Polar Coding Theory And Its Quantized Decoding Algorithm

Starting from Shannon’s celebrated1948channel coding theorem, re-searchers devote much efforts to the capacity-approaching codes. The gap of Turbo codes and LDPC under BPSK modulation to capacity is less than0.1dB. However, these results are obtained by simulation with long code length and there is no rigorous theoretical proof. Polar codes, proposed by Arikan, are the first proven capacity-achieving coding schemes to achieve the symmetric capacity of the binary-input discrete memoryless channels while having an explicit construction. It has attracted widespread attention from academics due to its low complexity encoding and decoding algo-rithms. This coding method has a number of advantages, such as capacity-approaching, high throughput utilizing parallel decoding architecture, which will be of importance in future communication systems.Starting from the general framework of channel polarization theory, this paper focuses on the quantization decoding of polar codes and the re-lated optimization algorithm. The study mainly focuses on the following three research points.First, three uniform quantizers are designed for successive cancellation (SC) decoding of polar codes based on either optimizing the equivalent channel capacity, cutoff rate or mean-squared error (MSE). Next, exploiting the cutoff rate maximizing criterion, a modified Gaussian approximation (GA) method is proposed to construct polar codes and estimate frame error rate (FER) performance under the quantized decoding algorithms. At last, utilizing the modified GA, the optimal quantization bits can be determined. In addition, some simple and practical quantization schems of SC list de-coding algorithm have proposed in the log-probability domain and the log-likelihood ratio (LLR) domain. Simulation results have shown that a6-bit uniform quantized SC de-coder can achieve a near floating point performance and the upper-bound of FER can be estimated precisely using the modified GA method. The pro-posed method consumes no more than4.5quantization bits under quantized decoding algorithms. For the quantized SC list decoding,4bit for the quan-tization of channel log-probability in the log-probability domain and in-creasing the number of quantization bits by one per stage can achieve the floating point performance. On the other hand,7bit for the quantization of LLR in the LLR domain can also achieve a near floating point performance and this method is more simple and practical.