Abstract: A method and apparatus for optimizing resource allocations is disclosed which utilizes the Karmarkar algorithm to proceed in the interior of the solution space polytope. The constraints on the allocation variables (the surfaces of the polytope) are partitioned into sparse and non-sparse partitions to permit applying a perturbation formula permitting rapid inversion of the resulting perturbed matrix products. Each successive approximation of the solution point, and the polytope, are normalized such that the solution point is at the center of the normalized polytope using a diagonal matrix of the current solution point, also partitioned into sparse and non-sparse portions. The objective function is then projected into the normalized space and the next step is taken in the interior of the polytope, in the direction of steepest-descent of the objective function gradient and of such a magnitude as to remain within the interior of the polytope.

Abstract: In an ADPCM coder and decoder including a so-called locking-unlocking adaptation speed control, the adaptation speed is locked to a very slow, almost constant, speed of adaptation for voiceband data and partial band energy signals, i.e., tones and tone like signals, and is unlocked to achieve a fast speed of adaptation for speech. When a so-called partial band energy signal is being inputted, the adaptation speed is biased toward the unlocked state and when a transition occurs from a partial band energy signal to another such signal, the adaptation speed is set to the totally unlocked state and coefficients of an adaptive predictor are set to prescribed values. This is done in both the coder and decoder to minimize generation of impulse noise in the decoder output.