  ..... 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.
