Non-binary low-density parity-check codes are robust to various channel impairments. However, based on the existing decoding algorithms, the decoder implementations are expensive because of their excessive computational complexity and memory usage. Based on the combinatorial optimization, we present an approximation method for the check node processing. The simulation results demonstrate that our scheme has small performance loss over the additive white Gaussian noise channel and independent Rayleigh fading channel. Furthermore, the proposed reduced-complexity realization provides significant savings on hardware, so it yields a good performance-complexity tradeoff and can be efficiently implemented.

We explore the use of Data-Level Parallelism (DLP) as a way of improving the energy efficiency and power consumption involved in running applications on an FPGA. We show that static power consumption is a significant fraction of the overall power consumption in an FPGA and that it does not change significantly even as the area required by an architecture increases, because of the dominance of interconnect in an FPGA. We show that the degree of DLP can be used in conjunction with frequency scaling to reduce the overall power consumption.

FPGAs are widely used for evaluating the error-floor performance of LDPC (low-density parity check) codes. We propose a scalable vector decoder for FPGA-based implementation of quasi-cyclic (QC) LDPC codes that takes advantage of the high bandwidth of the embedded memory blocks (called Block RAMs in a Xilinx FPGA) by packing multiple messages into the same word. We describe a vectorized overlapped message passing algorithm that results in 3.5times to 5.5times speedup over state-of-the-art FPGA implementations in literature.