The channel coding is one of the key technologies in communication systems and its traditional theory is based on algebra and the nite eld GF ( p ). This paper rstly establishes the mathematical model of the channel coding in noisy cases, then introduces the novel channel coding theory based on harmonic analysis and applies important tools of harmonic analysis including compressed sensing and Walsh-Hadamard transform to achieve the decoding and blind recognition of channel coding. Some elementary results and newly progress of channel coding based on harmonic analysis are surveyed including Gilbert-Varshamov bound theorem, l1 decoding, RIP condition, Walsh-Hadamard transform.