Bounds on the performance of partial selection networks

The evaluation of the performance of partial selection networks which select a set of M elements from a set of N inputs is addressed. The partial selection problem occurs when dealing with non-exhaustive multi-path breadth-first searches, like in the M algorithm or the bidirectional algorithm. These algorithms are used in the decoding of convolutional codes. The paper presents a set of bounds to evaluate the quality of regular, Delta class, networks of depth 1gN and width N/2, with respect to their selection capabilities. The results from the bounds are compared to Monte Carlo simulations of the selection capabilities of the Banyan and Alekseyev networks. Finally, the performance degradation associated with the use of these networks on the performance of a bidirectional decoder is presented. In particular, the authors show that even with imperfect selection, the bidirectional decoder can outperform a Viterbi decoder of comparable complexity.<>