To decode a representation, imported from a channel, of a codeword that encodes K information bits as N>K codeword bits, estimates of the codeword bits are updated by exchanging messages between N bit nodes and N−K check nodes of a graph in a plurality of iterations. In each of one or more of the iterations, some or all values associated with the bit nodes, and/or some or all values associated with check nodes, and/or some or all messages are modified in a manner that depends explicitly on the ordinality of the iteration and is independent of any other iteration. Alternatively, the modifications are according to respective locally heteromorphic rules.