Modified sphere decoding algorithms and their applications to some sparse approximation problems

This work presents modified sphere decoding (MSD) algorithms for optimal solution of some sparse signal modeling problems. These problems include multi-pulse excitation signal calculations for multi-pulse excitation (MPE), algebraic code excited linear predictive (ACELP) and -pulse maximum likelihood quantization (MP-MLQ) speech coders. With the proposed MSD algorithms, the optimal solution of these problems can be obtained at substantially lower computational cost compared with full search algorithm. The MSD algorithms are compared with a series of suboptimal approaches in sparse approximation of correlated Gaussian signals and low delay speech coding tasks.