Iterative Decoding of Product Codes Based on Syndrome Decoding of Sub-Codes

Yantao Qiao, Shigeru Shimamoto, Hu Wang +2 more

Nithin Raveendran, Narayanan Rengaswamy, Asit Kumar Pradhan +1 more

Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the iterative decoders for decoding quantum low-density parity-check (QLDPC) codes. Syndrome-based iterative belief propagation decoders are modified to utilize the syndrome-soft information to successfully correct both data and syndrome errors simultaneously, without repeated measurements. We demonstrate the advantages of extracting the soft information from the syndrome in our improved decoders, not only in terms of comparison of thresholds and logical error rates for quasi-cyclic lifted-product QLDPC code families, but also for faster convergence of iterative decoders. In particular, the new BP decoder with noisy syndrome performs as good as the standard BP decoder under ideal syndrome.

Nguyen Thi Hong Nhung, Pham Xuan Nghia, The Cuong Dinh +2 more

J. J. Wang, H. Chen, Huan Chang

R. Gayathri, Shobhit Bhatnagar, P. Vijay Kumar

Erasure decoding of quantum low-density paritycheck (QLDPC) codes has recently received a lot of interest as qubit erasures occur in many physical systems such as neutralatom systems, trapped-ion systems etc. However, decoding of QLDPC codes heavily relies on syndrome information, which may be unreliable as syndrome extraction circuits are prone to errors in practice. While syndrome errors are usually modeled as flipping of a binary syndrome bit, typically, measurement outcomes yield analog voltage/current values, which are then discretized to obtain the binary syndrome. Prior work on correcting qubit errors in the presence of syndrome noise shows that this soft (i.e., analog) information can be exploited to achieve performance improvement. In this paper, we consider the case of qubit erasures and present an iterative decoding algorithm, based on the hardware-friendly min-sum algorithm, that incorporates this soft information to perform check node updates. We show via simulations on hypergraph product codes and lifted product codes that our decoder achieves performance very close to that in the case of noiseless syndrome for a certain noise regime.

Hitoshi Tokushige, P C Fossorier Marc, Tadao Kasami