Quantum quasi-cyclic (QC) and quantum low-density parity-check (LDPC) codes have received significant attention due to their algebraic regularity and performance under low-complexity decoding. In this work, we explore a class of structured quantum codes based on reproducible matrices, which generalize known families such as cyclic, QC, and dyadic codes. Focusing on sparse quasi-dyadic (QD) structures, we investigate how their symmetries influence Tanner graph cycles. Moreover, we construct quantum LDPC codes within the Calderbank-Shor-Steane (CSS) framework, analyzing dual-containing configurations, and assess their error rates.
Quantum CSS LDPC Codes with Quasi-Dyadic Structure / Baldelli, Alessio; Battaglioni, Massimo; Santini, Paolo. - ELETTRONICO. - (2025). (Intervento presentato al convegno 2025 13th International Symposium on Topics in Coding (ISTC) tenutosi a Los Angeles, USA nel 18-22 August 2025) [10.1109/ISTC65386.2025.11154589].
Quantum CSS LDPC Codes with Quasi-Dyadic Structure
Alessio Baldelli;Massimo Battaglioni;Paolo Santini
2025-01-01
Abstract
Quantum quasi-cyclic (QC) and quantum low-density parity-check (LDPC) codes have received significant attention due to their algebraic regularity and performance under low-complexity decoding. In this work, we explore a class of structured quantum codes based on reproducible matrices, which generalize known families such as cyclic, QC, and dyadic codes. Focusing on sparse quasi-dyadic (QD) structures, we investigate how their symmetries influence Tanner graph cycles. Moreover, we construct quantum LDPC codes within the Calderbank-Shor-Steane (CSS) framework, analyzing dual-containing configurations, and assess their error rates.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
