Maximum-Likelihood Detection and Constrained Coding on Optical Channels

Abstract

The most probable error events for a long-haul optical communication system using sequence estimation are characterized, and the performance using a modulation code is analyzed. The modulation code is restricted to be a constrained code that enhances the minimum distance between received signal sequences. We investigate several constrained codes used in combination with 4- and 8-state Viterbi algorithms and apply them to a standard noncoherent NRZ system. The improvement using a rate 0.85 code can be as high as 5 dB relative to an uncoded system operating at the same symbol rate. If the coded and uncoded systems are constrained to have the same information rate, a more modest 1 dB improvement can be obtained for specific fiber distances. We also determine the effect of the code on the number of states of the Viterbi algorithm and the sensitivity of the sampling point. Using these codes, the tolerance of the receiver to sampling errors can be increased by a nearly a factor of two for specific distances. The performance improvements that these codes can provide make them attractive candidates when used in conjunction with sequence estimation.