System and methods for data compression and nonuniform quantizers

A network, comprising:

• a transmitting portion configured to (i) encode an input digitized sequence of data samples into a quantized sequence of data samples, the quantized sequence having a first number of digits per sample, according to a companding function C(x), where x is a normalized modulus of the input digitized sequence of data samples, (ii) map the quantized sequence of data samples into a mapped sequence of data samples having a second number of digits per sample, the second number being lower than the first number, and (iii) modulate the mapped sequence of data samples and transmit the modulated mapped sequence over a digital link;
• and
• a receiving portion configured to (i) receive and demodulate the modulated mapped sequence from the digital link, (ii) map the demodulated sequence from the second number of digits per sample into a decoded digital sequence having the first number of digits per sample, and (iii) output the decoded digital sequence.