Universal Reed-Solomon decoders based on the Berlekamp-Massey algorithm

Abstract

Universal Reed-Solomon decoders allow flexibility in some or all of the code parameters, and hence lend themselves to applications wherein adaptability and reconfigurability are important considerations. In this paper, we consider universal finite field arithmetics using either canonical polynomial basis or shifted polynomial basis, and propose a high-speed universal Reed-Solomon decoder by modifying the high-speed decoder proposed in [10].

High-speed area-efficient versatile Reed-Solomon decoder design for multi-mode applications

“…Thus [9] firstly researched this issue and provided a complete universal RS decoder. Constructed on decomposed iBM and RiBM architectures, two universal designs for all code parameters were presented in [10] [11] respectively. And the systolic ME architecture proposed in [12] is also able to accommodate variable finite field definitions.…”

“…7, by inserting register between two Montgomery multipliers and applying full pipelining to each of them (the dotted line represents pipelining registers), the universal multiplier can achieve the same critical path delay Tan~2Txur with another universal multiplier employed in [11]. Note that the versatile multiplier design in [11] computes the product of A and B as ad-mC with an extra scaling factor «"'. This scaling factor can be eliminated in BM algorithm; however, when employing other RS decoding algorithms, the scaling factor perhaps affects the validity of decoding.…”