Soft-Decision Error Correction Decoding With Grouped Reliability Selection

The patent segments the D-dimensional pulse amplitude modulation symbols into multiple groups, where each group contains a subset of dimensions. The soft decision unit processes each group separately to calculate hard decision bits and reliabilities, rather than processing all D dimensions simultaneously. This segmentation reduces the computational complexity from O(2^N * D) to O(2^N * (D/G)), where G is the number of groups, thereby reducing calculation processing time while maintaining decoding capability.

The patent performs preliminary calculation of hard decision bits and reliabilities for each dimension independently before combining them. The soft decision unit pre-calculates the hard decision bit and reliability for each dimension of the pulse amplitude modulation symbols, storing these intermediate results. This preliminary action allows subsequent decoding stages to use these pre-computed values without recalculating, significantly reducing the overall calculation processing time.

The patent divides the large D-dimensional lookup table requirement into multiple smaller lookup tables, each corresponding to a group of dimensions. Instead of creating a single lookup table with 2^N * D entries, the system creates G separate lookup tables, each with 2^N * (D/G) entries. This segmentation reduces the memory requirement from O(2^N * D) to O(2^N * (D/G)), making the system implementable for larger D values.

The patent transforms the problem from a single large D-dimensional lookup table into multiple smaller tables organized in a hierarchical structure. By introducing the grouping dimension, the system replaces a flat 2^N * D table with a structured arrangement of G tables, each of size 2^N * (D/G). This dimensional reorganization reduces the peak memory requirement and allows for more efficient memory management.