Uploaded June 2026 | Updated September 2026, 3 days ago
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 3, Session 2
Speaker: Pavel Panteleev (Moscow)
Title: The Mathematics of Bad LDPC Codes
Abstract: Almost all LDPC codes used in practice are built as lifts of small base graphs, using cyclic or, more generally, abelian lifts. Such codes are not asymptotically good, but they have strong advantages: compact descriptions, parallel decoding, and good real-world performance. In this talk, I will discuss the mathematics behind these “bad” LDPC codes. I will start with classical codes from graph lifts and explain how the base graph controls distance and girth through permanent-type bounds and inevitable cycles in abelian covers. I will then move to quantum CSS codes, where lifted-product constructions arise naturally from covers of products of graphs. I will describe analogous limitations for quantum LDPC codes, including permanent-type upper bounds and inevitable cycles.
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 3, Session 2
Speaker: Pavel Panteleev (Moscow)
Title: The Mathematics of Bad LDPC Codes
Abstract: Almost all LDPC codes used in practice are built as lifts of small base graphs, using cyclic or, more generally, abelian lifts. Such codes are not asymptotically good, but they have strong advantages: compact descriptions, parallel decoding, and good real-world performance. In this talk, I will discuss the mathematics behind these “bad” LDPC codes. I will start with classical codes from graph lifts and explain how the base graph controls distance and girth through permanent-type bounds and inevitable cycles in abelian covers. I will then move to quantum CSS codes, where lifted-product constructions arise naturally from covers of products of graphs. I will describe analogous limitations for quantum LDPC codes, including permanent-type upper bounds and inevitable cycles.
