This document compares Huffman coding and arithmetic coding for compressing DNA sequences. It finds that arithmetic coding achieves a higher compression ratio than Huffman coding when applied to DNA sequences. The document first describes the Huffman and arithmetic coding algorithms. It then applies both to sample DNA sequences and calculates the compression ratios achieved. The results show that arithmetic coding achieves compression ratios between 0.75-0.76, slightly outperforming Huffman coding. The document thus concludes that arithmetic coding is better for compressing DNA sequences.