Nash-Equilibrium-Based and Momentum-Accelerated ADMM Decoding for LDPC Codes in Low-Altitude Wireless Networks

Low-Altitude Wireless Networks (LAWN) require reliable and low-latency short-packet transmission under dynamic channels and limited receiver iteration budgets. Conventional Alternating Direction Method of Multipliers (ADMM)-based Low-Density Parity-Check (LDPC) decoders may suffer from unstable convergence and excessive iterations in this regime. To address these issues, this paper proposes two ADMM-based decoding algorithms for short-blocklength LDPC codes. For reliability-critical links, a Nash-equilibrium-driven ADMM decoder (ADMM-NE) adaptively updates penalty weights according to local utilities to improve decoding stability. For delay-sensitive links, a momentum-accelerated ADMM decoder (ADMM-MA) is developed to reduce the number of iterations. Simulation results over AWGN channels and fast flat Rayleigh fading channels show that ADMM-NE provides up to 0.22 dB coding gain over ADMM-L2, while ADMM-MA reduces the average number of iterations by up to 33.9%, indicating an effective balance between reliability and latency for LAWN-oriented URLLC services.