On box-operations for L-values and their applicability to soft-decision algorithms

Modern digital communication systems can benefit from soft-decision algorithms in receiver implementations. Such algorithms require reliability information about every data bit which is typically given in terms of Log-Likelihood Ratios (LLRs) or short L-Values. Several efficient receiver implementations based on L-Values have already been proposed in the literature. Many of them exploit the famous Box-Plus operation. Its inverse has also been introduced in terms of the Box-Minus operation. In this letter, at first the specific characteristics of both operations, the Box-Plus as well as the Box-Minus operation, will briefly be reviewed. Secondly, as a novelty we will define two more operators, the Box-Multiply and the Box-Divide operation. An illustrative example will demonstrate the necessity for these two new operators. Finally, we will propose a practical solution for eliminating a critical side constraint of the Box-Minus operation which was known to be a limiting factor so far.