Before revision:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
After revision:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.