Trellis codes with a good distance profile constructed from expander graphs
Information Theory
2026-02-17 v2 Data Structures and Algorithms
Combinatorics
math.IT
Abstract
We derive Singleton-type bounds on the free distance and column distances of trellis codes. Our results show that, at a given time instant, the maximum attainable column distance of trellis codes can exceed that of convolutional codes. Moreover, using expander graphs, we construct trellis codes over constant-size alphabets that achieve a rate-distance trade-off arbitrarily close to that of convolutional codes with a maximum distance profile. By comparison, all known constructions of convolutional codes with a maximum distance profile require working over alphabets whose size grows at least exponentially with the number of output symbols per time instant.
Cite
@article{arxiv.2602.08718,
title = {Trellis codes with a good distance profile constructed from expander graphs},
author = {Yubin Zhu and Zitan Chen},
journal= {arXiv preprint arXiv:2602.08718},
year = {2026}
}