Cell-free massive multiple-input multiple-output (CF mMIMO) systems are characterized by having many more access points (APs) than user equipments (UEs). A key challenge is to determine which APs should serve which UEs. Previous work has tackled this combinatorial problem heuristically. This paper proposes a sparse large-scale fading decoding (LSFD) design for CF mMIMO to jointly optimize the association and LSFD. We formulate a group sparsity problem and then solve it using a proximal algorithm with block-coordinate descent. Numerical results show that sparse LSFD achieves almost the same spectral efficiency as optimal LSFD, thus achieving a higher energy efficiency since the processing and signaling are reduced.