The gradient adaptive lattice algorithm in block floating point format

We present a novel scheme to implement the gradient adaptive lattice (GAL) algorithm using block floating point (BFP) arithmetic that permits processing of data over a wide dynamic range, at a cost significantly less than that of a floating point processor. Appropriate formats for the input data, the prediction errors and the reflection coefficients are adopted, taking care so that for the latter, they remain invariant to the coefficient updating process. Care is also taken to prevent overflow during prediction error computation and reflection coefficient updating by using an appropriate exponent assignment algorithm and an upper bound on the step size mantissa.