List Decoding of Short Codes for Communication over Unknown Fading Channels

In this paper, the advantages of list decoding for short packet transmission over fading channels with an unknown state are illustrated. The principle is applied to polar codes (under successive cancellation list decoding) and to general short binary linear block codes (under ordered-statistics decoding). The proposed decoders assume neither a-priori knowledge of the channel coefficients, nor of their statistics. The scheme relies on short pilot fields that are used only to derive an initial channel estimate. The channel estimate is required to be accurate enough to enable a good list construction, i.e., the construction of a list that contains, with high probability, the transmitted codeword. The final decision on the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. Numerical results are provided for the Rayleigh block-fading channel and compared to finite-length performance bounds. The proposed technique provides (in the short block length regime) gains of 1 dB with respect to a traditional pilot-aided transmission scheme.