  We consider the problem of distributed binary hypothesis testing of two
sequences that are generated by an i.i.d. doubly-binary symmetric source. Each
sequence is observed by a different terminal. The two hypotheses correspond to
different levels of correlation between the two source components, i.e., the
crossover probability between the two. The terminals communicate with a
decision function via rate-limited noiseless links. We analyze the tradeoff
between the exponential decay of the two error probabilities associated with
the hypothesis test and the communication rates. We first consider the
side-information setting where one encoder is allowed to send the full
sequence. For this setting, previous work exploits the fact that a decoding
error of the source does not necessarily lead to an erroneous decision upon the
hypothesis. We provide improved achievability results by carrying out a tighter
analysis of the effect of binning error; the results are also more complete as
they cover the full exponent tradeoff and all possible correlations. We then
turn to the setting of symmetric rates for which we utilize Korner-Marton
coding to generalize the results, with little degradation with respect to the
performance with a one-sided constraint (side-information setting).
