We studied the protonic structure and energy of a D (or L) defect in a zig-zag hydrogen-bonded system. It is shown that the extra (or missing) proton lowers its energy by creating a polarization defect to which it is coupled. We used a quantum description with intrasite and intersite tunneling, while taking properly into account the polarization state of the neighboring bonds. Pacs numbers : 61.70.-r, 61.70q.ey, 61.70. Yq, 72.90. + y.