Step 1: Recall the single defining cell asked about. The Reed-Sternberg cell - a giant cell with an "owl's eye" bilobed or multinucleated nucleus and big eosinophilic nucleoli - is the diagnostic cell of Hodgkin's lymphoma.
Step 2: Its presence is essentially required to diagnose Hodgkin's disease; conversely its absence carries a high negative predictive value.
Step 3: Markers $CD30^{+}$ and $CD15^{+}$ with $CD20^{-}$ and $CD45^{-}$ confirm the RS lineage from crippled germinal-center B cells.
Step 4: Sickle cell anaemia, thalassemia and chronic myeloid leukemia (CML) are unrelated hematologic disorders with distinct morphology (sickled cells, target cells, leukocytosis with basophilia), none of which contain RS cells.
\[\boxed{\text{Hodgkin's disease}}\]