Computer Science > Information Theory
[Submitted on 29 Sep 2010 (v1), last revised 20 Feb 2011 (this version, v3)]
Title:On the Optimal Compressions in the Compress-and-Forward Relay Schemes
View PDFAbstract:..... 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.
Submission history
From: Liang-Liang Xie [view email][v1] Wed, 29 Sep 2010 17:59:58 UTC (41 KB)
[v2] Thu, 7 Oct 2010 01:38:26 UTC (41 KB)
[v3] Sun, 20 Feb 2011 14:48:49 UTC (46 KB)
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