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Block coding for the binary symmetric broadcast channel with two receivers is investigated. A graph-theoretic approach to the construction of a class of block codes with unequal error protection for two different sets of messages is presented. A code in this class is a direct sum of two component codes; each set of messages is encoded based on one component code. The codes in this class are easy to implement. Decoding of these codes is presented, and lower bounds on the achievable rates of these codes are derived. The bounds are tighter than the Katsman's bounds.