Final Report Summary - INTCOMM (Interactive Communications in Noisy Channels)
This project is supported by the Marie Curie Career Integration Grant (CIG). The high-level goals of the project are: 1) Developing a theory of interactive communications over noisy channels from an information theoretic perspective, specifically under the feedback communication model and the two-way channel communication model; 2) exploring design methods for practical and efficient communications and communication-related protocols that make use of an interactive component in the above setups, with an emphasis on noisy communication and coordination between the terminals.
Our study began with the classical model of an Additive White Gaussian Noise (AWGN) forward channel with a noisy AWGN feedback channel. It is well known that when the feedback channel s completely noiseless, communication at the highest rate possible rate, the Shannon capacity of the AWGN forward channel, can be attained by a simple recursive scheme. When the feedback is noisy, schemes of this type break down completely, rendering then impractical. Thus to attain capacity, one practically uses complex (non-interactive) forward error correction codes. Our work is the first to suggest a practical low-complexity interactive protocol that approaches the capacity with a small error probability. This protocol provides a two orders-of-magnitude reduction in complexity and delay relative to state-of-the-art forward error correction non-interactive schemes, or alternatively a typical 6-8dB savings in power relative to non-interactive systems operating at the same low complexity regime and error probability. Our construction is based on a novel combination of recursive MMSE estimation and modulo arithmetic. We have also leveraged our techniques to provide new error exponent results for channel coding with noisy feedback, that outperform the best known, based on high-dimensional nested coding constructions. Furthermore, we have used a similar approach to derive a reduction from an AWGN multiple access (MAC) channel with a noisy AWGN broadcast channel feedback link, to another MAC with noiseless feedback, hence obtaining new capacity region results.
We have also studied the problem of target acquisition under measurement dependent noise, which is a natural dual problem to communication with feedback. In that setup, a target needs to be acquired by means of multiple sensing operations, where the sensing noise depends on the size of the probed region. We have characterized the fundamental limits of acquisition resolution in an adaptive (interactive) and non-adaptive (fixed) sensing model, and described low-complexity schemes that attain the optimal performance in the interactive case.
Our work then continued toward the study of the notoriously difficult problem of interactive channel capacity. We have suggested a simplified model where the protocol to be simulated over a noisy channel is Markovian, which is highly interactive yet bounded in memory. We have shown how to obtain rates close to the Shannon capacity (which trivially serves as an upper bound) via a novel combination of a certain universal source coding scheme and channel coding. We have recently improved on this result to show that surprisingly, the Shannon capacity is achievable for first order binary Markovian protocols.
Finally, we have studied a guessing game problem inspired by coding with feedback under the cut-off rate of the binary symmetric channel. We have characterized the most useful one bit noisy quantization of a general discrete random variable in terms of maximally reducing the expected guessing time of the random variable given that bit; this quantization turns out to be essentially universal with respect to the underlying distribution. A recursive application of this simple quantizer, which computes the parity of the random variable relative to a decreasing order of probabilities, results in a simple interactive scheme of a posterior-matching flavor that attains the cut-off rate of the binary symmetric channel with feedback.
The results above constitute major steps forward in our understanding of feedback, interaction, multi-user communications, and related disciplines.
Our study began with the classical model of an Additive White Gaussian Noise (AWGN) forward channel with a noisy AWGN feedback channel. It is well known that when the feedback channel s completely noiseless, communication at the highest rate possible rate, the Shannon capacity of the AWGN forward channel, can be attained by a simple recursive scheme. When the feedback is noisy, schemes of this type break down completely, rendering then impractical. Thus to attain capacity, one practically uses complex (non-interactive) forward error correction codes. Our work is the first to suggest a practical low-complexity interactive protocol that approaches the capacity with a small error probability. This protocol provides a two orders-of-magnitude reduction in complexity and delay relative to state-of-the-art forward error correction non-interactive schemes, or alternatively a typical 6-8dB savings in power relative to non-interactive systems operating at the same low complexity regime and error probability. Our construction is based on a novel combination of recursive MMSE estimation and modulo arithmetic. We have also leveraged our techniques to provide new error exponent results for channel coding with noisy feedback, that outperform the best known, based on high-dimensional nested coding constructions. Furthermore, we have used a similar approach to derive a reduction from an AWGN multiple access (MAC) channel with a noisy AWGN broadcast channel feedback link, to another MAC with noiseless feedback, hence obtaining new capacity region results.
We have also studied the problem of target acquisition under measurement dependent noise, which is a natural dual problem to communication with feedback. In that setup, a target needs to be acquired by means of multiple sensing operations, where the sensing noise depends on the size of the probed region. We have characterized the fundamental limits of acquisition resolution in an adaptive (interactive) and non-adaptive (fixed) sensing model, and described low-complexity schemes that attain the optimal performance in the interactive case.
Our work then continued toward the study of the notoriously difficult problem of interactive channel capacity. We have suggested a simplified model where the protocol to be simulated over a noisy channel is Markovian, which is highly interactive yet bounded in memory. We have shown how to obtain rates close to the Shannon capacity (which trivially serves as an upper bound) via a novel combination of a certain universal source coding scheme and channel coding. We have recently improved on this result to show that surprisingly, the Shannon capacity is achievable for first order binary Markovian protocols.
Finally, we have studied a guessing game problem inspired by coding with feedback under the cut-off rate of the binary symmetric channel. We have characterized the most useful one bit noisy quantization of a general discrete random variable in terms of maximally reducing the expected guessing time of the random variable given that bit; this quantization turns out to be essentially universal with respect to the underlying distribution. A recursive application of this simple quantizer, which computes the parity of the random variable relative to a decreasing order of probabilities, results in a simple interactive scheme of a posterior-matching flavor that attains the cut-off rate of the binary symmetric channel with feedback.
The results above constitute major steps forward in our understanding of feedback, interaction, multi-user communications, and related disciplines.