Discovering the Unequal Importance of Coded Bits in the Decoding of Polar Codes

Polar codes are a key component of modern wireless communication systems due to their capacity-achieving properties and low-complexity decoding algorithms. In conventional polar-coded systems, all coded bits are treated equally at the transmission stage, even though their contribution to successful decoding is not necessarily the same. In this paper, we investigate the unequal importance of coded bits in the decoding process of polar codes and study how this property can be exploited to improve system performance. We first address the problem of identifying the most important coded bits for a given polar decoder. Using a Binary Symmetric Channel (BSC) abstraction, we analyze how protecting a subset of coded bits affects the decoding Bit Error Rate (BER). For small block lengths, we determine the optimal set of important bits using brute-force search, and for larger block lengths, we employ surrogate and genetic optimization techniques to obtain near-optimal solutions. Our results clearly show that only a small subset of coded bits has a dominant impact on decoding performance. We then demonstrate how this insight can be translated into practical performance gains in wireless systems. By mapping the most important coded bits to the most reliable physical resources, such as well-estimated or high-gain Orthogonal Frequency Division Multiplexing (OFDM) subcarriers, significant BER improvements are achieved with virtually no additional complexity or signaling overhead. Furthermore, we extend the study to the full permutation problem, where all coded bits are reordered based on channel reliability when full Channel State Information (CSI) is available at the transmitter. This optimal permutation further enhances decoding performance and yields several-fold BER gains. Simulation results over BSC and multipath fading OFDM channels confirm the effectiveness of the proposed strategies, showing performance improvements of up to seven times compared to conventional mapping schemes. These findings highlight the practical value of exploiting coded-bit importance in polar-coded systems and open new directions for cross-layer code–channel-aware transmission design.