Conventional detectors/decoders in communication channel operate sequentially. Namely, the analog signal is first sampled to form a discrete-time signal which is then passed on to a detector. The detector performs detection decisions on the discrete-time signal and passes them to an error correction decoder, and in many cases to a second (outer) concatenated decoder. (Often the detector and decoder are merged to form a soft-decision decoder.)

The advent of Turbo Codes and the recent resurrection of Low Density Parity Check Codes have demonstrated that iterative decoding provides substantial gains over sequential one-time detection/decoding. In iterative decoding strategies, the coded information-bearing signal has a constellation that admits iterative detection/decoding. The decisions are refined in each iteration until they converge. Thus, the redundancy in the code is used to iteratively correct the effect of noise on the received waveform. This strategy has been demonstrated to approach the Shannon channel capacity up to a fraction of a dB at very low signal-to-noise-ratios. At these low signal-to-noise-ratios, however, the sequential timing recovery (sampling) circuits fail. If the sampling is not properly done, the advantages of iterative detectors/decoders will not be observed.

This research focuses on exploiting the redundancy of the code to correct not only the decisions regarding the information bits, but also to refine the sampling time instants and thus achieve a better overall performance. Hence the name 'soft'-decision directed timing recovery. Iterative decoding has been successfully explained by Tanner's notion of 'codes on graphs'. This research focuses on the notion of 'systems on graphs', where the entire receiver (including the timing recovery circuit, the detector and the decoder) is described by a suitable message passing algorithm performed on a system graph.