Systematic binary deterministic rateless codes

We investigate a systematic construction of binary deterministic rateless codes (BDRCs). The codes are for networks with erasure channels. With a maximum distance separable (MDS) property, non-systematic BDRCs were first proposed in [1] with encoding complexity O(K), and decoding complexity is O(K²). Here K is the length of information bits. To reduce complexity, we study systematic-BDRCs (SBDRCs). For SBDRCs, the source first transmits m - 1 uncoded blocks, where m is the number of source blocks. Then, the source produces and transmits coded blocks in a rateless way. These coded blocks are produced using only cyclic-shift and XOR (exclusive or). The SBDRCs can use a large number of information blocks (potentially infinite m). On receiving any m distinct blocks (uncoded or coded), a sink can rebuild the source. The SBDRCs have encoding complexity O(∈K), and decoding complexity O(∈²K²), where ∈ is the source-to-sink block erasure probability.