On Tanner-Graph Message-Passing Decoders of
Polar Codes in Erasures
Paper ID : 1034-IST
1Tarannom Rajaie, 2Shahram Yousefi *
2Queen's University, Canada
Polar codes, recently invented by Arikan, are the first low complexity family of codes proved to achieve the capacity of any symmetric binary-input memoryless channels asymptotically using Successive Cancellation (SC) decoding. However, the performance of finite-length polar codes is not record breaking. In this work, we study the factor graph representation of finitelength polar codes and their effect on the belief propagation (BP) decoding process over Binary Erasure Channel (BEC). Particularly, we study the parity-check-based as well as the generator-based factor graphs of polar codes. As these factor graphs are not unique for a code, we study and compare the performance of Belief Propagation (BP) decoders on a number of specific graphs. Error rates and decoding complexities are reported for a number of cases. Comparisons are also made with the SC decoder. High BP errors are related to the so-called stopping sets of the underlying graphs. we discuss the pros and cons of BP decoder over SC decoder for various code lengths.
Polar Codes, Belief Propagation decoder, Successive Cancellation decoder, DEcoding complexity, short polar codes, bit error rate