Improving the probability of complete decoding of random code by trading‐off computational complexity
Zan‐Kai Chong, Bok‐Min Goi, Hiroyuki Ohsaki, Cheng-Kuan Bryan Ng, Hong Tat Ewe · IET Communications · 2015
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.