For modern short block-length codes, a gap remains between practical decoding algorithms—such as belief propagation (BP) and successive cancellation (SC)—and optimal maximum likelihood (ML) decoding. Ensemble decoding schemes offer a promising approach to bridge this gap, improving both decoding latency and error correction performance. These schemes rely on multiple parallel decoding attempts, using either varied noise realizations or alternative representations of the decoding graph, to generate a diverse set of candidate codewords from which the final estimate is selected.

In this talk, we build an intuition for how ensemble decoding can enhance stand-alone decoders. We focus on three distinct species in the ensemble decoding zoo: generalized automorphism ensemble decoding, endomorphism ensemble decoding, and subcode ensemble decoding. Each of these approaches highlights how fundamental linear algebraic concepts can be leveraged to improve the decoding performance of modern short-length codes.