Elementary check node-based syndrome decoding using pre-sorted inputs

A decoder for determining an estimate of an encoded signal, the decoder comprising one or more variable node processing units and one or more check node processing units configured to exchange messages, each message comprising one or more components, a component comprising a symbol and a reliability metric associated with said symbol, wherein the decoder comprises:

• at least one vector permutation unit configured to receive a set of at least three variable node messages comprising variable node components from at least one variable node processing unit and to generate permuted messages depending on a plurality of the reliability metrics comprised in said variable node components, the variable node messages being sorted according to an order of the reliability metrics;
• and
• at least one check node processing unit configured to:
• calculate at two or more elementary check node processors a set of syndromes from said at least three permuted messages, a syndrome comprising a binary vector,
• generate at least one check node message from said set of syndromes depending on said binary vector, and
• send said at least one check node message to a signal estimation unit.