A computer-implemented method for determining the Walsh-Hadamard transform of N samples of a signal, comprises electing a plurality of hashing C matrices Σ1, . . . ΣC, computing C hashes of a particular length based at least on a hashing front end and the plurality of matrices Σ1, . . . ΣC, forming a bipartite graph with a plurality of variable nodes and a plurality of check nodes, the variable nodes being non-zero coefficients to recover, and the check nodes being hashed samples, finding an isolated check node and recovering non-zero coefficients connected to the isolated check node by employing collision detection and support estimation of the signal, peeling from the bipartite graph the recovered non-zero coefficients, and repeating the computing step, forming step, finding step and peeling step until all the nodes in the plurality of check nodes are zero.