Die Linke is in fact the successor to the Communist Party, although their ideology has shifted over time.
KPD (Kommunistische Partei Deutschlands) — in East Germany, merged with SPD (Sozialdemokratische Partei Deutschlands) in 1946 to form SED. In West Germany, banned after 1956.
SED (Sozialistische Einheitspartei Deutschlands) - ruled East Germany until the democratic transition in 1989. Rebranded as PDS in 1990.
PDS (Partei des Demokratischen Sozialismus) - Merged with the minor party WASG in 2007 to form Die Linke.