In this paper, we introduce a minimum noise structure for ladder-based biorthogonal (MINLAB) filter bank. The minimum noise structure ensures that the quantization error has a unity noise gain, even though the filter bank is biorthogonal. The coder has a very low design and implementation cost. Perfect reconstruction property is structurally preserved. Optimal bit allocation and coding gain formulas are derived. We show that the coding gain of the optimal MINLAB coder is always greater than or equal to unity. For both AR(1) process and MA(1) process, the MINLAB coder with two taps has a higher coding gain than the optimal orthonormal coder with an infinite number of taps. In addition to its superior decorrelation ability, it has many other desired features that make it a potentially valuable and attractive alternative to the orthonormal coder, especially for the high-fidelity compression.