Sparse Random Combinatorial Matrices for IRSA Over the Binary Adder Channel

This letter proposes an enhanced irregular repetition slotted ALOHA (IRSA) scheme for the binary adder channel (BAC) using sparse random combinatorial matrices as codebooks. Existing IRSA schemes for the BAC, which rely on dense Bernoulli matrices as codebooks, struggle to resolve a large number of collisions, primarily due to the high density of the codebook. To address it, we introduce a codebook construction using sparse random combinatorial matrices, where each codeword is a binary vector with exactly d ones, optimized to maximize the collision resolution capabilities. Furthermore, the proposed scheme eliminates pilot symbols by leveraging the codebook’s inherent sparsity and combinatorial structure. Numerical simulations show that the proposed scheme achieves a higher decoding threshold and superior average sum rate compared to existing schemes, thanks to its enhanced collision resolution capabilities.