# Poset-Markov Channels: Capacity via Group Symmetry

arXiv: https://arxiv.org/abs/2506.19305 · HTML: https://mlsanity.com/paper/2506.19305/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Warm-starting PDE solvers with any-dimensional machine learning](https://mlsanity.com/paper/2609.38916/) (2026)

## Abstract (arXiv)

Computing channel capacity is in general intractable because it is given by the limit of a sequence of optimization problems whose dimensionality grows to infinity. As a result, constant-sized characterizations of feedback or non-feedback capacity are known for only a few classes of channels with memory. This paper introduces poset-causal channelsunicodex2014a new formalism of a communication channel in which channel inputs and outputs are indexed by the elements of a partially ordered set (poset). We develop a novel methodology that allows us to establish a single-letter upper bound on the feedback capacity of a subclass of poset-causal channels whose memory structure exhibits a Markov property and symmetry. The methodology is based on symmetry reduction in optimization. We instantiate our method on two channel models: the Noisy Output is The STate (NOST) channelunicodex2014for which the bound is tightunicodex2014and a new two-dimensional extension of it.