Apologizing Comment on `Quantum Quasi-Cyclic Low-Density Parity-Check codes$\,$"

TL;DR

This paper issues an apology for overlapping ideas in a previous work on quantum quasi-cyclic LDPC codes, clarifying the similarities and differences in their construction methods and discussing limitations in practical applications.

Contribution

The paper clarifies the similarities between previous and recent quantum LDPC code constructions and discusses the limitations of the original approach in imperfect channel conditions.

Findings

Identified overlaps with prior work on quantum LDPC codes.

Highlighted weaknesses in the original coding approach for imperfect channels.

Provided insights for future improvements in quantum code constructions.

Abstract

In our recent paper entitled "Quantum Quasi-Cyclic Low-Density Parity-Check codes" [ICIC 2009. LNCS 5754], it was claimed that some new quantum codes can be constructed via the CSS encoding/decoding approach with various lengths and rates. However, the further investigation shows that the proposed construction may steal some ideas from the paper entitled "Quantum Quasi-Cyclic LDPC codes" [quant-ph/0701020v2]. We feel that the apologizing point of the original protocol is that some results are almost similar to that of construction methods with algebraic combinatorics although we suggest the different approach for improving them. Also, there is a weak point of the original coding approach while considering the application of codes in imperfect channels.