  We present a family of entanglement purification protocols that generalize
four previous methods, namely the recurrence method, the modified recurrence
method, and the two methods proposed by Maneva-Smolin and Leung-Shor. We will
show that this family of protocols have improved yields over a wide range of
initial fidelities F, and hence imply new lower bounds on the quantum capacity
assisted by two-way classical communication of the quantum depolarizing
channel. In particular, the yields of these protocols are higher than the yield
of universal hashing for F less than 0.993 and as F goes to 1.
