Dual Capacity Upper Bounds on Channels with Memory (PhD Viva Voce)

Abstract: Computing the capacity of noisy channels with memory and finite input alphabets is difficult to characterize explicitly in many cases. Exact capacity expressions are known only for special cases, making tight upper bounds essential for understanding fundamental limits. This work develops practical methods for computing such bounds using duality theory.

We study two channel classes with distinct types of memory: binary-input Gaussian channels with Inter-Symbol Interference (ISI), where memory arises from temporal dispersion, and Binary-Input Binary-Output (BIBO) channels with runlength constraints, where memory is imposed by input restrictions. For both classes, we employ the dual capacity bound with carefully designed Markov test distributions.

The key challenge in applying dual bounds is selecting test distributions that are both computationally tractable and yield tight bounds. For single-tap ISI channels, we introduce piecewise constant weighted test distributions combining Gaussian and constant density components. This construction leads to finite-dimensional optimization problems solvable by standard numerical methods. Computational complexity is further reduced by exploiting cycle basis representations and symmetry properties of the channel trellis.

We validate our approach on the dicode channel, a canonical ISI model extensively studied in the literature. Our bounds improve upon all previously published upper bounds across a wide range of SNRs. For BIBO channels with the constraint prohibiting consecutive 1s, we derive analytic expressions that improve upon feedback capacity bounds.

Finally, we extend our methodology to multi-tap ISI channels, demonstrating computational feasibility for two-tap cases and establishing a framework for analyzing channels with longer memory.

Event Details
Title: Dual Capacity Upper Bounds on Channels with Memory (PhD Viva Voce)
Date: June 18, 2026 at 04:00 PM
Venue: Google Meet (https://meet.google.com/bgp-texm-ujf)
Speaker: Mr. Ajay M (EE12D030)
Guide: Dr. Andrew Thangaraj
Type: PHD seminar