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Hybrid-ARQ-Aided Short Fountain Codes Designed for Block-Fading Channels

As a benefit of their inherent rateless nature, fountain codes constitute a favorable choice for protecting packet-based transmissions in the physical layer for wireless channels having varying quality. However, previous research has revealed that the performance of fountain codes substantially degrades as their block length is reduced. Three structural phenomena of the Tanner graph were identified by Mackay in the hard decoding of fountain codes on binary erasure channels (BECs), which may be referred to as having “no degree-one check nodes (CNs),” “no emerging degree-one CNs,” and “uncovered variable nodes (VNs).” In this paper, we explicitly analyzed how these structural phenomena influence their soft decoding algorithm. Furthermore, these phenomena are shown to be responsible for the high error floors when fountain codes are transmitted over noisy fading channels, particularly for the transmissions of short blocks. To eliminate the influence of these structural phenomena, we conceived a technique of generating a few specifically encoded bits with the aid of the associated Tanner graph. Simulation results have demonstrated that our improved Raptor (IRaptor) codes significantly reduce the packet loss ratio (PLR) of conventional fountain codes, despite imposing reduced low complexity. Finally, we conceive a novel adaptive hybrid automatic repeat request (HARQ) scheme based on a lookup table (LUT)-aided technique, which may adapt its coding rate for each transmission. Our simulation results demonstrated that the proposed IRaptor HARQ achieves a similar performance to the Long-Term Evolution (LTE) turbo-coded HARQ scheme or even outperforms the LTE arrangement for block length in excess of 1000 bits.