Stepping-Random Code: A Rateless Erasure Code for Short-Length Messages

SUMMARY Rateless erasure code is an error correction code that isable to encode a message of k uncoded symbols into an infinite numberof coded symbols. One may reconstruct the original message from any k (1 +) coded symbols, where denotes the decoding inefficiency. Thispaper proposes a hybrid code that combines the stepping code and randomcode and name it as Stepping-Random (SR) code. The Part I (first k ) codedsymbols of SR code are generated with stepping code. The rest of the codedsymbols are generated with random code and denoted as Part II coded sym-bols. The numerical results show that the new hybrid code is able to achievea complete decoding with no extra coded symbol ( =0) if all the Part Icoded symbols are received without loss. However, if only a portion of PartI coded symbols are received, a high probability of complete decoding isstill achievable with k +10 coded symbols from the combination of PartI and II. SR code has a decoding complexity of O ( k ) in the former and O an infinite number of coded symbols. Typically, a receiver(β

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