Improving the probability of complete decoding of random code by trading-off computational complexity

Random code is a rateless erasure code that can reconstruct the original message of k symbols from any k + 10 encoded symbols with high probability of complete decoding (PCD), i.e. 99.9% successful decoding, irrespective of the message length, k. Nonetheless, random code is inefficient in reconstructing short messages. For example, a message of k = 10 symbols requires k + 10 = 20 encoded symbols, i.e. two times the original message length in order to achieve high PCD. In this study, the authors propose micro-random code that encodes and decodes the original message using symbols of smaller dimensions, namely micro symbols. The authors´ analysis and numerical simulations show that micro-random code achieves high PCD with only k + 1 encoded symbols. As the trade-off for such a gain, the number of steps for decoding increases exponentially with each incrementing segmentation factor, α. In addition, the numerical results show that the decoding time increases by about 400% at α = 10, depending on the processing power of the system.