Hamming coded modulation

An optical system comprising:

• a first digital signal processor (DSP) configured to:
• receive a group of input bits,
• encode the group of input bits using an (8,4) Hamming encoder, and
• provide symbols, associated with the group of input bits based on encoding the group of input bits;
• a digital-to-converter (DAC) configured to:
• receive the symbols, and
• provide a voltage corresponding to the symbols;
• a laser configured to provide an input optical signal;
• a modulator configured to:
• receive the voltage and the input optical signal,
• modulate the input optical signal based on the voltage to form an output signal, and
• provide the output signal;
• a second DSP configured to:
• receive first samples of a digital signal corresponding to the output signal,
• correlate the first samples to a plurality of groups of second samples to determine a plurality of correlation values,
• each of the plurality of groups of second samples corresponding to a respective plurality of code words,
• each of the plurality of correlation values corresponding to a correlation measurement between the first samples and each of the plurality of groups of second samples,
• determine a particular code word, of the plurality of code words, corresponding to one of the correlation values of the plurality of correlation values,
• determine output bits based on bits of the particular code word and the one of the correlation values, and
• provide the output bits,
• the output bits including data associated with the output signal.

An optical system comprising:

• a local oscillator configured to provide a reference optical signal;
• a hybrid mixer configured to:
• receive an input signal,
• receive the reference signal, and
• provide an optical signal corresponding to the input signal and the reference signal,
• a photodetector configured to:
• receive the optical signal, and
• provide a voltage signal corresponding to the optical signal;
• an analog-to-digital converter (ADC) configured to:
• receive the voltage signal, and
• provide the digital signal based on receiving the voltage signal;
• a digital signal processor (DSP) configured to:
• receive first samples of the digital signal,
• the first samples of the digital signal being Hamming encoded,
• correlate the first samples to a plurality of groups of second samples to determine a plurality of correlation values,
• each of the plurality of groups of second samples corresponding to a respective plurality of code words,
• each of the plurality of correlation values corresponding to a correlation measurement between the first samples and each of the plurality of groups of second samples,
• determine a particular code word, of the plurality of code words, corresponding to one of the correlation values of the plurality of correlation values,
• determine output bits based on bits of the particular code word and the one of the correlation values, and
• provide the output bits,
• the output bits including data associated with the digital signal.