On <inline-formula> <tex-math notation="LaTeX">$A^{\ast}$</tex-math></inline-formula> Algorithms for Decoding Short Linear Block Codes

Abstract

The $A^{\ast}$ algorithm for decoding linear block codes is an efficient tree-search method for decoding short linear block codes. The information contained in the parity bits are potentially useful for reducing the edges needed in the tree search. We propose to extract the information embedded in the parity bits by considering sums of parity bits which can be decided by part of the message bits. Analysis for the number of required message bits for obtaining sums of parity bits is provided. The information contained in the parity bits can help to reduce the number of search tree edges.