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It is well known that the human visual system can perceive high frequencies in 3D stereo video, even if that information is present in only one of the views. Therefore, the best perceived 3D stereo video quality may be achieved by asymmetric coding where the reference and auxiliary (right and left) views are coded at unequal PSNR. However, the questions of what is the best level of asymmetry in order to maximize the perceived quality and whether asymmetry should be achieved by spatial resolution reduction or PSNR (quality) reduction have been open issues. We conducted extensive subjective tests, which indicate that if the reference view is encoded at sufficiently high quality and the auxiliary view is encoded at a lower quality but above a certain PSNR threshold, then the degradation in 3D video quality is unnoticeable. Since asymmetric coding by PSNR reduction gives finer control over achievable PSNR values over spatial resolution reduction, asymmetry by PSNR reduction allows us to encode at a point more close to this just-noticeable asymmetry PSNR threshold; hence will be preferred over the spatial resolution reduction method. Subjective tests also indicate that below this just-noticeable asymmetry threshold, where subtle artifacts start to appear, symmetric coding performs better than asymmetric coding in terms of perceived 3D video quality. Therefore, we show that the choice between asymmetric vs. symmetric coding depends on PSNR; hence, the available total bitrate. This paper also proposes a novel asymmetric scalable stereo video coding framework to enable adaptive stereoscopic video streaming taking full advantage of these observations and subjective test results.