Efficient ADMM Decoding of LDPC Codes Using Lookup Tables

Linear programming decoding with the alternating direction method of multipliers (ADMM) is a promising decoding technique for low-density parity-check (LDPC) codes, where the computational complexity of Euclidean projections onto check polytopes becomes a prominent problem. In this paper, the problem is circumvented by building lookup tables (LUTs) and quantizing the inputs to approach approximate Euclidean projections at low computational complexities. To challenge the huge memory cost of LUTs, we first propose two commutative compositions of Euclidean projection and self-map, and show the existence of a small quantization range which does not alter the Euclidean projection. Then, we investigate the design and simplification of the LUTs by exploiting the commutative compositions and check node decomposition techniques. An efficient algorithm for the LUT-based projection is demonstrated by using one simplification method. Simulation results show that for both the regular and irregular LDPC codes, the ADMM decoding using LUT-based projection can substantially reduce the decoding time while maintaining the error rate performance at a comparatively large memory cost.