Polar Encoding Matrix Layout for Lower Decoding Complexity

The patent divides the large code length N into multiple smaller code lengths n by constructing a generator matrix G_N composed of multiple sub-matrices G_n arranged in a specific pattern. This segmentation allows the encoding process to be broken down into multiple smaller encoding operations rather than one large operation, thereby reducing the overall encoding/decoding complexity while achieving the desired large code length.

The patent employs a nested structure where multiple generator matrices of smaller code length n are embedded within a larger generator matrix of code length N. The generator matrix G_N is constructed by arranging multiple G_n matrices in a specific pattern with zero matrices, creating a hierarchical structure that enables the system to achieve large code length N while performing only smaller-scale encoding operations, thus maintaining low complexity.

The patent applies local quality by designing a specific structure for the generator matrix where different regions serve different purposes. The generator matrix G_N is constructed with non-zero sub-matrices G_n positioned at specific locations and zero matrices at other locations, creating a structured sparsity pattern. This local structural design optimizes the encoding performance for large code lengths by ensuring that information is distributed across multiple reliable sub-codes rather than being concentrated in a single large code.