Polar Code Trellis Decoder

Abstract

A single code trellis decoding algorithm is pro-posed to decode a polar code. Key features of a polar tree are exploited to identify critical states into which branches must enter. For a rate 1/2 polar code with K = 4, there are two states which need to be first established. Thereafter, the rest of the symbols are corrected making use of this constraint. Only Euclidean distance calculations were used within the algorithm to create a simple sub-optimal decoder. Its performance is the same as the equivalent standard SC-polar decoder if only Euclidean distance calculations are used. The single code trellis interpretation of the polar decoder provides the insight to a simple method to accurately predict decoding errors of the standard polar decoder over low SNRs. Specifically, the predicted FER closely matches that of a Genie algorithm that has knowledge of the transmitted symbols.