Channel Coding

Figure 3 : Performance of the turbo BCH(63,57) code for different number of iterations using BPSK over the AWGN channels. The associated Shannon limit of the respective coding rate is also shown.

Turbo coding is a novel form of channel coding capable of achieving a performance near the Shannon limit. Generally, so-called Recursive Systematic Convolutional codes are used as their component codes. However, block codes can also be employed as their component codes and they have been shown to perform impressively even at near-unity coding rates. Generally, block codes are appropriate for high rates and convolutional codes for rates below 2/3.

In the early stage of Tong Hooi's research, binary BCH block codes were investigated and used as the component codes in turbo block codes. Figure 3 shows that we can achieve impressive results by iterative decoding of the turbo code. At a BER of 10^{-5} the performance of the turbo BCH(63,57) code is only 1.1 dB away from the Shannon limit.

The family of so-called Redundant Residue Number System (RRNS) codes also constitutes an exciting subject of my research, where substantial performance advantages were achieved upon contriving their turbo decoding. Tong Hooi's recent interests are focused on the class of space-time codes.
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Figure 4 :Turbo Trellis-Coded Modulation scheme

In classical digital communication systems, modulation and error-correction coding are considered as two different entities. However, the combination of error-correction coding with modulation leads to the concept of Trellis-Coded Modulation (TCM). TCM is a bandwidth efficient scheme, where the redundancy introduced by the coding does not expand the bandwidth since the parity bits are absorbed by the extended signal constellation. One of the objecties of our research is to design TCM schemes for dispersive fading channels. As a further advance in channel coding, turbo coding was proposed in 1993. The databits are encoded twice and two decoders assist each other during decoding. This approach produces remarkable performance results, which are close to the Shannon
limits. Turbo coding can be combined with trellis-coded modulation in order to produce Turbo TCM (TTCM) codes. The optimum
design of TTCM scheme for dispersive fading channel is our goal in this field.