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Overview: Fountain codes is a typical rateless coding scheme, which can also provide reliable guarantee for data transmission without channel feedback or channel estimation, and exhibit excellent adaptability to complex and variable optical wireless communication (OWC) channels. This paper reviews the development of fountain codes proposed nearly three decades ago. In 1998, Luby and other scholars proposed the concept of digital fountain in the context of solving large-scale data reliability transmission and broadcasting or multicast. Until 2002, Luby and his team designed the first practical fountain codes which be called Luby transform (LT) codes. In the theory of LT codes, robust soliton distribution (RSD) is innovatively proposed to regularize the choice of source symbols. In 2004, in order to solve the disadvantages of LT codes such as the high complexity and disability of realizing linear-time encoding or decoding, Shokrollahi et al. proposed a novel encoding scheme named Raptor (rapid tornado) codes that creatively concatenates linear block codes and LT codes together. They also optimized the fixed distribution function of Raptor codes for different information lengths. After that, some new digital fountain codes such as system fountain codes, incremental codes, spinal codes and Kite codes were successively proposed these years. Although the fountain codes was originally proposed for erasure channels, since it has great adaptivity in various channel conditions, the research of fountain code has been extended to the wireless channel in 2006, and the soft decision decoding algorithm for the fountain codes under wireless channels was obtained. At present, the fountain codes has been widely applied in wireless communication relay, space diversity, wireless cooperative transmission, etc. Thanks to its rateless characteristics, any number of coded packets can be adaptively generated according to channel conditions, producing excellent performance under erasure channel. However, when fountain codes are used in wireless channels, the design of the coding and degree distribution need to be reconsidered, which often causes the problem of high complexity and error floor. Therefore, the research hotspot of the fountain code under optical wireless communication is to cascade it with the channel coding schemes with capability of error detection, so that the fountain code can also exert its advantages under the noise channel. In short, the application prospects of fountain codes in OWC will be promising. This review focuses on the principle of fountain code and the fountain code with excellent performance, and it sheds some light on the future application of fountain code in scenario of OWC.
Schematic diagram of fountain code principle
(a) Coding principle of fountain code; (b) Decoding principle of fountain code
Encoding process of LT code
Probability density distribution of RSD at K=10000, δ=0.05, c=0.2, 0.3, 0.4, 0.5, 0.6
Encoding process of Raptor code
BP decoding method for LT codes
Performance of BP and GE decoding of LT codes under different code length K