The official name of East Germany is German Democratic Republic (GDR) and existed from 1949 to 1990. East Germany covered the area of the present-day German states of Mecklenburg-Vorpommern, Brandenburg, Berlin (excluding West Berlin), Sachsen, Sachsen-Anhalt and Thüringen.

East Germany was the Soviet zone of occupation and thus had to put up with “anti-fascist” consequences, i.e. a Marxist-Leninist-influenced party dictatorship was legitimised. People in East Germany were living under a communist regime and constant fear. Of course, no free speech as you would be thrown into prison if you said anything bad about the government.
However, one of the good things about the life in the East Germany is every one had a job.

For more, you can read from the following sites:
www.scansw.com.au/eastgermany.html
www.tatsachen-ueber-deutschland.de/en/history/main-content-0
en.wikipedia.org/wiki/History_of_East_Germany