RXO-LDPC: A Physics-Inspired Relaxation Oscillator-Based Solver Leveraging Six-Body Spin Interactions for Soft Decoding of LDPC Codes

Physics-inspired computing harnesses continuous-time (CT) operation, massive parallelism, and direct compute load mapping to coupled CMOS-based spins to accelerate solving complex optimization problems. This work advances the field by introducing relaxation oscillator (RXO)-low-density parity check (LDPC), a combinatorial optimization problem (COP) engine that natively supports six-body spin interactions for efficient, robust, and one-shot oscillator-based soft decoding of LDPC codes. The proposed RXO spins feature a capacitor-DAC-based initialization structure, allowing precise mapping of soft information to initial spin phases for high-performance decoding. A crossbar-based feedback system facilitates six-body spin interactions by directly coupling spins based on the COP graph. Implemented in 28-nm CMOS technology, the prototype achieves a frame error rate (FER) and bit error rate (BER) of $1.36{\times }10{^{-6}}$ and $1.89{\times }10{^{-7}}$ , respectively, at 7-dB SNR. The measured BER is more than three orders of magnitude lower than for belief propagation (BP) decoding, for channels with 2–5-dB SNR. The measured energy efficiency of 7.28 pJ/bit exceeds the normalized efficiencies of state-of-the-art decoders. Evaluated with more than 100 million decoding cycles, the system demonstrates reliable performance across a wide range of SNRs, supply voltages, temperatures, and for different dies. These measurement results highlight the RXO-based architecture’s potential as an accelerator for directly solving COPs with multi-body spin interactions.