Fast, Flexible, and Area-efficient Decoders for Polar Codes

Book excerpt: "Polar codes have received a great deal of attention in the past few years to the extent that they are selected to be included in the 5th Generation of Wireless Communications Standard (5G). Specifically, polar codes were selected as the coding scheme for the Enhanced Mobile Broadband (eMBB) control channel which requires codes of short length. The main bottleneck in the deployment of polar codes in 5G is the design of a decoder which can achieve good error-correction performance, with low hardware implementation cost and high throughput. Successive-Cancellation (SC) decoding was the first algorithm under which polar codes could achieve capacity when the code length is very high. However, for finite practical code lengths, SC decoding falls short in providing a reasonable error-correction performance because of its sub-optimality with respect to the Maximum-Likelihood (ML) decoder. Sphere Decoding (SD) is an algorithm that can achieve the performance of ML decoding with a very high complexity. In order to close the gap between SC and ML decoding, Successive-Cancellation List (SCL) decoding keeps a list of candidates and selects the one with the best Path Metric (PM). Although SCL provides a good error-correction performance, it comes at the cost of higher complexity and lower throughput. In this thesis, we first propose a low complexity SD algorithm which provides a good trade-off between the error-correction performance and the complexity of the decoder for polar codes of short lengths. We then propose algorithms to speed up the SCL decoders. We prove that while these algorithms have much higher throughput than the conventional SCL decoder, they incur no error-correction performance loss. We further propose several techniques to reduce the area occupation in the hardware implementation of SC and SCL decoders by reducing their memory requirements. We solve the flexibility issue of fast SC-based decoders and introduce a completely rate-flexible scheme. Hardware architectures for the proposed algorithms are presented and comparisons with state of the art are made. Finally, we evaluate the performance of polar codes in 5G and we show that polar codes can be used in practical applications by proposing a blind detection scheme with polar codes." --