Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes

• Main Authors: Daryus Chandra, Zunaira Babar, Soon Xin Ng, Lajos Hanzo
• Format: Article
• Language: English
• Published: IEEE 2019-01-01
• Series: IEEE Access
• Subjects: Quantum error detection codes; quantum error correction codes; concatenated codes; iterative decoding; topological codes; quantum turbo codes
• Online Access: https://ieeexplore.ieee.org/document/8691729/

Quantum stabilizer codes (QSCs) suffer from a low quantum coding rate since they have to recover the quantum bits (qubits) in the face of both bit-flip and phase-flip errors. In this treatise, we conceive a low-complexity concatenated quantum turbo code (QTC) design exhibiting a high quantum coding rate. The high quantum coding rate is achieved by combining the quantum-domain version of short-block codes (SBCs) also known as single parity check (SPC) codes as the outer codes and quantum unity-rate codes (QURCs) as the inner codes. Despite its design simplicity, the proposed QTC yields a near-hashing-bound error correction performance. For instance, compared to the best half-rate QTC known in the literature, namely the QIrCC-QURC scheme, which operates at the distance of D = 0.037 from the quantum hashing bound, our novel QSBC-QURC scheme can operate at the distance of D = 0.029. In addition, it is worth mentioning that this is the first instantiation of QTCs capable of adjusting the quantum encoders according to the quantum coding rate required for mitigating the Pauli errors, given the different depolarizing probabilities of the quantum channel.