Theory of Computing ------------------- Title : The One-Way Communication Complexity of Hamming Distance Authors : T. S. Jayram, Ravi Kumar, and D. Sivakumar Volume : 4 Number : 6 Pages : 129-135 URL : https://theoryofcomputing.org/articles/v004a006 Abstract -------- Consider the following version of the Hamming distance problem for {1,-1}-vectors of length n: the promise is that the distance is either at least (n/2)+sqrt{n} or at most (n/2)-sqrt{n}, and the goal is to find out which of these two cases occurs. Woodruff (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2004) gave a linear lower bound for the randomized one-way communication complexity of this problem. In this note we give a simple proof of this result. Our proof uses a simple reduction from the indexing problem and avoids the VC-dimension arguments used in the previous paper. As shown by Woodruff (loc. cit.), this implies an Omega(1/epsilon^2)-space lower bound for approximating frequency moments within a factor 1+epsilon in the data stream model.