Erasure selection for errors-and-erasures decoding algorithms is investigated and analyzed, where declaring erasures provides additional gain for hard decision decoding. To derive an analytical criterion for optimal erasure selection, we first investigate erasure effects on decoding performance, by which a metric function for erasure selection is derived. From the derived metric, a suboptimal threshold is defined, which can be used for errors and erasures decoding of large code-distance channel codes. Moreover, application to M-ary (M>2) PAM constellation is also described. For verification of the proposed erasure threshold, simulation results with popular channel codes are included.

A new scheme is proposed to optimally reduce the modulation modes for bit and power allocation algorithm in multi-carrier transmissions. By reducing the modulation modes, computational load and hardware complexity can be reduced without any performance degradation. When modulation modes for rectangular QAM are available at a transmitter, it is shown that the modulation modes for rectangular QAM can be reduced to those for square QAM which is the subset of rectangular QAM. After identifying a power allocation property of rectangular QAM, it is proved that the optimal allocation with square QAM has exactly the same performance as that with rectangular QAM. Numerical results show the reduction of computational load and verify our theoretic presentations.