Towards quantum belief propagation for LDPC decoding in wireless networks

We present Quantum Belief Propagation (QBP), a Quantum Annealing (QA) based decoder design for Low Density Parity Check (LDPC) error control codes, which have found many useful applications in Wi-Fi, satellite communications, mobile cellular systems, and data storage systems. QBP reduces the LDPC decoding to a discrete optimization problem, then embeds that reduced design onto quantum annealing hardware. QBP's embedding design can support LDPC codes of block length up to 420 bits on real state-of-the-art QA hardware with 2,048 qubits. We evaluate performance on real quantum annealer hardware, performing sensitivity analyses on a variety of parameter settings. Our design achieves a bit error rate of 10--8 in 20 μs and a 1,500 byte frame error rate of 10--6 in 50 μs at SNR 9 dB over a Gaussian noise wireless channel. Further experiments measure performance over real-world wireless channels, requiring 30 μs to achieve a 1,500 byte 99.99% frame delivery rate at SNR 15-20 dB. QBP achieves a performance improvement over an FPGA based soft belief propagation LDPC decoder, by reaching a bit error rate of 10--8 and a frame error rate of 10--6 at an SNR 2.5--3.5 dB lower. In terms of limitations, QBP currently cannot realize practical protocol-sized (e.g., Wi-Fi, WiMax) LDPC codes on current QA processors. Our further studies in this work present future cost, throughput, and QA hardware trend considerations.