21 September 2007 LDPC decoder with a limited-precision FPGA-based floating-point multiplication coprocessor
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Implementing the sum-product algorithm, in an FPGA with an embedded processor, invites us to consider a tradeoff between computational precision and computational speed. The algorithm, known outside of the signal processing community as Pearl's belief propagation, is used for iterative soft-decision decoding of LDPC codes. We determined the feasibility of a coprocessor that will perform product computations. Our FPGA-based coprocessor (design) performs computer algebra with significantly less precision than the standard (e.g. integer, floating-point) operations of general purpose processors. Using synthesis, targeting a 3,168 LUT Xilinx FPGA, we show that key components of a decoder are feasible and that the full single-precision decoder could be constructed using a larger part. Soft-decision decoding by the iterative belief propagation algorithm is impacted both positively and negatively by a reduction in the precision of the computation. Reducing precision reduces the coding gain, but the limited-precision computation can operate faster. A proposed solution offers custom logic to perform computations with less precision, yet uses the floating-point format to interface with the software. Simulation results show the achievable coding gain. Synthesis results help theorize the the full capacity and performance of an FPGA-based coprocessor.
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Raymond Moberly, Raymond Moberly, Michael O'Sullivan, Michael O'Sullivan, Khurram Waheed, Khurram Waheed, } "LDPC decoder with a limited-precision FPGA-based floating-point multiplication coprocessor", Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 66970R (21 September 2007); doi: 10.1117/12.733510; https://doi.org/10.1117/12.733510

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