  We use a combination of analytical and numerical techniques to calculate the
noise threshold and resource requirements for a linear optical quantum
computing scheme based on parity-state encoding. Parity-state encoding is used
at the lowest level of code concatenation in order to efficiently correct
errors arising from the inherent nondeterminism of two-qubit linear-optical
gates. When combined with teleported error-correction (using either a Steane or
Golay code) at higher levels of concatenation, the parity-state scheme is found
to achieve a saving of approximately three orders of magnitude in resources
when compared to a previous scheme, at a cost of a somewhat reduced noise
threshold.
