  The so-called fast polar decoding schedules are meant to improve the decoding
speed of the sequential-natured successive cancellation list decoders. The
decoding speedup is achieved by replacing various parts of the serial decoding
process with efficient special-purpose decoder nodes. This work incorporates
the fast decoding schedules for polar codes into their quantized finite
alphabet decoding. In a finite alphabet successive cancellation list decoder,
the log-likelihood ratio computations are replaced with lookup operations on
low-resolution integer messages. The lookup tables are designed using the
information bottleneck method. It is shown that the finite alphabet decoders
can also leverage the special decoder nodes found in the literature. Besides
their inherent decoding speed improvement, the use of these special decoder
nodes drastically reduces the number of lookup tables required to perform the
finite alphabet decoding. In order to perform quantized decoding using lookup
operations, the proposed decoders require up to 93% less unique lookup tables
as compared to the ones that use the conventional successive cancellation
schedule. Moreover, the proposed decoders exhibit negligible loss in error
correction performance without necessitating alterations to the lookup table
design process.
