Negligible Cooperation: Contrasting the Maximal- and Average-Error Cases

• Published in: IEEE transactions on information theory 2021-09, Vol.67 (9), p.5885-5902
• Main Authors: Noorzad, Parham, Langberg, Michael, Effros, Michelle
• Format: Article
• Language: English
• Subjects: Capacity planning; Capacity region continuity; Coders; Communication networks; Cooperation; cooperation facilitator; Decoding; edge removal problem; Errors; Interference; maximal-error capacity region; multiple access channel; Network coding; Performance measurement; Source coding; Upper bound
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2021.3093891

In communication networks, cooperative strategies are coding schemes where network nodes work together to improve performance metrics such as the total rate delivered across the network. This work studies encoder cooperation in the setting of a discrete multiple access channel (MAC) with two encoders and a single decoder. A network node, here called the cooperation facilitator (CF), that is connected to both encoders via rate-limited links, enables the cooperation strategy. Previous work by the authors presents two classes of MACs: (i) one class where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero, and (ii) a second class of MACs where the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work contrasts the power of the CF in the maximal- and average-error cases, showing that a constant number of bits communicated over the CF output link can yield a positive gain in the maximal-error sum-capacity, while a far greater number of bits, even a number that grows sublinearly in the blocklength, can never yield a non-negligible gain in the average-error sum-capacity.