Research on the Optimal Decoding Overhead of LT Codes

The LT codes can generate coded symbols as much as needed, which property makes the LT codes be the first class of rateless codes. As the encoding process of a traditional LT code would depends on the feedback message, which code can suit for various channel states, at the cost of affected by twice transmission delay. But in many scenarios, the feedback messages would bring some drawbacks, such as the feedback channels are not existed or the transmission distances are too much, etc.. And the error performances of LT codes also can be pre-determined by using different output degree distributions. For these reasons, if the encoder can pre-known the channel states, there is a chance to make the data transmitted with a optimal efficiency. As in the research field on rateless codes, the code rate were barely to be concerned, instead of its reciprocal, which named as overhead. In this paper, by quantized the transmission efficiency by using the proposed notation Recovery Ratio Per Symbol (RRPS), the optimal decoding overhead and optimal encoding overhead which are related to the maximum coding efficiency, and which would make the LT codes have the potential to transmit data without feedback messages with a higher transmission efficiency.