Beta encoders are an alternative to traditional approaches to pulse-code modulation.
[1][2] As a form of non-integer representation, beta encoding contrasts with traditional approaches to binary quantization, in which each value is mapped to the first N bits of its base-2 expansion.
An early beta encoder, the Golden ratio encoder[4] used the golden ratio base for its value of beta, but was susceptible to hardware errors.
Although integrator leaks in hardware elements make some beta encoders imprecise, specific algorithms can be used to provide exponentially accurate approximations for the value of beta, despite the imprecise results provided by some circuit components.
[5] An alternative design called the negative beta encoder (called so due to the negative eigenvalue of the transition probability matrix) has been proposed to further reduce the quantization error.