  We demonstrate that a periodic waveguide comprising of uniform lossless
segments together with discrete gain and radiating elements supports
exceptional points of degeneracy (EPDs). We provide analytical expressions for
all possible conditions that guarantee the occurrence of an EPD, i.e., the
coalescence of eigenvalues and eigenvectors. We show that EPDs are not only
achieved using symmetric gain and radiation periodic loading, but they are also
obtained using asymmetric gain and radiation loss conditions. We illustrate the
characteristics of the degenerate electromagnetic modes, showing the dispersion
diagram and discussing the tunability of the EPD frequency. We show a special
condition, we refer to it as parity-time (PT)-glide symmetry, which leads to a
degeneracy that is occurring at all frequencies of operation. The class of EPDs
proposed in this work is very promising for many applications that incorporate
discrete-distributed coherent sources and radiation-loss elements; operating in
the vicinity of such special degeneracy conditions leads to potential
performance enhancement in a variety of microwave and optical resonators,
antennas, and devices and can be extended to a new class of active integrated
antenna arrays and radiating laser arrays.
