  The groupcast index coding (GIC) problem is a generalization of the index
coding problem, where one packet can be demanded by multiple users. In this
paper, we propose a new coding scheme called independent user partition
multicast (IUPM) for the GIC problem. The novelty of this scheme compared to
the user partition multicast (UPM) (Shanmugam \textit{et al.}, 2015) is in
removing redundancies in the UPM solution by eliminating the linearly dependent
coded packets. We also prove that the UPM scheme subsumes the packet partition
multicast (PPM) scheme (Tehrani \textit{et al.}, 2012). Hence, the IUPM scheme
is a generalization of both PPM and UPM schemes. Furthermore, inspired by
jointly considering users and packets, we modify the approximation partition
multicast (CAPM) scheme (Unal and Wagner, 2016) to achieve a new
polynomial-time algorithm for solving the general GIC problem. We characterize
a class of GIC problems with $\frac{k(k-1)}{2}$ packets, for any integer $k\geq
2$, for which the IUPM scheme is optimal. We also prove that for this class,
the broadcast rate of the proposed new heuristic algorithm is $k$, while the
broadcast rate of the CAPM scheme is $\mathcal{O}(k^2)$.
