The achievable sum rate of the multi-letter Ahlswede-Han scheme for the modulo-sum problem is investigated. For auxiliary random variables induced by the parity check matrix of the repetition code, a compact expression of the achievable sum rate in terms of the source distribution's parameters is obtained. It is numerically demonstrated that the multi-letter Ahlswede-Han scheme strictly improves the sum rate of the Slepian-Wolf scheme and the Korner-Marton scheme for wide ranges of parameters.