[Paper Review] On the Optimality of Successive Decoding in Compress-and-Forward Relay Schemes

Xiugang Wu, Liang‐Liang Xie|arXiv (Cornell University)|Sep 29, 2010

Cooperative Communication and Network Coding9 citations

TL;DR

This paper demonstrates that in compress-and-forward relay networks, successive decoding consistently achieves the optimal rate for the original message, even with multiple relays or joint decoding. It proves that compressions not supporting successive decoding yield strictly lower rates, and that joint decoding offers no rate improvement over successive decoding—highlighting that delayed block-by-block backward decoding, not repetitive encoding, is the true source of rate gains in recent frameworks.

ABSTRACT

..... joint decoding provides more freedom in choosing the compression at the relay. However, the question remains whether this freedom of selecting the compression necessarily improves the achievable rate of the original message. It has been shown in (El Gamal and Kim, 2010) that the answer is negative in the single-relay case. In this paper, it is further demonstrated that in the case of multiple relays, there is no improvement on the achievable rate by joint decoding either. More interestingly, it is discovered that any compressions not supporting successive decoding will actually lead to strictly lower achievable rates for the original message. Therefore, to maximize the achievable rate for the original message, the compressions should always be chosen to support successive decoding. Furthermore, it is shown that any compressions not completely decodable even with joint decoding will not provide any contribution to the decoding of the original message. The above phenomenon is also shown to exist under the repetitive encoding framework recently proposed by (Lim, Kim, El Gamal, and Chung, 2010), which improved the achievable rate in the case of multiple relays. Here, another interesting discovery is that the improvement is not a result of repetitive encoding, but the benefit of delayed decoding after all the blocks have been finished. The same rate is shown to be achievable with the simpler classical encoding process of (Cover and El Gamal, 1979) with a block-by-block backward decoding process.

Motivation & Objective

• To determine whether joint decoding improves the achievable rate in compress-and-forward relay schemes with multiple relays.
• To investigate whether compressions not supporting successive decoding can enhance the original message rate.
• To clarify the role of repetitive encoding and delayed decoding in recent rate improvements for multiple-relay networks.
• To establish conditions under which compression choices are ineffective for decoding the original message.

Proposed method

• Analytical comparison of achievable rates under successive decoding versus joint decoding in compress-and-forward relay networks.
• Formal derivation of rate bounds for compress-and-forward schemes with multiple relays, considering different compression strategies.
• Evaluation of the repetitive encoding framework by Lim et al. (2010) to isolate the contribution of delayed decoding from that of repetition.
• Use of block-by-block backward decoding in classical encoding to replicate the rate gains observed in repetitive schemes.
• Identification of compressions that are not decodable even with joint decoding and their irrelevance to original message decoding.

Experimental results

Research questions

• RQ1 Does joint decoding provide a higher achievable rate than successive decoding in multiple-relay compress-and-forward networks?
• RQ2 Can compressions that do not support successive decoding improve the rate of the original message?
• RQ3 Is the rate improvement in the repetitive encoding framework by Lim et al. (2010) due to repetition or delayed decoding?
• RQ4 Are there compressions that contribute nothing to the decoding of the original message, even under joint decoding?

Key findings

• Joint decoding does not improve the achievable rate over successive decoding in multiple-relay compress-and-forward schemes.
• Compressions that do not support successive decoding lead to strictly lower achievable rates for the original message.
• Any compression not decodable even with joint decoding contributes nothing to the decoding of the original message.
• The rate improvement in the repetitive encoding framework by Lim et al. (2010) is due to delayed decoding, not repetition.
• The same achievable rate as in the repetitive framework can be obtained using classical encoding with block-by-block backward decoding.