Data processing apparatus and methods are provided. One data processing apparatus comprises: a plurality of pipelined stages, each of the plurality pipelined stages being operable in each processing cycle to receive a group of data elements from an earlier pipelined stage; permute logic operable to buffer ‘n’ of the groups of data elements over a corresponding ‘n’ processing cycles thereby creating a bubble within pipelined stages, and forwarding logic operable, once the ‘n’ of the groups of data elements have been buffered by the permute logic, to forward permuted groups of data elements comprising the data elements reordered by the permute logic to fill the bubble within the pipelined stages. By forwarding the data elements to fill the bubble an improved throughput can be achieved and since a constant stream of data can be transformed without the need to increase the number of input or output registers required to support the permute logic, the need to duplicate the permute logic or the need to introduce any additional storage elements.