An apparatus , comprising: circuitry, the circuitry comprising: a probabilistic amplitude shaping symbol source circuit configured, in response to receipt of input data , to produce a first stream of symbols of a constellation for modulation, wherein: the frequency of occurrence of symbols in the first stream is dependent upon a probability-amplitude distribution for symbols of the constellation, wherein the probability-amplitude distribution is a probability-amplitude distribution that causes low-amplitude symbols to occur more frequently on average in the stream than high-amplitude symbols; and a constellation re-mapper circuit configured, in response to receipt of the first stream of symbols, to: map the first stream of symbols to a second stream of symbols of the constellation for modulation; to produce the second stream of symbols wherein the second stream of symbols has a lower kurtosis than the first stream of symbols; and to transmit the second stream of symbols of the constellation to a modulator for modulation onto a carrier wherein: a frequency of occurrence of symbols in the second stream is dependent upon a probability-amplitude distribution for symbols of the constellation, wherein the probability-amplitude distribution has a kurtosis less than a target value for 64QAM of 1.8 and a shape of the probability-amplitude distribution causes low-amplitude symbols to occur more frequently on average in the stream than high-amplitude symbols. a probabilistic amplitude shaping symbol source circuit configured, in response to receipt of input data , to produce a first stream of symbols of a constellation for modulation, wherein: the frequency of occurrence of symbols in the first stream is dependent upon a probability-amplitude distribution for symbols of the constellation, wherein the probability-amplitude distribution is a probability-amplitude distribution that causes low-amplitude symbols to occur more frequently on average in the stream than high-amplitude symbols; and a constellation re-mapper circuit configured, in response to receipt of the first stream of symbols, to: map the first stream of symbols to a second stream of symbols of the constellation for modulation; to produce the second stream of symbols wherein the second stream of symbols has a lower kurtosis than the first stream of symbols; and to transmit the second stream of symbols of the constellation to a modulator for modulation onto a carrier wherein: a frequency of occurrence of symbols in the second stream is dependent upon a probability-amplitude distribution for symbols of the constellation, wherein the probability-amplitude distribution has a kurtosis less than a target value for 64QAM of 1.8 and a shape of the probability-amplitude distribution causes low-amplitude symbols to occur more frequently on average in the stream than high-amplitude symbols. map the first stream of symbols to a second stream of symbols of the constellation for modulation; to produce the second stream of symbols wherein the second stream of symbols has a lower kurtosis than the first stream of symbols; and to transmit the second stream of symbols of the constellation to a modulator for modulation onto a carrier wherein: a frequency of occurrence of symbols in the second stream is dependent upon a probability-amplitude distribution for symbols of the constellation, wherein the probability-amplitude distribution has a kurtosis less than a target value for 64QAM of 1.8 and a shape of the probability-amplitude distribution causes low-amplitude symbols to occur more frequently on average in the stream than high-amplitude symbols. <EOS>