Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space - Part I:180°

Convolutional channel coding with expanded signal space improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. Due to the phase ambiguity(ies) in the expanded signal space, it is desirable to design the code´ to be transparent to signal element rotations. In this paper, design rules and procedures for 180° rotationally invariant codes are presented. In a companion paper, we extend these rules and procedures to codes which are transparent to 90, 180, and 270° signal element rotations. We illustrate these rules and procedures by designing simple codes that achieve coding gain of 3-4 dB. These are the codes of practical interest. Codes with higher coding gain can be obtained using the same rules and procedures. Both feedforward and feedback codes are considered.