A Compressed Sensing Approach for Distribution Matching
This work addresses distribution matching for communication systems, offering a novel method that enables nonbinary symbol-level matching and joint channel coding, though it appears incremental as it builds on existing compressed sensing and coding paradigms.
The paper tackles the problem of fixed-length distribution matching by formulating it as a Bayesian inference problem and proposing a solution based on compressed sensing and sparse superposition codes, achieving asymptotically optimal performance where the rate tends to the entropy of the target distribution with vanishing reconstruction error.
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.