Non-binary decoding using tensor product transforms

A method and data storage system receives a confidence vector for a non-binary symbol value read from a memory cell of a non-volatile memory device, where the confidence vector includes a first plurality of confidence values and transforms the first plurality of confidence values into a first plurality of likelihood values using a forward tensor-product transform. A respective binary message passing decoding operation is performed with each of the first plurality of likelihood values to generate a second plurality of likelihood values, and the second plurality of likelihood values are transformed into a second plurality of confidence values of the confidence vector using a reverse tensor-product transform.