Nested linear/lattice codes for structured multiterminal binning

Ram Zamir*, Shlomo Shamai, Uri Erez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 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, recent 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 recent 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.

Original languageEnglish
Pages (from-to)1250-1276
Number of pages27
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2002


  • Binning
  • Digital watermarking
  • Error-correcting codes
  • Gelfand-Pinsker
  • Memory with defects
  • Multiresolution
  • Multiterminal
  • Nested lattice
  • Side information
  • Slepian-Wolf
  • Writing on dirty paper
  • Wyner-Ziv


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