  Quantum communication typically involves a linear chain of repeater stations,
each capable of reliable local quantum computation and connected to their
nearest neighbors by unreliable communication links. The communication rate in
existing protocols is low as two-way classical communication is used. We show
that, if Bell pairs are generated between neighboring stations with a
probability of heralded success greater than 0.65 and fidelity greater than
0.96, two-way classical communication can be entirely avoided and quantum
information can be sent over arbitrary distances with arbitrarily low error at
a rate limited only by the local gate speed. The number of qubits per repeater
scales logarithmically with the communication distance. If the probability of
heralded success is less than 0.65 and Bell pairs between neighboring stations
with fidelity no less than 0.92 are generated only every T_B seconds, the
logarithmic resource scaling remains and the communication rate through N links
is proportional to 1/(T_B log^2 N).
