Implementation and modeling of parametrizable high-speed Reed Solomon decoders on FPGAs

Abstract. One of the most important error correction codes in digital signal processing is the Reed Solomon code. A lot of VLSI implementations have been described in literature. This paper introduces a highly parametrizable RS-decoder for FPGAs. By implementing resource-sharing and by using a fully pipelined multiplier/adder-unit in GF(2^m) it was possible to achieve high throughput rates up to 1.3Gbit/s on a standard FPGA, while using only an attractive small amount of logical elements (LE). The implementation, written in a hardware description language (HDL), is based on an inversionless Berlekamp Algorithm (iBA), whose structure leads to a chain of identical processing elements (PE). The critical path of one PE runs only through one adder and one multiplier. A detailed description of a resource-sharing methodology for this Berlekamp Algorithm and the achievable gain are presented in this paper.

The benchmarking for the design was done for different 8bit-codes against state-of-the-art FPGA-solutions and showed a gain of up to a factor of six regarding the AT-product, compared to other implementations.