Feedback is known to decrease the encoding effort and reduce the decoding error for the single-user channel and it can even enlarge the capacity and the achievable sum rate for the multiple access channel (MAC). Quantization is a major aspect in modern communication systems as it is responsible for the conversion from the analog to the digital domain and it is often modeled as lossy source coding. We focus on the limited blocklength, as it is very important in the communication nowadays due to complexity and delay constraints especially with the increasing demand of the real-time communication such as audio and video streaming for mobile devices. We propose a quantized feedback scheme for the single-user AWGN channel and the two-user MAC with additive Gaussian noise. The quantized feedback link is modeled as an information bottleneck subject to a rate constraint. Furthermore, we study the decoding error probability given a transmit rate and the maximum achievable rate of the quantized feedback scheme and compare it with other schemes like Schalkwjik-Kailath and Polyanskiy. Additionally, we study in detail in what blocklength regions the quantized feedback is beneficial.
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