Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space - Part II: Nonlinear Codes

Abstract
This is the second paper on rotationally invariant convolutional channel coding with expanded signal space. Signal space with 90, 180, and 270° phase ambiguities is generally preferred to signal space with only 180° phase ambiguity. In this paper, design rules and procedures for 180° rotationally invariant convolutional codes in the previous paper are extended to rotationally invariant codes with expanded signal space having 90, 180, and 270° phase ambiguities. As in the previous paper, we illustrate these rules and procedures by designing simple codes with coding gain of 4 dB. Nonlinear convolutional codes result from these design rules and procedures. These simple nonlinear convolutional codes are being considered as international standards on voiceband modems at rate greater than or equal to 9.6 kbits/s. Codes with higher coding gain can be obtained using the same rules and procedures. Both feedforward and feedback codes are considered. In addition, a new class of codes described as "generalized feedback" is also considered.