Cooperative Diversity: Capacity Bounds and Code Designs - Adaptive Signal Processing in Wireless Communications - page 359

rate gain at the price of receive collision. The design in [29] exploits turbo coding with
binary phase shift keying (BPSK) modulation [6]. It is consistent with the optimal DF
scheme for the half-duplex relay channel described in section 12.3.2, with the simpli-
fication that coefficient A in (12.8) is always set to zero. Decoding is based on parallel
Gaussian channel arguments [28]. Similar to the MAC setting, the destination exploits a
MAP detector to extract information from the received mixture signal. Recent work [42]
on low-density parity-check (LDPC) code [43] design for the half-duplex relay channel
based on DF also reported a similar loss of 1.2 dB to the theoretical limit.
The systems in [28, 29, 32, 35] demonstrate the great advantage of relaying as com-
pared to direct and multihop transmission. However, because these systems exploit AF
or DF, they can approach the lower bound of DF at best, which is far away from the CF
limit in many cases. Indeed, as shown in section 12.3.2, when the relay is close to the
destination, CF gives rate points that are not achievable with any other coding strategies.
Moreover, it was shown in [44] that CF achieves optimal diversity-multiplexing trade-off
in half-duplex relay systems.
Practical CF code designs for the half-duplex relay channel recently appeared in
[45-47]. The design of [45] is a quantize-forward scheme that does not exploit WZC at
the relay. The design of [46] is based on WZC at the relay and uses scalar quantization
and convolutional codes, but it does not exploit the limit-approaching CF scheme of [24],
and no theoretical bounds or performance comparisons (to the bounds) were given.
A practical CF code design based on WZC for the half-duplex Gaussian relay channel,
which closely follows the CF scheme outlined in section 12.3.2, is proposed in [47]. The
scheme of [47] exploits BPSK modulation; hence, the signal to be compressed by WZC at
the relay and the side information at the destination are not jointly Gaussian as assumed
in section 12.3.2 and [36]. Instead, the source and the side information are Gaussian
mixture generated from the BPSK modulation. Although the theoretical achievable
rate of WZC for this model is yet unknown, a lower bound and an upper bound are
derived in [47], which in the case when the relay is close to the destination are close to
each other, indicating practically system capacity. The code design relies on practical
WZC based on nested lattice quantization [48] followed by Slepian-Wolf coding [15]
of the nested quantization index as a second stage of binning for further compression
[49]. Thus, Slepian-Wolf coding here plays the role of conditional entropy coding of the
nested quantization indices (given the decoder side information).
Practical Slepian-Wolf coding is implemented via channel coding (see [ 19 ] for a review
of channel code designs for Slepian-Wolf coding). Since the Slepian-Wolf compressed
bitstream is to be transmitted over a noisy channel from the relay to the destination,
channel coding is needed to protect them. This calls for distributed joint source-channel
coding (DJSCC) [50], i.e., joint Slepian-Wolf compression and channel protection. In
the practical implementation of [47], irregular repeat-accumulate (IRA) codes [51] were
used by designing one multilayer code to take care of two channels: one is the physical
noisy channel between the relay and the destination, and another is the “virtual” cor-
relation channel [19], which characterizes the correlation between the quantized source
at the relay and the decoder side information at the destination.
In particular, the message m is split at the source into two parts, m 1 and m 2 , which
are protected independently by two different LDPC codes [43] and BPSK modulated