Capacity of the Discrete-Time AWGN Channel Under Output Quantization

Details Capacity of the Discrete-Time AWGN Channel Under Output Quantization Capacity of the Discrete-Time AWGN Channel Under Output Quantization

2008-01-08

arxiv.org/abs/0801.1185v2

Computer Science

Information Theory

To appear at ISIT 2008. (Some changes in the content (in Section IV) compared to the first version uploaded on Jan 08, 2008.)

Scientific paper

We investigate the limits of communication over the discrete-time Additive White Gaussian Noise (AWGN) channel, when the channel output is quantized using a small number of bits. We first provide a proof of our recent conjecture on the optimality of a discrete input distribution in this scenario. Specifically, we show that for any given output quantizer choice with K quantization bins (i.e., a precision of log2 K bits), the input distribution, under an average power constraint, need not have any more than K + 1 mass points to achieve the channel capacity. The cutting-plane algorithm is employed to compute this capacity and to generate optimum input distributions. Numerical optimization over the choice of the quantizer is then performed (for 2-bit and 3-bit symmetric quantization), and the results we obtain show that the loss due to low-precision output quantization, which is small at low signal-to-noise ratio (SNR) as expected, can be quite acceptable even for moderate to high SNR values. For example, at SNRs up to 20 dB, 2-3 bit quantization achieves 80-90% of the capacity achievable using infinite-precision quantization.

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