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This work presents an efficient ASIC implementation of successive cancellation (SC) decoder for polar codes. SC is a low-complexity depth-first search decoding algorithm, favorable for beyond-5G applications that require extremely high throughput and low power. The ASIC implementation of SC in this work exploits many techniques including pipelining and unrolling to achieve Tb/s data throughput without compromising power and area metrics. To reduce the complexity of the implementation, an adaptive log-likelihood ratio (LLR) quantization scheme is used. This scheme optimizes bit precision of the internal LLRs within the range of 1-5 bits by considering irregular polarization and entropy of LLR distribution in SC decoder. The performance cost of this scheme is less than 0.2 dB when the code block length is 1024 bits and the payload is 854 bits. Furthermore, some computations in SC take large space with high degree of parallelization while others take longer time steps. To optimize these computations and reduce both memory and latency, register reduction/balancing (R-RB) method is used. The final decoder architecture is called optimized polar SC (OPSC). The post-placement-routing results at 16nm FinFet ASIC technology show that OPSC decoder achieves 1.2 Tb/s coded throughput on 0.79 mm$^2$ area with 0.95 pJ/bit energy efficiency.