Near-capacity turbo trellis coded modulation design based on union ...

2038 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 12, DECEMBER 2008
BER
1
10 -1
10 -2
10 -3
10 -4
10 -5
10 -6
ttcmiq-xfad-ber-bound.gle
8PSK
[13 2 4] 8
16QAM
[27 2 4 10] 8
32QAM
[41241020] 8
64QAM
[4124102040]
Capacity
Bound
5.38dB, =2
7.21dB, =3
9.98dB, =4
10 -7
4 6 8 10 12 14 16
E b /N 0 [dB]
Fig. 11. The BER and the error floor bound performance of the various
IQ-TTCM schemes when communicating over uncorrelated Rayleigh fading
channels using a block length of N =10, 000 symbols. The product distance
spectrum and Hamming distance spectrum used for generating the union
bound was truncated at Δ P max =60and Δ H max =6, respectively.
convergence due to having a closed tunnel in its EXIT chart.
Hence, the BER performance of the 16QAM TTCM scheme
employing the proposed GP of [272410] 8 is significantly
better than that of the benchmarkers, as it is evidenced in
Fig 8.
As depicted in Fig. 11, when we increased the block length
to N =10, 000 symbols, the IQ-TTCM schemes exhibit lower
error floors and a decoding convergence closer to the estimated
thresholds summarised in Tab. I, compared to the scenario
using a block length of N = 1000 symbols, as shown in
Figs. 7 to 10. Hence, <strong>capacity</strong>-approaching TTCM schemes
can be successfully <strong>design</strong>ed <strong>based</strong> on the proposed symbol<strong>based</strong>
EXIT chart aided and the truncated union bound assisted
code <strong>design</strong>. Furthermore, the proposed technique may also be
employed for <strong>design</strong>ing symbol-interleaved space-time TTCM
schemes for approaching the multiple-input multiple-output
channel <strong>capacity</strong>.
VII. CONCLUSIONS
We have <strong>design</strong>ed <strong>capacity</strong>-approaching TTCM schemes by
performing a search for good constituent TCM component
codes with the aid of symbol-<strong>based</strong> EXIT charts and truncated
symbol-<strong>based</strong> union bounds. The prime <strong>design</strong> criterion of
<strong>capacity</strong>-approaching TTCM schemes is that of finding an
open tunnel in the corresponding EXIT charts at the lowest
possible SNR values, while maintaining a sufficiently low
error floor, rather than maximising the ‘punctured’ minimal
distance of the constituent codes [4]. Hence, we can reduce
the code search space by fixing the feed-forward GPs and then
search for the best feed-back GP that provides an open tunnel
in the EXIT chart at the lowest possible SNR value. Although
the independence of the extrinsic information and systematic
information is not always satisfied by the symbol-<strong>based</strong> TTCM
scheme, most of the good constituent codes found assist the
TTCM schemes in performing near the channel <strong>capacity</strong>.
12.71dB, =5
APPENDIX
The set χ = χ(y, m) ={z} in Eq. (19) can be generated
by using the following recursive function:
Find Symbol Error Set(y, m, χ, 0), which is defined as:
Find Symbol Error Set(int ỹ,intb,int*χ,int¯z){
if(b =1)add(¯z +ỹ)intoχ
else {
⌊ ⌋
for (z b =0; z b ≤ ỹ
b
; z b ++)
Find Symbol Error Set(ỹ − b · z b , b − 1, χ, ¯z + z b )
}
return
}
where the values of the variables ỹ, b and ¯z could change
during the transition from the parent loop to the child loops.
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