  Continuous-Variable Quantum Key Distribution (CVQKD) at large distances has
such high noise levels that the employed error-correcting codes must have very
low rate. In this regime it becomes feasible to implement random-codebook error
correction, which is known to perform close to capacity. We propose a
random-codebook reverse reconciliation scheme for CVQKD that is inspired by
spread-spectrum watermarking. Our scheme has a novel way of achieving
statistical decoupling between the publicly sent reconciliation data and the
secret key. We provide a theoretical analysis of the secret key rate and we
present numerical results. The best performance is obtained when the message
size exceeds the mutual information I(X;Y) between Alice and Bob's
measurements. This somewhat counter-intuitive result is understood from a
tradeoff between code rate and frame rejection rate, combined with the fact
that error correction for QKD needs to reconcile only random data. We obtain
secret key lengths that lie far above the Devetak-Winter value I(X;Y)-I(E;Y).
