Research Fields

 

Digital communications technology

General error correction coding and design of practical decoders with competitive performance

Error correction coding or channel coding allows one to reliable send information across unreliable (noisy) channels. As an example, signals containing a digital image transmitted from a satellite at thousands of miles away will suffer from significant attentuation and other types of distortion when they are received on the earth. By using an error correction code, which adds some redundant information to the signal prior to transmission, the distorted image can be perfectly recovered.

The group has established strong research in the areas of

  • iteratively decodable error correcting codes such as turbo and low-density parity-check (LDPC) codes;
  • improving the convergence of iterative decoders;
  • weight spectra of iteratively decodable codes;
  • combined modulation and coding (trellis-coded modulation); and
  • coding for multiple-access communications.

Aside from iteratively decodable codes, the group also have research interest in general linear block, convolutional and concatenated codes and their practical soft-decision decoding algorithms.

The group is also interested in the mathematics of error correcting codes. Self-dual codes, double-circulant codes and their weight distributions, algebraic geometry codes are some examples of our research topics.

 

Constructions of new codes improving on best known linear codes

The minimum distance of a code is an important parameters since it determines the error-correcting abilities of the code. Markus Grassl maintains a database containing the lower-bounds and upper-bounds of minimum distance of linear codes over finite-fields. The lower-bound corresponds to the largest minimum distance for a given length and dimension that has been found and verified to date. Constructing codes which are improvements over these codes is an ongoing research activity in coding theory.

 

Erasure coding for packet networks

Packet networks such as IP networks are increasingly being used to deliver real-time delay-critical information such as voice (voice-over-IP), audio (Internet radio) and television (IPTV). IP networks are not designed for these types of applications. Real-time transport using IP networks is prone to packet loss and error correcting codes can be used to recover the lost packets. In the context of coding, these lost packets are treated as erasures.

 

Watermarking

In the watermarking of static images there are two basic approaches:

  1. to add a pseudo noise sequence, sign modulated with data to the image; and
  2. to quantise the image in the spatial domain or in a transform domain prior to the addition of a coded watermark in that domain.
Either way the most efficient error correcting code is required which operates at the lowest possible Eb/No value. The main difficulty is that efficiency is a function of the number of information bits, and only a limited number of information bits may be impressed on a watermark before it becomes readily visible. The objective is to add the watermark to the image with the lowest possible SNR per pixel and still be able to recover the data from the watermark free from errors.The useful range of information bits is probably limited to 16 bits to 256 bits. Below 16 bits the optimum practical scheme is perhaps to use a bi-orthogonal code with maximum likelihood decoding, implemented using a Fast Fourier Transform (FFT). Above 16 bits the choice is between Turbo codes and low-density parity-check (LDPC) codes. Accordingly the best short LDPC codes and Turbo codes suitable for iterative decoding have been determined or designed for this purpose. For LDPC codes the approach is to use cyclic codes because these have n low weight parity check equations that contribute extrinsic information instead of the n-k equations for an ad hoc designed code, and this leads to better convergence. Additionally the cyclic codes are chosen such that there are no cycles of length 4, or equivalently they are chosen such that all differences between parity check bit positions are distinct. The Turbo code designs feature low memory encoders for good convergence and a short cyclic-redundancy-check (CRC) of 4 bits to thin the weight spectra and to improve the stopping criteria for the iterative decoder

 

Modulation and equalisation of wireless channels

Wireless channels are increasingly being used for high speed communications and Internet access particularly within buildings. As such, the radio frequency carriers are subject to multipath distortion, noise and interference. Bandwidth efficiency is important and the choice of modulation methods plays a key role. Equalisation is necessary to combat multipath and error correction coding may be used to mitigate the noise degradation associated with equalisation. We are investigating the benefits of single-carrier operations in competition with Orthogonal Frequency Division Mutiplexing (OFDM) involving hundreds of parallel channels.

 

Image and video compression

In modern multimedia communications, compression is a key part of the system to minimise capacity utilisation consistent with high quality image and video to the end users. MPEG2 and MPEG4 are in common use, but latency is becoming more important for several applications. We are specialising in this area which presents challenges as much of the video compression comes from the processing of past and future video frames. By taking a more analytical approach, we have demonstrated a low latency MPEG4 compatible high fidelity video compression system.

 

 

Mobile Communications and Wireless Networks

For research areas within mobile communications and wireless networks, please click here.