Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications
Finite precision analysis for space-time decoding
IEEE Transactions on Signal Processing
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This paper provides new insight into the classical problem of determining both the capacity of the discrete-time channel with uniform output quantization and the capacity achieving input distribution. It builds on earlier work by Gallager and Witsenhausen to provide a detailed analysis of two particular quantization schemes. The first is saturation quantization where overflows are mapped to the nearest quantization bin, and the second is modulo quantization where overflows are mapped to the nearest quantization bin after reduction by some modulus. Both the capacity of modulo quantization and the capacity achieving input distribution are determined. When the additive noise is gaussian and relatively small, the capacity of saturation quantization is shown to be bounded below by that of modulo quantization. In the limit of arbitrarily many uniform quantization levels, it is shown that the difference between the upper and lower bounds on capacity given by Ihara is only 0.26 bits.