  Non-uniform message quantization techniques such as
reconstruction-computation-quantization (RCQ) improve error-correction
performance and decrease hardware complexity of low-density parity-check (LDPC)
decoders that use a flooding schedule. Layered MinSum RCQ (L-msRCQ) enables
message quantization to be utilized for layered decoders and irregular LDPC
codes. We investigate field-programmable gate array (FPGA) implementations of
L-msRCQ decoders. Three design methods for message quantization are presented,
which we name the Lookup, Broadcast, and Dribble methods. The decoding
performance and hardware complexity of these schemes are compared to a layered
offset MinSum (OMS) decoder. Simulation results on a (16384, 8192)
protograph-based raptor-like (PBRL) LDPC code show that a 4-bit L-msRCQ decoder
using the Broadcast method can achieve a 0.03 dB improvement in
error-correction performance while using 12% fewer registers than the OMS
decoder. A Broadcast-based 3-bit L-msRCQ decoder uses 15% fewer lookup tables,
18% fewer registers, and 13% fewer routed nets than the OMS decoder, but
results in a 0.09 dB loss in performance.
