Methods of converting or reconverting a data signal and method and system for data transmission and/or data reception

A method (RC) for reconverting a converted data signal (Y), the method comprising:

• providing an input symbol stream (IBp) of input symbols (Bj′), the input symbol stream (IBp) being representative for an amplitude sequence of the underlying converted data signal (Y) to be reconverted or a derivative thereof, and
• applying to said input symbol stream (IBp) or to a derivative thereof an inverse distribution matching process (DM−1) to generate and output a final output symbol stream (OB′),
• wherein
• the inverse distribution matching process (DM−) is formed by a preceding inverse amplitude mapping process (AM−1) and a succeeding inverse shell mapping process (SM−),
• said inverse amplitude mapping process (AM−1) is configured to assign for tuples of amplitude values conveyed by or derived from said input symbol stream (IBp) a shell index (s), thereby outputting to the inverse shell mapping process (SM−) a sequence of shell indices (s),
• said inverse shell mapping process (SM−) is configured to form and output for each disjunct consecutive partial sequence (sq) of a number of q consecutive shell indices (s) covering said sequence of shell indices (s), a partial output symbol sequence (OBp′) of a number of p final output symbols (OBj′), thereby forming and outputting a (re)converted signal (V),
• q is a fixed natural number,
• p is a fixed natural number, and
• wherein amplitude values or a sequence thereof are obtained from a preceding inverse probabilistic amplitude shaping process (PAS−1) evaluating input constellation point amplitudes or a sequence thereof, respectively, as said input symbol stream (IB′) being representative for the converted data signal (Y) to be reconverted in forward error corrected form.