Source coding with a helper is one of the most fundamental fixed-length source coding problem for correlated sources. For this source coding, Wyner and Ahlswede-Körner showed the achievable rate region which is the set of rate pairs of encoders such that the probability of error can be made arbitrarily small for sufficiently large block length. However, their expression of the achievable rate region consists of the sum of indefinitely many sets. Thus, their expression is not useful for computing the achievable rate region. This paper deals with correlated sources whose conditional distribution is related by a binary-input output-symmetric channel, and gives a parametric form of the achievable rate region in order to compute the region easily.