This study evaluates large language models (LLMs) in generating code from algorithm descriptions in recent NLP papers. The task requires two key competencies: (1) algorithm comprehension: synthesizing information from papers and academic literature to understand implementation logic, and (2) coding expertise: identifying dependencies and correctly implementing necessary APIs. To facilitate rigorous evaluation, we introduce SciReplicate-Bench, a benchmark of 100 tasks from 36 NLP papers published in 2024, featuring detailed annotations and comprehensive test cases. Building on SciReplicate-Bench, we propose Sci-Reproducer, a dual-agent framework consisting of a Paper Agent that interprets algorithmic concepts from literature and a Code Agent that retrieves dependencies from repositories and implements solutions. To assess algorithm understanding, we introduce reasoning graph accuracy, which quantifies similarity between generated and reference reasoning graphs derived from code comments and structure. For evaluating implementation quality, we employ execution accuracy, CodeBLEU, and repository dependency/API recall metrics. In our experiments, we evaluate various powerful non-reasoning and reasoning LLMs as foundational models. The best-performing LLM using \ModelName~achieves only 39% execution accuracy, highlighting the benchmark's difficulty. Our analysis identifies missing or inconsistent algorithm descriptions as key barriers to successful reproduction. We make available our benchmark and code at https://github.com/xyzCS/SciReplicate-Bench and project homepage at https://xyzcs.github.io/scireplicate.github.io/.