Systematic rateless erasure code for short messages transmission

• Systematic Random code reconstruct the original message with zero extra coded symbols if the first k coded symbols are received intact.
• Reconstruct the original message with 99.9% success probability using extra ten overhead symbols.
• In channels of low erasure probability, systematic Random code outperforms Random code in term of lesser extra coded symbols and decoding steps to achieve complete decoding.

In this paper, we propose a systematic rateless erasure code, namely systematic Random (SYSR) code based on Random code for short messages transmission. Given a message of k   symbols, the sender will first send the message to the receiver as Part I coded symbols. The rest of coded symbols starting from (k+1)k+1th onwards are termed as Part II coded symbols and they are generated by adding the message symbols randomly (XOR operation). The receiver reconstructs the original message instantly if all the Part I coded symbols are received intact. Otherwise, the receiver reconstructs the original message from any k+10k+10 coded symbols of Part I and II with high probability of complete decoding (PCD), i.e. 99.9% success probability. Though SYSR code inherits the high decoding complexity of Random code, i.e. O(k3)O(k3), both analysis and simulation results show that SYSR code achieves better PCD and fewer decoding steps than Random code.

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