The paper presents a Design Space Exploration (DSE) experiment which has been carried out in order to determine the optimum FPGA-based Variable-Length Decoder (VLD) computing resource and its associated instructions, with respect to an entropy decoding task which is to be executed on the FPGA-augmented TriMedia/CPU64 processor. We first outline the extension of the TriMedia/CPU64 architecture, which consists of an FPGA-based Reconfigurable Functional Unit (RFU) and the associated generic instructions. Then we address entropy decoding and propose a strategy to partially break the data dependency related to variable-length decoding. Three VLDs (VLD-1, VLD-2, VLD-3) instructions which can return 1, 2, or 3 symbols, respectively, are subsequently analyzed. After completing the DSE, we determined that VLD-2 instruction leads to the most efficient entropy decoding in terms of instruction cycles and FPGA area. The FPGA-based implementation of the computing resource associated to VLD-2 instruction is subsequently presented. When mapped on an ACEX EP1K100 FPGA from Altera, VLD-2 exhibits a latency of 8 TriMedia cycles, and uses all the Electronic Array Blocks and 51% of the logic cells of the device. The simulation results indicate that the VLD-2-based entropy decoder is 43% faster than its pure software counterpart.