In the envisioned beyond-fifth-generation (B5G) and sixth-generation (6G) scenarios which expect massive multiple-input multiple-output (mMIMO) and high frequency communications in the millimeter-wave (mmWave) and Terahertz (THz) bands, efficiency in both energy and spectrum is of increasing significance. To that extent, a novel ISAC framework called "sparse codesigned communication and radar (SCCR)" systems is described, which codesigns both communication and radar signals by a sparsification of the resource domain and the waveform spectrum domain. This improves the spectral and energy efficiency, but at the inherent cost of missing radar spectrum and irregular beampattern, and decreased throughput and diversity. Such challenges can however be corroborated, by leveraging various sparsity-robust signal processing techniques such as sparse radar reconstruction and index modulation (IM). In light of the above, the white paper aims to outlined the proposed article which provide an overview and a novel classification of the relevant state-of-the-art (SotA) methods and the implications of the challenges in the sparse codesign of the system, followed by a variety of novel SCCR frameworks.