Low-energy heterogeneous digit-serial Reed-Solomon codecs

Reed-Solomon (RS) codecs are used for error control coding in many applications such as digital audio, digital TV, software radio, CD players, and wireless and satellite communications. This paper considers software-based implementation of RS codecs where special instructions are assumed to be used to program finite field multiplication datapaths inside a domain-specific programmable digital-signal processor (DS-PDSP). A heterogeneous digit-serial approach is presented, where the heterogeneity corresponds to the use of different digit-sizes in the multiply-accumulate (MAC for polynomial multiplication) and degree reduction (DEGRED for polynomial module operation) subarrays. The salient feature of this digit-serial approach is that only the digit-cells are implemented in hardware, the finite field multiplications are performed digit-serially in software by dynamically scheduling the internal digit-level operations in RS encoders and decoders. It is concluded that, for 2-error-correcting RS(n,k) codec implementations over finite field GF(2⁸), a parallel MAC unit (of digit-size 8) and a DEGRED unit with digit-size 2 is the best datapath, with respect to least energy consumption and energy-delay products. With this datapath architecture and appropriate digit-serial scheduling strategies, more than 60% energy reduction and more than 1/3 energy delay reduction can be achieved compared with the parallel multiplication datapath based approach