Systems and modules for use in trellis-based decoding of encoded sets of data bits. A memory system has multiple arrays for storing an index for each one of multiple states. With each array element being associated with a state through which a decoding path may pass through, the contents of each array element is an index which points to an immediately preceding state. This immediately preceding state is represented by another array element in another array. Each array is populated with array element entries as encoded data set are received by a separate decoder which generates the indices. For every given number of arrays in a group, a trace-back process traces back the path followed by an encoding procedure for encoding the encoded set. By tracing back this path through the various arrays, the original unencoded set of data bits can be found.