Edit distance is a computational grand challenge problem to quantify the minimum number of editing operations required to modify one string of characters to the other, finding many applications of natural language processing. In recent years, relevant and increasing interest has also emerged from deoxyribonucleic acid (DNA) applications, like Next Generation Sequencing and DNA storage technologies. Both applications share two crucial features: i) the information is coded into the four bases of DNA and ii) the level of operational noise is still high causing errors in the data, requiring inclusion in the workflow of the computation of algorithms such as the edit distance for finding similarities between sequences. To boost this computation many solutions are available in the literature. Among them, the FPGAs are largely used since the data domain of those applications is strings of 4 characters represented as two-bit values, inconveniently fitting the basic data types of ordinary CPUs and GPUs, with additional benefits of providing a high level of parallelism and low processing latency. This contribution presents a computing- and energy-efficient design implementing the edit distance algorithm combining metaprogramming and High-Level Synthesis. We also assess the performance of our design targeting recent FPGA-based accelerators. Our solution uses nearly 90% of FPGA basic-block hardware resources achieving about 90% of computing efficiency delivering a maximum throughput of 16.8 TCUPS and an energy efficiency of 46 Mpair/Joule, enabling the use of FPGAs as a new class of accelerators for High Performance Computing in DNA applications. • Computing- and energy-efficient edit distance algorithms running on FPGA accelerators. • Targeting short reads for DNA data storage and long reads for genomics applications. • Combining metaprogramming and HLS to design and optimize C codes for FPGA devices. • Achieving about 90% of computing efficiency and near 90% FPGA resources occupancy. • Delivering a peak throughput of 16.8 TCUPS and an energy efficiency of 46 Mpair/Joule.

Non-binary low-density parity-check (NB-LDPC) codes are known to offer several advantages over their binary counterparts, but the higher complexity, and the resource-hungry nature of decoding algorithms have so far restricted their practical usage. In this paper, we propose a new decoding algorithm for NB-LDPC codes over finite fields of characteristic 2, based on a novel binary expansion of the Q-ary Tanner graph. While it offers substantial complexity gains, simulation results demonstrate that the performance loss of the new algorithm, in comparison to the best known decoder, is quite small. Furthermore, due to being based on a binary graph, it is particularly attractive for hardware implementations. We also suggest a simplified version of the algorithm, which offers even higher gains in complexity.

This paper presents a majority-logic decoding (MLgD) algorithm for non-binary LDPC codes based on a novel expansion of the Tanner graph. The expansion introduced converts the Q-ary graph into a binary one, which makes the new MLgD algorithm more attractive for hardware implementations. Proposed algorithm performs significantly better than the existing MLgD algorithms in the waterfall region, and it shows a much lower error-floor as well. Algorithm only requires integer additions, comparisons, finite field operations and some binary operations. Thus, it offers an effective trade-off between performance and complexity in decoding non-binary LDPC codes.