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Channel Coding and Modulation
- Turbo Code and Concatenated Code
- Irregular Code and EXIT Chart Design
- LDPC Code, Rateless Code and Fountain Code
- Coded Modulation, Superposition Coded Modulation and Sphere Packing Modulation
- Turbo Trellis Coded Hierarchical Modulation
Turbo Code and Concatenated Code
In his legendary contribution Shannon set out the performance limits of channel coding and modulation schemes as early as 1948. However, apart from Galleger’s radical idea of low density parity check (LDPC) codes disseminated as early as 1962, no schemes were capable of approaching Shannon’s capacity limits until the genesis of turbo codes in 1993. It remains a mystery, why the appealing concept of exploiting the so-called extrinsic information provided by the surrounding bits of a bit-stream for any bits in the stream remained largely unexploited before the invention of turbo codes. The now classic turbo-coding scheme is based on a composite codec constituted by two parallel concatenated codecs. Since their invention, turbo codes have evolved at an unprecedented pace and have reached a state of maturity within just a few years due to the intensive research efforts of the turbo coding community. As a result of this dramatic evolution, turbo coding has also found its way into standardized systems, such as, for example, the recently ratified third-generation (3G) mobile radio systems. Even more impressive performance gains can be attained with the aid of turbo coding in the context of video broadcast systems, where the associated system delay is less critical than in delaysensitive interactive systems.
Irregular Code and EXIT Chart Design
Irregular coding has been proposed for the reliable transmission of information at channel SNRs that are close to the channel’s capacity bound without imposing an excessive decoding complexity and latency. The concept was originally introduced in the context of LDPC codes. These may be represented using bipartite graphs, comprising a number of check nodes and a number of variable nodes. In the bipartite graph of an irregular LDPC code, the check nodes are connected to various numbers of variable nodes and vice versa . This is in contrast to regular LDPC codes, where all check nodes are connected to the same number of variable nodes and vice versa. Hence, a higher degree of freedom is facilitated during the design of irregular LDPC codes and this supports operation at channel SNRs that are closer to the channel’s capacity bound. |
Following the introduction of irregular LDPC codes, irregular coding was also applied in the context of turbo codes. These employ a parallel concatenation of two iteratively decoded CCs, which consider the original order of the source bits and an interleaved version, respectively. Whilst each source bit is encoded just once by each of the two parallel concatenated CCs in a regular turbo code, some source bits are encoded more than once by the CCs in the irregular scheme. As a result, it was possible to achieve a coding gain of 0.23 dB and operation within 25 dB of the channel’s Eb/N0 capacity bound by employing Monte Carlo simulations in order to ﬁnd the required number of times that each source bit is encoded.
The serial concatenation and iterative decoding of an irregular outer code with a regular inner code was proposed by Tchler and Hagenauer. Here, the irregular outer code is comprised of N number of component codes, having a variety of inverted EXIT function shapes. These component codes are invoked for generating speciﬁc fractions of the encoded bit sequence, which may be speciﬁcally chosen in order to shape the irregular EXIT function.
Figure 1: Inverted CC EXIT functions. The inverted EXIT function is provided for the corresponding IrCC arrangement, together with the URC EXIT function corresponding to a BPSK-modulated Rayleigh fading channel SNR of +0.2 dB. Inverted CC EXIT functions are labelled using the format CCn (R(CCn ), αn ).
The application of EXIT chart matching invoking Irregular Variable Length Coding(IrVLC) is motivated for the sake of near-capacity joint source and channel coding of source symbol sequences having values exhibiting unequal occurrence probabilities. Instead of the component CCs employed in IrCC schemes, the proposed IrVLC scheme employs component VLC codebooks. These have different coding rates and are used for encoding appropriatedly selected fractions of the input source sysmbol stream. In this way, the resultant composite inverted EXIT function may be shaped for ensuring that it does not cross the EXIT function of the inner channel codec.
LDPC Code, Rateless Code and Fountain Code
Looking back over the last five decades or so, one can reasonably surmise that the family of low-density parity-check codes (LDPC) and that of turbo codes, constitute the two most practical realizations of Shannon’s theory, which have revolutionized the field of error correction coding. It was precisely the year 1948, when Claude E. Shannon, who at that time was a researcher at Bell Labs, published one of the most important theories, which inspired the research community for many years to come. At that time, his theories disproved the widely supported belief that increasing the amount of information-carrying bits transmitted over the channel per second, imposes an increase in the probability of error. Shannon demonstrated that it is possible to transmit information arbitrarily reliably over any unreliable channel, provided that the information transmission rate is lower than the capacity of the channel. Therefore, the channel capacity sets the bound on how much information we can transmit over a channel.
Shannon’s claim can be realized by a technique referred to as forward error correction (FEC). The basic idea is that of incorporating redundant bits, or check bits, together with the original information bits, thus creating what is known as a codeword. If the check bits are introduced in a “appropriate manner” so as to make each codeword sufficiently distinct from each other, the receiver will then become capable of determining the most likely codeword that has been transmitted. The channel capacity will determine the exact amount of redundancy that has to be incorporated by the encoder in order to be able to correct the errors imposed by the channel. However, Shannon’s theory only quantifies the maximum attainable rate, but refrains from specifying the means of achieving it. This triggered widespread research efforts resulting in diverse extensions, deeper interpretations and practical realizations of Shannon’s original work, which reached its pinnacle in the definition of LDPC and turbo codes.
Coded Modulation, Superposition Coded Modulation and Sphere Packing Modulation
Figure 1 :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.
Turbo Trellis Coded Hierarchical Modulation |
Prof Lajos Hanzo, Dr. Soon Xin Ng, Mr Hua Sun
 Turbo Trellis Coded hierarchical modulation for cooperative communications
 Joint Source and Turbo Trellis Coded Hierarchical Modulation for Context-aware Medical Image Transmission [More Publications]
Hierarchical Modulation (HM), which is also known as layered modulation, has been widely adopted in industry nowadays. Its strict backward compatibility and low complexity let it becomes an efficient solution to the problems of upgrading wireless communication services. The potential employment of HM scheme in cooperative communications to increase the throughput and to lower the power consumption has drawn more and more attentions. Nowadays, the researchers had discussed several possible ways to combine HM scheme and CM scheme in cooperative communication system. The common choice is to use multiple lower modulation level encoder blocks and combine the independently coded bits by HM scheme to produce higher modulation level symbols.