Title: A Compressed Sensing Approach for Distribution Matching,
Abstract: In this work, we formulate the fixed-length distribution matching as a
Bayesian inference problem. Our proposed solution is inspired from the
compressed sensing paradigm and the sparse superposition (SS) codes. First, we
introduce sparsity in the binary source via position modulation (PM). We then
present a simple and exact matcher based on Gaussian signal quantization. At
the receiver, the dematcher exploits the sparsity in the source and performs
low-complexity dematching based on generalized approximate message-passing
(GAMP). We show that GAMP dematcher and spatial coupling lead to asymptotically
optimal performance, in the sense that the rate tends to the entropy of the
target distribution with vanishing reconstruction error in a proper limit.
Furthermore, we assess the performance of the dematcher on practical
Hadamard-based operators. A remarkable feature of our proposed solution is the
possibility to: i) perform matching at the symbol level (nonbinary); ii)
perform joint channel coding and matching.