Reducing the decoding complexity of RaptorQ codes for delay sensitive applications using a simplified and scaled-down matrix

Abstract

RaptorQ codes, a class of fountain codes, are widely used as a way to achieve forward error correction at the application layer. Whereas RaptorQ codes perform impressively in terms of symbol recovery, its high computational complexity limits its applicability in demanding real-time scenarios. As a way to resolve this inefficiency, we propose using a novel matrix structure designed to reduce the decoding complexity of RaptorQ codes. Specifically, we replace Luby Transform codes and Low-density Parity Check (LDPC) codes in RaptorQ code operations using a novel binary matrix based on Kolchin’s Theorem. Our proposed improvements remove the need for LDPC codes to decrease the dimension of the matrix, and it reduces the latency resulting from matrix inversions. Given that the resulting latency from this process dominates the entire RaptorQ code decoding process, our changes offer the potential for reducing the latency dramatically. Based on an extensive set of simulations using our proposed matrix structure under various configurations, we show that the proposed decoding latency is faster than that of RaptorQ codes, while maintaining an at-par decoding-failure probability.