Partial-Decode-Forward for Relay Networks

Project Description:

Figure 1. General discrete memoryless relay network.

Figure 1. General discrete memoryless relay network.

In this project we study a practical channel in sensor and ad hoc networks, namely a relay network consisting of one source, one destination, and N relays as shown in Figure 1. We design a scheme based on the partial decode-forward (PDF) relaying scheme for this channel and show that it includes the PDF scheme for a relay channel with single relay as a special case. The proposed scheme is based on rate splitting with Nth-order superposition block Markov encoding and simultaneous sliding window decoding.

 

Proposed scheme:

Consider an arbitrary order of the relays in the network as shown in Figure 2. The source splits its message (m)

Figure 2. The proposed private message scheme for a single-source single-destination network with N relays

Figure 2. The proposed private message scheme for a single-source single-destination network with N relays

into one common (m0) and N + 1 private parts (m1,m2,…,m(N+1)), one intended for each relay. It encodes these message parts using Nth-order block Markov coding, in which each private message part is independently superimposed on the common parts of the current and N previous blocks. Using simultaneous sliding window decoding, each relay fully recovers the common message and its intended private message with the same block index, then forwards them to the following nodes in the next block.

The codebook generation in block (j) is shown in Figure 3 where

  • Wk carries common message of different blocks. All Wk are successively superimposed on each other as in block Markov encoding.
  • Uk carries private message to be decoded at relay k and not decoded at other relays. Each Uk is superimposed on all Wk.
  • Xk is the codeword sent by relay k which supports the forwarding of the message in Uk (of the previous block) and all Wl (l < k).
  • X0 is the codeword sent by the source which carries all messages including the remaining message m(N+1)  to be decoded only at the destination. X0 is superimposed on all Wk, Uk and Xk.

Each relay and the destination employ sliding window decoding. For this particular relay order, the achievable rate is obtained from the decoding at the relays and destination. Then, the total achievable rate is the supremum of all rates obtained for each relay order.

Figure 3. Encoding diagram of a single-source single-destination network with N relays (arrows denote superposition coding)

Figure 3. Encoding diagram of a single-source single-destination network with N relays (arrows denote superposition coding)

Publications:

  1. “Exhaustive Message Splitting for Partial Decode-Forward in Single-Source Single-Destination Relay Networks,”
    Y. Tang, A. Abu Al Haija and M. Vu,  the 48th Annual Conf. on Information Sciences and Systems (CISS), Mar 2014.
  2. A Partial Decode-Forward Scheme For A Network with N relays,”
    Y. Tang and M. Vu, 47th Annual Conf. on Information Sciences and Systems (CISS), Mar 2013.