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We implemented a soft-decision decoder of (204,188)-Reed-Solomon code, which is used widely in standards for satellite, terrestrial, and other broadcasting systems. The decoder employs a list decoding technique using iterative adaptive belief propagation and bounded distance decoding. One decoded word is chosen from the list by MAP decoding, and some ideas are applied to reduce its complexity. When the channel throughput is 32 Mbps, the decoder works at 88 MHz in an FPGA, and obtains 1 dB performance gain compared with ordinary hard-decision decoders.