Error Bounds of Polar Codes Under Varying Channel Conditions

Abstract:
Polar codes are the first linear block codes provably achieving the capacity of any binary-input discrete memoryless channel. Construction is explicit and both low-complexity encoding and decoding methods are available. As polar codes are constructed in a channel-specific manner, we investigate their performance under varying channel conditions. Focussing on the setting established in Arikan’s seminal work, we present a survey on the performance guarantees as implied by the successive cancellation decoder. Having established the theoretical setting, we present results for both binary erasure channels as well as binary symmetric channels.