Coding Schemes for the Two-Way Relay Channel

Project Description:

Figure 1. Discrete memoryless two-way relay channel model.

Figure 1. Discrete memoryless two-way relay channel model.

In this project, we propose various coding schemes for the two-way relay channel, which consists of two sources exchanging information with the help of a relay. We also compare between our proposed scheme and existing schemes. The proposed schemes include partial decode-forward (PDF), quantize-forward, and combined decode-forward (DF) and layered noisy network coding (LNNC) scheme.

 

Figure 2. Full-duplex Gaussian two-way relay channel model.

Figure 2. Full-duplex Gaussian two-way relay channel model.

Partial Decode-Forward (PDF) scheme:

In this scheme, each user splits its message into two parts and uses superposition coding to encode them. The relay only decodes one message part of each user, re-encodes the decoded message pair together, and broadcasts this. The relay can either re-encode each message pair separately or divide the message pair into a list and only encode the list index. The users then decode the message from the other user by joint typicality decoding of both the current and previous blocks.

 
 

Figure 3. Partial decode-forward achieves rates outside the time-shared region of decode-forward and direct transmission in the full-duplex TWRC.

Figure 3. Partial decode-forward achieves rates outside the time-shared region of decode-forward and direct transmission in the full-duplex TWRC.

Figure 4. PDF achieves time-shared region of decode-forward and direct transmission in the full-duplex TWRC.

Figure 4. PDF achieves time-shared region of decode-forward and direct transmission in the full-duplex TWRC.

Figures 3 and 4 provide numerical results for the Gaussian channel shown in Figure 2. Figure 3 shows an example in which partial decode-forward achieves rates outside of the time-shared region of decode-forward and direct transmission. Figure 4 shows an example where partial decode-forward achieves the time-shared region of decode-forward and direct transmission. In both cases, the proposed PDF scheme outperforms pure DF.

 
 
 
 
 
 

Quantize-Forward scheme:

Quantize-forward relaying is similar to compress-forward (CF) relaying, but without Wyner-Ziv binning. In this scheme, each user sends a new message in each transmission block using an independently generated codebook. At the end of each block, the relay sends a description of its received signal from both users. Then, it sends the codeword for the description index at the next block (instead of partitioning the description index into bins and sending the codeword for the bin index as in the original CF scheme). Each user jointly decodes the description index and message from the other user based on signals received in both the current and previous blocks.

Figure 5. Rate regions for P = 20; gr1 = g1r = 2; gr2 = g2r = 0:5; g12 =g21 =0:1.

Figure 5. Rate regions for P = 20; gr1 = g1r = 2; gr2 = g2r = 0:5; g12 =g21 =0:1.

Rate regions for P = 20; gr1 = 0:5; g1r = 2; gr2 =2; g2r = 0:5; g12 =g21 =0:1.

Figure 6. Rate regions for P = 20; gr1 = 0:5; g1r = 2; gr2 =2; g2r = 0:5; g12 =g21 =0:1.

Figures 5 and 6 compare between the proposed scheme and the existing compress-forward (CF) and noisy network coding (NNC) schemes. Compared with the original CF scheme, the proposed scheme achieves the same rate region in a symmetric channel and a strictly larger rate region in an asymmetric channel. Compared with the noisy network coding (NNC) scheme, the proposed scheme has a smaller rate region. However, for some channel configurations, it achieves the same rate region but with a much shorter decoding delay.

 
 

Figure 7. Achievable rate region comparison for the two-way relay channel with P = 3; gr1 = 6; g1r = 2; gr2 = 2; g2r = 3; g12 = 1; g21 = 0:5.

Figure 7. Achievable rate region comparison for the two-way relay channel with P = 3; gr1 = 6; g1r = 2; gr2 = 2; g2r = 3; g12 = 1; g21 = 0:5.

Combined DF and Layered NNC (LNNC) scheme:

This scheme combines decode-forward and layered noisy network coding (LNNC). Each user splits its message into three parts: an independent common, a Markov common, and a private message. The independent and Markov common messages are encoded differently at the source and are different for each block; both are decoded at both the relay and destination as in decode-forward. The private message is the same for all blocks and is decoded only at the destination as in noisy network coding. Each user encodes the Markov common message with block Markov encoding, then superimposes the independent common message on top of it without Markovity, and at last superimposes the private message on top of both. The relay decodes the two common messages and compresses the rest into two layers: a common and a refinement layer. In the next block, the relay sends a codeword which encodes the two decoded common messages and two layered compression indices. Then at the end of each block, each user decodes two common messages of the other user by sliding-window decoding over two consecutive blocks. At the end of all blocks, one user uses the information of the common layer to simultaneously decode the private message of the other user, while the other user uses the information of both the common and refinement layers to decode the other user’s private message.

Figure 7 shows that the proposed scheme encompasses all DF and NNC schemes.

Publications:

  1. Combined Decode-Forward and Layered Noisy Network Coding Schemes for Relay Channels,”
    P. Zhong and M. Vu, IEEE Int’l Symposium on Info. Theory (ISIT), July 2012.
  2. Partial Decode-forward Coding Schemes for the Gaussian Two-Way Relay Channel,
    P. Zhong and M. Vu, IEEE Int’l Conf. on Comm. (ICC), June 2012.
  3. On Compress-Forward without Wyner-Ziv Binning for Relay Networks,
    P. Zhong, A. Abu Al Haija and M. Vu, submitted to IEEE Trans. on Information Theory, Nov. 2011.
  4. Compress-Forward without Wyner-Ziv Binning for the One-Way and Two-Way Relay Channels,
    P. Zhong and M. Vu, Forty-Ninth Annual Allerton Conference, Sept 2011.
  5. Decode-forward and Compute-forward Coding Schemes for the Two-Way Relay Channel,
    P. Zhong and M. Vu, IEEE Information Theory Workshop, Oct 2011.