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IEEE Information Theory Workshop (ITW)

Entanglement-Assisted Quasi-Cyclic LDPC Codes

Pavan Kumar, Abhi Kumar Sharma, Shayan Srinivasa Garani

Published Nov 24, 2024• 1 citation
Publisher

Abstract

We provide code constructions along with code properties for a few families of entanglement-assisted (EA) Calderbank-Shor-Steane (CSS) codes derived from quasi-cyclic (QC) low-density parity check (LDPC) codes. These codes require only a minimum number of Bell pairs to be shared between the transmitter and the receiver. The Tanner graph of the proposed EA QC LDPC code has girth$> 4$. We evaluate the performance of these codes using both random and Markovian noise models to assess random and burst error performance using a modified-version of the min-sum algorithm.

DOI
10.1109/itw61385.2024.10806978

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We provide code constructions along with code properties for a few families of entanglement-assisted (EA) Calderbank-Shor-Steane (CSS) codes derived from quasi-cyclic (QC) low-density parity check (LDPC) codes. These codes require only a minimum number of Bell pairs to be shared between the transmitter and the receiver. The Tanner graph of the proposed EA QC LDPC code has girth>4> 4>4. We evaluate the performance of these codes using both random and Markovian noise models to assess random and burst error performance using a modified-version of the min-sum algorithm.
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We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Shor-Steane (CSS) construction do not need to satisfy the dual-containing property as long as pre-shared entanglement is available to both sender and receiver. We can use this to avoid the many 4-cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.
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