This paper proposes an extended coded caching scheme based on piggyback coding for single-server multi-user networks with decentralized caching. The proposed scheme is obtained by adapting Polar codes and extending the original coded caching scheme, which is based on index coding and a data assignment that can be implemented via minimum graph-colouring. Polar codes are adapted so that users can apply parts of their cache contents as the frozen bits for Polar decoding, and the coded caching is adapted so as to account for different user coding rates and to combine transmissions to cache-aided and cache-free users. Numerical simulations prove that our piggyback-coding based scheme achieves higher rates than previous schemes also in the finite block-length regime. Finally, real testbed measurements are presented, which validate the practical implementation.