Optimal and suboptimal channel precoding and decoding matrices for linear video coding

Linear video coding (LVC) has recently emerged as a very promising paradigm for robust video delivery over unreliable channels. The pioneering LVC paper, introducing SoftCast, showed that, a cross-layer approach, based on linear-only processing followed by analog modulation, was able to improve the quality of received video with respect to traditional, layered approaches, when unreliable links to several users are considered. This paper considers the power allocation problem when the transmission channel consists of several sub-channels, each with its own power constraint. This framework models, e.g., multi-antenna, DSL, or powerline transmission systems. Minimizing the mean-square error at a receiver leads to an precoding and decoding matrix design problem. Our contributions consist in (1) formulating the matrix design problem in such a way that a multi-level water-filling solution proposed for MIMO channels can be adapted to LVC; (2) the proposal of three suboptimal power allocations techniques, with different trade-offs between complexity and efficiency; (3) a precoding matrix design for the multiple receivers scenario; (4) extensive simulations of the power allocation methods. The proposed optimal power allocation largely outperforms a simple adaptation of the allocation considered in SoftCast for the per-subchannel power constrained problem; moreover two of the suboptimal solutions perform very close to the optimal one, with a sensibly reduced complexity.