Multiple-Access Channel Coding with Non-Signaling Correlations

• URL: http://arxiv.org/abs/2206.10968v3
• Date: Wed, 13 Sep 2023 10:45:28 GMT
• Title: Multiple-Access Channel Coding with Non-Signaling Correlations
• Authors: Omar Fawzi, Paul Ferm\'e
• Abstract summary: We address the problem of coding for classical multiple-access channels (MACs) with the assistance of non-signaling correlations between parties. We show that using non-signaling assistance, the sum-rate $1.5425$ can be reached even with zero error. We also show that the capacity region with non-signaling assistance shared only between each sender and the receiver independently is the same as without assistance.
• Score: 7.215767098253206
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the problem of coding for classical multiple-access channels (MACs) with the assistance of non-signaling correlations between parties. It is well-known that non-signaling assistance does not change the capacity of classical point-to-point channels. However, it was recently observed that one can construct MACs from two-player non-local games while relating the winning probability of the game to the capacity of the MAC. By considering games for which entanglement increases the winning probability, this shows that for some specific kinds of channels, entanglement between the senders can increase the capacity. We make several contributions towards understanding the capacity region for MACs with the assistance of non-signaling correlations. We develop a linear program computing the optimal success probability for coding over $n$ copies of a MAC $W$ with size growing polynomially in $n$. Solving this linear program allows us to achieve inner bounds for MACs. Applying this method to the binary adder channel, we show that using non-signaling assistance, the sum-rate $1.5425$ can be reached even with zero error, which beats the maximum sum-rate capacity of $1.5$ in the unassisted case. For noisy channels, where the zero-error non-signaling assisted capacity region is trivial, we can use concatenated codes to obtain achievable points in the capacity region. Applied to a noisy version of the binary adder channel, we show that non-signaling assistance still improves the sum-rate capacity. Complementing these achievability results, we give an outer bound on the non-signaling assisted capacity region that has the same expression as the unassisted region except that the channel inputs are not required to be independent. Finally, we show that the capacity region with non-signaling assistance shared only between each sender and the receiver independently is the same as without assistance.

Related papers

• Error exponent of activated non-signaling assisted classical-quantum channel coding [12.221087476416056]
  We find that the optimal exponent--also called reliability function--is equal to the well-known sphere packing bound. Remarkably, there is no critical rate and our characterization remains tight for arbitrarily low rates below the capacity.
  arXiv  Detail & Related papers  (2024-10-01T21:26:17Z)
• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates [53.66705737169404]
  We consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Our main findings are that the maximum number of messages thus identifiable scales super-exponentially as $2R,nlog n$ with the block length $n$. Results are shown to generalise directly to classical-quantum channels with finite-dimensional output quantum system.
  arXiv  Detail & Related papers  (2024-02-14T11:59:30Z)
• The Multiple-Access Channel with Entangled Transmitters [67.92544792239086]
  Communication over a classical multiple-access channel (MAC) with entanglement resources is considered. We establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters. Using superdense coding, entanglement can double the conferencing rate.
  arXiv  Detail & Related papers  (2023-03-18T16:51:08Z)
• Channel Simulation: Finite Blocklengths and Broadcast Channels [13.561997774592667]
  We study channel simulation under common randomness assistance in the finite-blocklength regime. We identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance.
  arXiv  Detail & Related papers  (2022-12-22T13:08:55Z)
• On the separation of correlation-assisted sum capacities of multiple access channels [13.572917264310119]
  We show that it is possible to compute the sum capacity of a family of MACs with multiple senders. In the second part, we showcase algorithms for non-local optimization of functions we call Lipschitz-like functions. In the third part, we show that one can use techniques to compute the sum capacity of an two-enders to a fixed precision of quasi-nomial time.
  arXiv  Detail & Related papers  (2022-05-26T17:58:11Z)
• The Quantum Multiple-Access Channel with Cribbing Encoders [78.7611537027573]
  Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered. Based on the no-cloning theorem, perfect cribbing is impossible. A partial decode-forward region is derived for a quantum MAC with non-robust cribbing.
  arXiv  Detail & Related papers  (2021-11-30T17:31:48Z)
• Computable limits of optical multiple-access communications [1.14219428942199]
  Communication rates over quantum channels can be boosted by entanglement. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses. We show that entanglement-assisted capacity of a single-sender and single-receiver channel is additive.
  arXiv  Detail & Related papers  (2021-10-04T19:27:59Z)
• Computation-aided classical-quantum multiple access to boost network communication speeds [61.12008553173672]
  We quantify achievable quantum communication rates of codes with computation property for a two-sender cq-MAC. We show that it achieves the maximum possible communication rate (the single-user capacity), which cannot be achieved with conventional design.
  arXiv  Detail & Related papers  (2021-05-30T11:19:47Z)
• One-shot multi-sender decoupling and simultaneous decoding for the quantum MAC [0.0]
  We prove a novel one-shot multi-sender theorem generalising Dupuistrivial result. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC) Our work is the first one to obtain a non- simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and iid settings.
  arXiv  Detail & Related papers  (2021-02-03T18:30:41Z)
• Quantum Channel State Masking [78.7611537027573]
  Communication over a quantum channel that depends on a quantum state is considered when the encoder has channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. A full characterization is established for the entanglement-assisted masking equivocation region, and a regularized formula is given for the quantum capacity-leakage function without assistance.
  arXiv  Detail & Related papers  (2020-06-10T16:18:03Z)
• Permutation Enhances Classical Communication Assisted by Entangled States [67.12391801199688]
  We show that the capacity satisfies the strong converse property and thus the formula serves as a sharp dividing line between achievable and unachievable rates of communication. As examples, we derive analytically the classical capacity of various quantum channels of interests.
  arXiv  Detail & Related papers  (2020-01-07T01:49:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.