Efficient Bit-to-Symbol Likelihood Mappings

This innovation is an efficient algorithm designed to perform bit-to-symbol and symbol-to-bit likelihood mappings that represent a significant portion of the complexity of an error-correction code decoder for high-order constellations. Recent implementation of the algorithm in hardware has yielded an 8-percent reduction in overall area relative to the prior design. This gain resulted from changing just two operations in a complex decoder. Larger gains are possible for larger constellations that are of interest for deep-space optical communications. The algorithm structures the bit-to-symbol/symbol-to-bit operations like a tree that forms a portion of a Fast-Fourier-Transform (FFT). Much like an FFT, the parallel computation may be structured in order to reduce repeated computations. Symmetry in the values was noted and allowed for the reduction of the bit-to-symbol mapping by a factor of 2.