Quantization of a Low-Density Parity-Check (LDPC) Decoder: Limited-Precision Digital Design of the Sum-Product Algorithm (SPA) for Wireless Voice and Video Communication Channels

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of the Dissertation Quantization of a Low-Density Parity-Check (LDPC) Decoder: Limited-Precision Digital Design of the Sum-Product Algorithm (SPA) for Wireless Voice and Video Communication Channels. by Raymond B Moberly Claremont Graduate University and San Diego State University: 2012 This dissertation presents two-bit and three-bit quantizations for Sum Product Algorithm (SPA) decoding of Low-Density Parity-Check (LDPC) codes. The study involves evaluation of both decoding performance and hardware implementation requirements. Trade-o s between these factors are considered. The quantizations are simulated in software to measure decoding performance. While quantization e ects are the focal point of the research, a comparison of the number of decoding iterations and of the number of bits of precision used in the decoder are both presented along with the quantization experiments. Decoder performance, measured in terms of both Bit Error Rate (BER) and Frame Error Rate (FER), is tested for each two-bit and three-bit quantization over a range of Signal to Noise Ratio (SNR) values. No single quantization outperforms all other quantizations for the entire tested SNR range. Analysis of the SPA is performed, revealing strategies for computational e ciency and digital design. The hardware designs combine the parity-check and variable-node update steps of the SPA into a single update computation. The update computation is implemented in a hardware design language (HDL), synthesized to programmable logic, and then tested on a Field Programmable Gate Array (FPGA). Hardware implementation requirements, as measured from the synthesis results, are evaluated and compared to a selection of other published works, particularly the work of Planjery et al. A exible implementation is proposed that can adapt the quantization as the channel conditions change.

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