Efficient sphere decoding of polar codes

The performance of the original successive cancellation decoder of short-length polar codes is inferior to that of the maximum-likelihood decoder. Existing sphere decoding algorithms of polar codes have a high computational complexity even for short lengths. This is because, when exploring the tree defined by the generator matrix of the code, existing algorithms employ loose branching conditions and end up visiting many more nodes than needed. We propose improved branching conditions that significantly reduce the search complexity. A simple example reports an improvement of two orders of magnitude at E_b over N₀ = 4 dB compared to the standard sphere decoders.