This paper presents a refined analysis of the block error rate (BLER) of polar codes over symmetric binary-input discrete memoryless channels under successive cancellation (SC) and successive cancellation list (SCL) decoding. A novel expression for the BLER under SC decoding is derived directly in terms of the decoder's LLRs. Building on this formulation, we propose a polar code construction algorithm optimized for SC decoding and evaluate its performance under SC and dynamic SC flip (DSCF) decoding against established SC-optimized constructions, including Gaussian approximation (GA)-based and Tal-Vardy polar codes. Furthermore, by decomposing the BLER into path loss and path selection components, we derive a novel LLR-based expression for the path loss probability, which enables an SCL-optimized polar code construction method. The proposed constructions are evaluated under SCL decoding with list sizes 2, 4, and 8, and are compared with 5G standard polar codes, GA-based designs, and Reed-Muller polar codes. Simulation results show that the proposed SC-optimized polar codes achieve up to a 0.2 dB performance gain under DSCF decoding over the AWGN channel compared to benchmark constructions, and exhibit superior performance over binary symmetric channels. For SCL-optimized polar codes, the proposed method achieves comparable or improved performance across all considered list sizes, with gains of up to 0.4 dB relative to benchmark designs.

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