Rematch-and-forward: Joint source-channel coding for parallel relaying with spectral mismatch

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The Gaussian parallel relay network, introduced by Schein and Gallager, consists of a concatenation of a Gaussian additive broadcast channel from a single encoder to a layer of relays followed by a Gaussian multiple-access channel from the relays to the final destination (decoder), where all noises are independent. This setup exhibits an inherent conflict between digital and analog relaying; while analog relaying [known as amplify-and-forward (A&F)] suffers from noise accumulation, digital relaying (known as decode-and-forward) looses the potential coherence gain in combining the relay noises at the decoder. For a large number of relays, the coherence gain is large, and thus analog relaying has better performance; however, it is limited to white channels of equal bandwidth. In this paper, we present a generalization of the analog approach to the case of bandwidth mismatch. Our strategy, coined rematch and forward (R&F), is based upon applying joint source-channel coding techniques that belong to a certain class of maximally analog schemes. Using such techniques, R&F converts the bandwidth of the broadcast section to that of the multiple-access section, creating an equivalent matched-bandwidth network over which A&F is applied. It is shown that this strategy exploits the full bandwidth of the individual channels, without sacrificing the coherence gain offered by A&F. Specifically, for given individual-link capacities, R&F remains within a constant gap from the network capacity for any number of relays and any bandwidth ratio between the sections. Finally, the approach is extended to the case of colored channels.

Original languageEnglish
Article number6649975
Pages (from-to)605-622
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2014


  • ISI channel
  • Parallel relay network
  • amplify-and-forward
  • bandwidth mismatch
  • broadcast channel
  • coherence gain
  • hybrid digital-analog transmission
  • joint source-channel coding
  • modulo-lattice modulation
  • multiple access channel
  • network capacity


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