Line a 9 x 5-inch loaf pan with buttered wax paper; set aside.
Combine corn syrup, water and sugar in small heavy saucepan. Cook over medium heat, stirring constantly, until sugar dissolves and mixture comes to a boil. Wash down side of pan with pastry brush dipped in hot water frequently, to remove sugar crystals. Add candy thermometer. Continue to cook until mixture reaches the hard-ball stage (255° F).
Meanwhile, beat egg white and cream of tartar with heavy duty electric mixer, until stiff but not dry. Slowly pour hot syrup into egg white, beating constantly. Add vanilla extract. Beat until candy forms soft peaks and starts to lose its gloss. Spoon fondant into prepared pan. Cut into three strips lengthwise, then crosswise in center. Freeze until firm.
Line a baking sheet with wax paper, set aside. Melt caramels with water in small heavy saucepan, over low heat, stirring occasionally. Arrange pecans on wax paper. Working quickly, drop 1 piece of the frozen fondant into melted caramels to coat. Roll in pecans to completely coat. Place on prepared baking sheet to set. Repeat with remaining fondant pieces, reheating caramel mixture if it becomes too thick. Cut logs into 1/2-inch slices. Store in the refrigerator in an airtight container between layers of wax paper or freeze up to 3 months.