On iterative decoding of polar codes: Schedule-dependent performance and constructions

Abstract

Polar codes asymptotically achieve the symmetric capacity of any binary-input discrete memoryless channel under sequential decoding algorithms such as successive cancellation decoding. However, for applications with high throughput requirements, other decoding approaches may be a better fit, as sequential decoders are inherently difficult to parallelize in order to increase their throughput. Iterative belief-propagation decoding may pose a valid approach for such parallel decoders. In this work, we present an extensive study of polar codes under both sequential and parallel message schedules in iterative decoding, and reveal a strong dependency of the code performance on the schedule used for decoding. To overcome performance impairments observed when using polar codes optimized for sequential scheduling under parallel schedules, we present a method to optimize codes for iterative decoders working with parallel scheduling.