Branching MERA codes: a natural extension of polar codes

Understand

We introduce a new class of circuits for constructing efficiently decodable error-correction codes, based on a recently discovered contractible tensor network.

• We perform an in-depth study of a particular example that can be thought of as an extension to Arikan's polar code.
• 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.