On Fast SC-based Polar Decoders: Metric Polarization and a Pruning Technique

Abstract: Short- to medium-block-length polar-like and polarization-adjusted convolutional (PAC) codes have demonstrated exceptional error-correction performance through sequential decoding. Successive cancellation list (SCL) decoding of polar-like and PAC codes can potentially match the performance of sequential decoding though a relatively large list size is often required. By benefiting from an optimal metric function, sequential decoding can find the correct path corresponding to the transmitted data by following almost one path on average at high Eb/N0 regimes. When considering a large number of paths in SCL decoding, a main bottleneck emerges that is the need for a rather expensive sorting operation at each level of decoding of data bits. In this paper, we propose a method to obtain the optimal metric function for each depth of the polarization tree through a process that we call polarization of the metric function. One of the major advantages of the proposed metric function is that it can be utilized in fast SC-based (FSC) and SCL-based (FSCL) decoders, i.e., decoders that opt to skip the so-called rate-1 and rate-0 nodes in the binary tree representation for significantly more efficient implementation. Furthermore, based on the average value of the polarized metric function of FSC-based decoders, we introduce a pruning technique that keeps only the paths whose metric values are close to the average value. As a result, our proposed technique significantly reduces the number of required sorting operations for FSCL-based decoding algorithms. For instance, for a high-rate PAC(128,99) code, SCL decoding with a list size of 32 achieves error-correction performance comparable to the Fano algorithm. Our method reduces the number of sorting operations of FSCL decoding to 33%, further decreasing latency.