Partial Order-Based Decoding of Rate-1 Nodes in Fast Simplified Successive-Cancellation List Decoders for Polar Codes

Abstract

Polar codes are the first family of error-correcting codes that can achieve channel capacity. Among the known decoding algorithms, Successive-Cancellation List (SCL) decoding supported by a Cyclic Redundancy Check (CRC) shows the best error-correction performance at the cost of a high decoding complexity. The decoding of Rate-1 nodes belongs to the most complex tasks in SCL decoding. In this paper, we present a new algorithm that largely reduces the number of considered candidates in a Rate-1 node and generate all required candidates in parallel. For this purpose, we use a partial order of the candidate paths to prove that only a specified number of candidates needs to be considered. Further complexity reductions are achieved by an extended threshold-based path exclusion scheme at the cost of negligible error-correction performance loss. We present detailed Application-Specific Integrated Circuit (ASIC) implementation data on a 28 nm Fully Depleted Silicon on Insulator (FD-SOI) Complementary Metal-Oxide-Semiconductor (CMOS) technology for decoders with code length 128. We show that the new decoders outperform state-of-the-art reference decoders. For list size 8, improvements of up to 158.8% and 62.5% in area and energy efficiency are observed, respectively.