This paper proposes a novel distributed encoding procedure to realize codes that resemble LT codes (rateless codes for erasure correction) in both structure and performance. For the case of two sources communicating with a single sink via a common relay, this technique separately encodes k/2 symbols of information onto slightly more than k code symbols at each source. These two codewords are then selectively XOR-ed at the relay, such that the result can be decoded by the sink to recover all k information symbols. It is shown that, for the case of four sources communicating to a single sink, the use of a similar distributed LT code leads to a 50% reduction in overhead at the sink, compared to the use of four individual LT codes.