In 4-level QAM, or QAM-4, each symbol represents two bits of digital information. This is analogous to mapping the four DNA bases (A, C, G, T) to four points in the complex plane. The simplest form of QAM-4 maps these points to the corners of a square centered at the origin of the complex plane:
This is similar to the example mapping of DNA bases:
Both in 4-level QAM and DNA base mapping, the representation of information (be it digital data or biological sequences) in the complex plane enables sophisticated analysis and processing. In telecommunications, QAM maximizes the efficiency of data transmission by exploiting both amplitude and phase variations. In genomic signal processing, mapping DNA bases to complex numbers allows for the application of complex analysis techniques, offering new ways to examine the structure and function of genetic sequences.
The analogy extends to signal processing techniques applied to analyze the encoded signals. Fourier transforms, filtering, and error correction are staple methods in both fields. In genomics, these techniques can help identify patterns, mutations, or regulatory elements within DNA sequences. In telecommunications, they ensure accurate data transmission over noisy channels.
Both fields benefit from the complex plane representation for pattern recognition and analysis. In QAM, constellations (patterns of symbols in the complex plane) are crucial for understanding signal integrity and error rates. In genomic signal processing, patterns in the mapping of codons or DNA sequences can reveal biological significance, such as gene locations, regulatory motifs, or evolutionary relationships.