What is the burden of proving substantial rights to a defendant in a motion to dismiss a claim of plain error?

Olano holds that a defendant, in showing an error affected "substantial rights," generally bears the burden of establishing that the error affected the outcome of the case. --- U.S. at ----, 113 S.Ct. at 1778. "[F]ederal courts have consistently interpreted the plain-error doctrine as requiring an appellate court to find that the claimed error ... had [a] prejudicial impact on the jury's deliberations." Id. (quoting United States v. Young, 470 U.S. 1, 17 n. 14, 105 S.Ct. 1038, 1047 n. 14, 84 L.Ed.2d 1 (1985)).