It is well known that increasingly better performance may be obtained from q-ary LDPC codes as q increases, albeit not necessarily monotonically. Such improvements can however be at the expense of disproportionate increases in decoding complexity. Motivated by these considerations, the notion of LDPC codes over mixed Galois fields is introduced to provide a controlled means of trading performance improvements for proportionate increases in decoding complexity. A subclass of these codes are LDPC codes over F₁, extended with additional redundant symbols defined over an extension field F₂ of F₁. Simulations have shown that under belief propagation (BP) decoding on an AWGN channel as well as a fast Rayleigh fading channel, for a fixed code rate and binary length, (i) improving BER performance can be obtained as the number of redundant symbols defined over F₂ is increased – thus, these codes can perform better than their single-alphabet counterparts; (ii) performance improvements are more significant on a fading channel than on an AWGN channel. We have also considered the counterparts of this class of codes over mixed integer residue rings. Not surprisingly, they behave in the same way as their mixed finite field counterparts. In addition, we have looked at the effects that zero divisors as edges weights, in the Tanner graph representation of these codes have. One fascinating observation is that cycles of length 4 are not bad, provided at least one of the corresponding 4 edge weights is a zero divisor. We have also devised a new decoding technique for LDPC codes over Z_q where q is a prime power. This decoder sequentially invokes the BP decoder to decode the homomorphic images of a Z_q code, first over Z₂, then over Z₄, and so on, to arrive at an estimate of the transmitted codeword. For Z₄ codes, this decoder can yield an additional coding gain of 0.1 dB over conventional single-stage BP decoding on an AWGN channel under binary signaling, while incurring an additional computational overhead of less than 1% over the latter decoder.  

Further details may be found in the following articles.

 K.S. Ng and M.A. Armand, “LDPC codes over mixed alphabets,” Electronics Letters, vol. 42, no. 22, pp. 1290-1291, Oct 2006.

 E. Mo and M.A. Armand, “Design and performance of LDPC codes extended with parity-check symbols from a larger alphabet,” submitted to Int. Conf. Information, Communications and Signal Processing 2007.

 M.A. Armand and K.S. Ng, “Decoding LDPC codes over integer residue rings,” IEEE Trans. Inf. Theory, vol. 52, no. 10, pp. 4680-4686, Oct 2006.

Today, the freedom of mobility brought by wireless technologies has given rise to a growing need for location-aware services.  These services are particularly appealing to the mobile user because they are relevant and valuable at that specific location and instant.  The ability to pinpoint the location of a mobile device is thus critical to potential service providers who desire to enter the multi-billion dollar location-based services (LBS) industry.  

While the well-known satellite-based Global Positioning System (GPS) is very useful for outdoor positioning purposes, it is unsuitable for indoor use because the GPS signals are not designed to penetrate most construction materials.  As a result, there is a keen interest among both the academia and the industry to design new positioning technologies that work indoors.  Technologies based on infrared (IR), ultrasound, ultra-wideband (UWB), Wi-Fi, and Bluetooth, have been proposed previously.  Among these technologies, Wi-Fi and Bluetooth are particularly attractive as they are widely available in laptops, mobile phones and personal digital assistants (PDAs); positioning techniques based on these technologies typically do not require any additional specialized hardware, and are therefore more economical to deploy.   

Our research seeks to develop indoor positioning techniques for mobile devices that are equipped with one or more radio interfaces, such as Wi-Fi, Bluetooth, etc.  In particular, we focus on fusing multiple wireless technologies to achieve better accuracy and availability.  

We have currently installed a test bed in one of the lecture theatres within NUS campus.  The figure shows a Web interface of our positioning engine.  Our system currently achieves an average accuracy of about three meters, for both Wi-Fi and Bluetooth devices.   

Related publications:

A.K.M. Mahtab Hossain, Hien Nguyen Van, Yunye Jin and Wee-Seng Soh, "Indoor Localization using Multiple Wireless Technologies, " IEEE MASS, Pisa, Italy, Oct. 2007.

A.K.M. Mahtab Hossain and Wee-Seng Soh, "A Comprehensive Study of Bluetooth Signal Parameters for Localization," IEEE PIMRC, Athens, Greece, Sep. 2007.