  We derive upper and lower bounds for the error exponents of lossless
streaming compression of two correlated sources under the blockwise and
symbolwise settings. We consider the linear scaling regime in which the delay
is a scalar multiple of the number of symbol pairs of interest. We show that
for rate pairs satisfying certain constraints, the upper and lower bounds for
the error exponent of blockwise codes coincide. For symbolwise codes, the
bounds coincide for rate pairs satisfying the aforementioned constraints and a
certain condition on the symbol pairs we wish to decode---namely, that their
indices are asymptotically comparable to the blocklength. We also derive
moderate deviations constants for blockwise and symbolwise codes, leveraging
the error exponent results, and using appropriate Taylor series expansions. In
particular, for blockwise codes, we derive an information spectrum-type strong
converse, giving the complete characterization of the moderate deviations
constants. For symbolwise codes, under an additional requirement on the backoff
from the first-order fundamental limit, we can show that the moderate
deviations constants are the same as the blockwise setting.
