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Recently, soft video multicasting has gained a lot of attention, especially in broadcast and mobile scenarios where the bit rate supported by the channel may differ across receivers, and may vary quickly over time. Unlike the conventional designs that force the source to use a single bit rate according to the receiver with the worst channel quality, soft video delivery schemes transmit the video such that the video quality at each receiver is commensurate with its specific instantaneous channel quality. In this paper, we present a soft video multicasting system using an adaptive block-based compressed sensing (BCS) method. The proposed system consists of an encoder, a transmission system, and a decoder. At the encoder side, each block in each frame of the input video is adaptively sampled with a rate that depends on the texture complexity and visual saliency of the block. The obtained BCS samples are then placed into several packets, and the packets are transmitted via a channel-aware OFDM (orthogonal frequency division multiplexing) transmission system with a number of subchannels. At the decoder side, the received BCS samples are first used to build an initial approximation of the transmitted frame. To further improve the reconstruction quality, an iterative BCS reconstruction algorithm is then proposed that uses an adaptive transform and an adaptive soft-thresholding operator, which exploits the temporal similarity between adjacent frames to achieve better reconstruction quality. The extensive objective and subjective experimental results indicate the superiority of the proposed system over the state-of-the-art soft video multicasting systems.