. In our experimental study we calculate the information rates of 2-D ISI channels and of hexagonal Wyner cellular networks with binary inputs, for which formerly only bounds were known.

Explore related subjects

cs.IT math.IT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ori Shental, Noam Shental, Shlomo Shamai. 2005-02-18. On the Achievable Information Rates of Finite-State Input Two-Dimensional Channels with Memory. https://arxiv.org/abs/cs/0502077

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

KEEP EXPLORING

Related papers

arXiv2026

A mathematical study of the excess growth rate

The excess growth rate, defined as the gap in Jensen's inequality for the logarithm, is a fundamental functional in portfolio theory. In this paper, we present a mathematical study motivated by information theory. We begin by establishing its properties and showing that it has rich connections with information-theoretic concepts such as the Helmholtz free energy, L. Campbell's measure of average code length and large deviations. Our main results consist of three axiomatic characterization theorems of the excess growth rate, in terms of (i) the relative entropy, (ii) the gap in Jensen's inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. Furthermore, we study maximization of the excess growth rate and compare it with Kelly's growth optimal portfolio. Our results not only provide theoretical justifications of the significance of the excess growth rate, but also establish new connections between information theory and quantitative finance.

cs.IT↗

arXiv2026

A Unified Pulse-Shaped OFDM Framework for Chirp-Domain Waveforms: Continuous-Time Modeling and Practical I/O Analysis

A unified framework for chirp-domain waveforms, including orthogonal chirp division multiplexing (OCDM) and affine frequency division multiplexing (AFDM), is developed. Their continuous-time representations are shown to fall within the conventional Weyl-Heisenberg (WH) framework for multicarrier waveforms, with the root chirp as the prototype pulse. Since the root chirp has constant envelope and is transparent to subcarrier orthogonality, these waveforms can be further interpreted as pulse-shaped (PS) orthogonal frequency division multiplexing (OFDM) signals, whose power spectral density is derived analytically. The derived spectrum reveals that implementations based on the discrete affine Fourier transform rely on sub-Nyquist samples and exhibit frequency aliasing. We prove that the corresponding aliased chirps are only conditionally orthogonal, whereas sample-wise root-Nyquist pulse shaping of the discrete-time AFDM (DT-AFDM) sequence produces mutually orthogonal pulse-shaped chirps, resulting in the pulse-shaped AFDM (PS-AFDM) waveform. We then derive an exact waveform-level input-output (I/O) relation for PS-AFDM over delay-Doppler (DD) channels, showing that the effective channel at a practical receiver is generally not a superposition of pure path-wise DD components. Waveform simulations verify the derived relation to machine precision, while the conventional sequence-level I/O relation for DT-AFDM exhibits a substantial mismatch with waveform behavior for practical channels with continuous-valued delays.

cs.IT↗

arXiv2026

Domain-Adaptive Deep Joint Source-Channel Coding for Image Classification

Deep joint source--channel coding (Deep JSCC) can suffer from domain shift between training and deployment data. We study single-source domain adaptation for image classification over wireless channels. A Gaussian example shows that improving channel quality does not necessarily improve target-domain accuracy under a fixed source-trained classifier. We further proposed an information objective to reduce domain information while preserving class information. Motivated by the analysis, we develop a domain-adaptive Deep JSCC method that combines class-wise adversarial alignment with pseudo-label supervised contrastive learning. The former uses all target samples to reduce class-conditional domain differences, while the latter selects high-confidence target samples to obtain class-discriminative received representations. We relate these losses to the information objective, and analyze the effects of pseudo-label errors and confidence-based selection. Experiments on SVHN--MNIST and PACS over AWGN and Rayleigh channels demonstrate improved target-domain classification without additional inference-time networks. The proposed method achieves 98.15\% accuracy on SVHN $\rightarrow$ MNIST at 10~dB CSNR.

cs.IT↗