High-Dimensional Sipser-Spielman Codes - IPAM at UCLA

Explore high-dimensional Sipser-Spielman codes in this 51-minute lecture by Pavel Panteleev from Moscow State University, presented at IPAM's Topology, Quantum Error Correction and Quantum Gravity Workshop. Delve into the generalization of Sipser-Spielman expander codes to high-dimensional expanders (HDXs) and their significance in coding theory. Examine the extension of simplicial HDX theory over GF(2) to cellular sheaves, incorporating various cell complexes and local systems of abelian groups. Understand the concept of block Hamming weight and its role in adapting standard definitions to cellular sheaves. Focus on coboundary expansion in the links of expander code products and its crucial role in constructing good locally testable codes (LTCs) and quantum low-density parity-check (qLDPC) codes. Gain insights from Panteleev's collaborative research with Gleb Kalachev, advancing the field of coding theory and its applications in quantum error correction.