Modified Viterbi decoders for joint data detection and timing recovery of convolutionally encoded PPM and OPPM optical signals

Synchronization plays a key role in the successful reception of data in a direct-detection optical communications system. Recently, jointly optimal receivers, capable of providing data reception in the absence of timing information for random data systems, have been investigated. In this analysis, two novel Viterbi decoders are introduced. The proposed decoders take advantage of the jointly-optimal concept to arrive at joint symbol synchronization and data recovery for convolutionally encoded optical pulse-position modulation (PPM) and overlapping PPM (OPPM) channels. The first proposed architecture, known hereafter as joint Viterbi decoder (JVD), employs a count metric to achieve the Viterbi decoding of the transmitted symbols in the absence of slot and symbol synchronization. The second proposed architecture, hereafter referred to as enhanced Viterbi decoder (EVD), uses delay time quantization to achieve joint data recovery and timing acquisition. The proposed EVD architecture utilizes the built-in memory array to consider all possible delay estimates simultaneously. This in turn results in a substantial reduction in the computing time. In the initial stage, computer simulations are used to shed light on the superiority of the EVD scheme in terms of computing time over the previously proposed jointly optimal receiver and the JVD architecture. Furthermore, it is shown that for the same quantization level, the EVD and JVD architectures yield identical performances in terms of bit error rate. To substantiate the computer simulation results and to arrive at analytical performance measures, performances of convolutionally encoded PPM and OPPM signaling under perfect synchronization are evaluated. The performance of a convolutionally encoded PPM scheme is well established in the literature. Due to the absence of orthogonality among transmitted symbols, however, the conventional performance upper bounds, obtained by weight-based transfer function of the convolutional encoder, do not adequately characterize the performance of a convolutionally encoded OPPM signaling. An innovative ensemble average upper bound is introduced. This method employs the "chip distance" between symbols which emphasizes the inherent non-orthogonality of the OPPM signaling scheme. With the aid of simulation, this ensemble average bound is shown to provide an accurate estimate of the performance of a convolutionally encoded OPPM signaling. Finally, using the above novel techniques for performance characterization of convolutionally encoded PPM and OPPM schemes, the performance of JVD and EVD architectures are estimated and are compared with the simulation results. The estimated performance measures are shown to be relatively accurate for medium to large signal counts, and thus may be used as reasonable performance predictors for the JVD and EVD architectures.