state evolution

Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes

We study the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel and extend our preliminary work. We use heuristic statistical-physics-based tools, such as the cavity and the replica …

Adaptive damping and mean removal for the generalized approximate message passing algorithm

The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of x observed from a noisy version of the transform coefficients z = Ax. In fact, for large zero-mean i.i.d sub-Gaussian A, GAMP …

Robust error correction for real-valued signals via message-passing decoding and spatial coupling

We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and the …