Nested linear/lattice codes for structured multiterminal binning

TLDR

Network information theory promises high gains over point‑to‑point communication, but practical use has been limited by a lack of structured coding schemes; nested linear and lattice codes extend algebraic binning to lossy or noisy scenarios, linking theory to linear and lattice coding with strong practical potential. This work reviews these developments and examines their connections to shaping, precoding, memory‑defect coding, and watermarking, while proposing several novel applications within a unified framework. The authors analyze nested parity‑check and lattice codes, and develop a unified approach that integrates these concepts for new applications in structured multiterminal binning.

Abstract

Network information theory promises high gains over simple point-to-point communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning scheme. Wyner (1974, 1978) and other researchers proposed various forms of coset codes for efficient binning, yet these schemes were applicable only for lossless source (or noiseless channel) network coding. To extend the algebraic binning approach to lossy source (or noisy channel) network coding, previous work proposed the idea of nested codes, or more specifically, nested parity-check codes for the binary case and nested lattices in the continuous case. These ideas connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications. We review these developments and explore their tight relation to concepts such as combined shaping and precoding, coding for memories with defects, and digital watermarking. We also propose a few novel applications adhering to a unified approach.