This paper introduces Shannon-Kotelnikov (SK) mapping in the SoftCast joint source-channel video coding scheme. On bandwidth constrained channels, the performance of SoftCast saturates, due to the large amount of data (chunks) dropped to match the bandwidth requirements. Using SK mapping, it is possible to increase the number of chunks that may be transmitted without increasing the bandwidth requirements. The resulting scheme has an increased number of design parameters for which we present a transmission-power constrained optimization. This extends range of channel SNRs over which the PSNR gracefully increases and improves the end-to-end performance at medium to high SNRs. The price to be paid is a performance degradation at low SNRs.