In this work, a new approach to analyse and design the rectangular shaped low index core dielectric waveguide (LICDW) structure is proposed, which is based on derivation of the generic transcendental characteristic equations for the corresponding geometry using the effective dielectric constant method. The proposed method is not based on the image theory, and hence the derived characteristic equations can effectively be utilized to compute all possible modes of the LICDW structure quite accurately. The propagation constant of the LICDW structure is computed here as a function of the core-cladding parameters using the proposed characteristic equations. The reflection coefficient at the core-cladding interface of the structure in the specified frequency band is also computed to show the effect of the total reflection along the LICDW. The LICDW structure is fed using a newly proposed fully planar transition, which is realized by the SIW based magneto-electric dipole array feeding technique. For validating the proposed approach, a prototype structure comprising the LICDW along with the transition in the Ku-band is designed, fabricated, and tested. The proposed LICDW structure can be integrated with the corresponding dielectric radiator for the miniaturization of conventional Ku-band VSAT network.