Capacity of the Discrete-Time AWGN Channel Under Output Quantization (original) (raw)
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Single-bit Quantization Capacity of Binary-input Continuous-output Channels
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We consider a channel with discrete binary input X that is corrupted by a given continuous noise to produce a continuous-valued output Y. A quantizer is then used to quantize the continuous-valued output Y to the final binary output Z. The goal is to design an optimal quantizer Q* and also find the optimal input distribution p*(X) that maximizes the mutual information I(X; Z) between the binary input and the binary quantized output. A linear time complexity searching procedure is proposed. Based on the properties of the optimal quantizer and the optimal input distribution, we reduced the searching range that results in a faster implementation algorithm. Both theoretical and numerical results are provided to illustrate our method.
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In this paper, we investigate the achievable rate region of Gaussian multiple access channels (MAC) with finite input alphabet and quantized output. With finite input alphabet and an unquantized receiver, the two-user Gaussian MAC rate region was studied. In most high throughput communication systems based on digital signal processing, the analog received signal is quantized using a low precision quantizer. In this paper, we first derive the expressions for the achievable rate region of a two-user Gaussian MAC with finite input alphabet and quantized output. We show that, with finite input alphabet, the achievable rate region with the commonly used uniform receiver quantizer has a significant loss in the rate region compared. It is observed that this degradation is due to the fact that the received analog signal is densely distributed around the origin, and is therefore not efficiently quantized with a uniform quantizer which has equally spaced quantization intervals. It is also observed that the density of the received analog signal around the origin increases with increasing number of users. Hence, the loss in the achievable rate region due to uniform receiver quantization is expected to increase with increasing number of users. We, therefore, propose a novel non-uniform quantizer with finely spaced quantization intervals near the origin. For a two-user Gaussian MAC with a given finite input alphabet and low precision receiver quantization, we show that the proposed non-uniform quantizer has a significantly larger rate region compared to what is achieved with a uniform quantizer.
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Design and Analysis of Optimal Noisy Channel Quantization With Random Index Assignment
—This paper studies the design of vector quantization on noisy channels and its high rate asymptotic performance. Given a tandem source-channel coding system with vector quan-tization, block channel coding, and random index assignment, a closed-form formula is first derived for computing the average end-to-end distortion (EED) of the system, which reveals a structural factor called the scatter factor of a noisy channel quantizer. Based on this formula, we propose a noisy-channel quantiza-tion design method by minimizing the EED. Experiments and simulations show that quantizers jointly designed with channel conditions significantly reduce the EED when compared with quantizers designed separately without reference to channel conditions, which reveals a practical and effective design for noisy-channel quantization as to simplify the channel model by considering a random index assignment. Furthermore, we have presented the high rate asymptotic analysis of the EED for the tandem system, while convergence analysis of the iterative algorithm is included in the Appendix. Index Terms—Joint source channel coding, noisy channel quan-tization, random index assignment.
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