  A multiple round quantum dense coding (MRQDC) scheme based on the quantum
phase estimation algorithm is proposed. Using an $m+1$ qubit system, Bob can
transmit $2^{m+1}$ messages to Alice, through manipulating only one qubit and
exchanging it between Alice and Bob for $m$ rounds. The information capacity is
enhanced to $m+1$ bits. We have implemented the scheme in a three- qubit
nuclear magnetic resonance (NMR) quantum computer. The experimental results
show a good agreement between theory and experiment.
