An FPGA-Based LDPC Decoder With Ultra-Long Codes for Continuous-Variable Quantum Key Distribution

In this paper, we propose a good decoding performance, low-complexity, and high-speed decoder architecture for ultra-long quasi-cyclic LDPC codes by using the layered sum-product decoding scheme. To reduce implementation complexity and hardware resource consumption, the messages in the iteration process are uniformly quantified and the function $\Psi (x)$ is approximated with second-order functions. The decoder architecture improves the decoding throughput by using partial parallel and pipeline structures. A modified construction method of parity check matrices was applied to prevent read&write conflicts and achieve high-speed pipeline structure. The simulation results show that our decoder architecture has good performance at signal-to-noise ratios (SNRs) as low as −0.6 dB. We have implemented our decoder architecture on a Virtex-7 XC7VX690T field programmable gate array (FPGA) device. The implementation results show that the FPGA-based LDPC decoder can achieve throughputs of 108.64 Mb/s and 70.32 Mb/s at SNR of 1.0 dB when the code length is 262,144 and 349,952, respectively. The decoder can find useful applications in those scenarios that require very low SNRs and high throughputs, such as the information reconciliation of continuous-variable quantum key distribution.