The minimum distance of classical and quantum turbo-codes

TL;DR

This paper develops a theoretical framework for quantum stabilizer turbo-encoders with unbounded minimum distance, highlighting the conditions needed for such codes to achieve optimal error correction capabilities.

Contribution

It introduces a unified theory for classical and quantum turbo-encoders, specifying conditions like recursiveness and systematic structure for unbounded minimum distance.

Findings

Inner seed encoder must be recursive

Encoder should be systematic or have a recursive truncated decoder

Theory applies to quantum stabilizer codes

Abstract

We present a theory of quantum stabilizer turbo-encoders with unbounded minimum distance. This theory is presented under a framework common to both classical and quantum turbo-encoding theory. The main conditions to have an unbounded minimum distance are that the inner seed encoder has to be recursive, and either systematic or with a totally recursive truncated decoder. This last condition has been introduced in order to obtain a theory viable in the quantum stabilizer case, since it was known that in this case the inner seed encoder could not be recursive and systematic in the same time.