A variable gain optical amplifier, in which homogeneous gain broadening is dominant, has first and second fixed gain rare-earth doped optical waveguide amplifiers optically in series together with an intervening variable attenuation optical attenuator. The first circular wall, the second circular wall, and the plurality of removable dividers define a row of compartments. The digital audio decoder uses fixed point arithmetic but a variable word format to represent the intermediate computations and pre-stored look-up table entries.