PAM codes for optical scan intersymbol interference channel

Multilevel amplitude modulation codes over noisy optical scan channel modeled by 1+4D+D² are described. Even though this channel is as good as the perfect response (no ISI) channel if a maximum likelihood sequence estimator (MLSE) based on the channel trellis is employed, conventional trellis coded modulation (TCM) cannot guarantee large coding gains due to the channel memory. To avoid the channel input error sequences which lead to small differences of the Euclidean distance in the channel trellis, a nonlinear block code as an inner code can be designed with some bandwidth expansion. With two sets of nonlinear block codes, a simple multiple trellis code whose edges are labeled from an inner code is constructed as an outer code to increase the minimum Euclidean distance further in the decoder trellis, combining the trellis of the encoder and channel as one. The inner codes have many desirable features such as large coding gains, low decoding complexity and good synchronization property as well as mitigating the channel ISI problem. With the slight expense of the decoding complexity and some data rate loss with respect to an uncoded MLSE system, this multiple TCM scheme offers approximately asymptotic coding gains of about 6 to 9 dB