Probabilistic shaping techniques for high performance coherent optical transceivers

A transceiver comprising:

• a splitter configured to receive a random sequence of bits, and split the random sequence of bits into a first sequence of bits and a second sequence of bits;
• a mapper configured to convert encoded data to symbols having respective signs and amplitudes, set the signs of the symbols based on the first sequence of bits, set the amplitudes of the symbols based on the encoded data, and transmit the symbols from the transceiver;
• and
• a distribution matching encoder configured to encode the second sequence of bits to generate the encoded data comprising codewords, the encoding of the second sequence of bits comprising controlling a number of ‘1’ bits in each of the codewords such that the codewords have a same average transmission energy after the encoded data is converted to the symbols by the mapper, an amount of transmission energy to transmit each respective one of the codewords being based on the number of ‘1’ bits in the respective one of the codewords.