This paper considers two sub-optimal transmission schemes for a family of parallel Gaussian vector broadcast channels. One of the schemes is based on the QR precoding of Ginis et al. (2000). In QR precoding, the maximum achievable throughput depends on the order in which users are encoded. This scheme is a new algorithm for obtaining the best user ordering and channel-input covariance matrix that maximizes the total channel throughput. The proposed algorithm has linear complexity in the number of multi-carrier frequencies. The simplicity of a linear transmitter-and-receiver architecture is attractive for a transmission scheme. The design of a linear transmitter and multiple linear receivers that maximize the total throughput is studied. It is shown that under discrete bit loading assumption for each user, this problem reduces to solving a series of second order cone programming problems.