Branching MERA codes: a natural extension of polar codes

We introduce a new class of circuits for constructing efficiently decodable error-correction codes, based on a recently discovered contractible tensor network [1]. We perform an indepth study of a particular example that can be thought of as an extension to Arikan’s polar code [2]. Notably, our numerical simulation show that this code polarizes the logical channels more strongly while retaining the log-linear decoding complexity using the successive cancellation decoder. These codes also display improved error-correcting capability with only a minor impact on decoding complexity. Efficient decoding is realized using powerful graphical calculus tools developed in the field of quantum manybody physics. In a companion paper [3], we generalize our construction to the quantum setting and describe more in-depth the relation between classical and quantum error correction and the graphical calculus of tensor networks.