Coding Theory
Our research explores the relations among coding theory, information theory, and related areas of computer science and mathematics. In error control coding, our team is concerned with the design, performance analysis and decoding of efficient modern error control systems such as wavelet codes, rateless codes, low density parity check codes (LDPC) and other types of iterative coding schemes. We are particularly interested in coding techniques for erasure channels, unequal error protecting codes, rate compatible codes, nonuniform codes, and two-dimensional codes for digital communication/storage systems and wireless ad hoc networks.
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Rateless codes are a relatively new class of linear error-control codes. The idea behind the rateless codes is that every receiver continues collecting the encoded data until the decoding can be finished successfully. To generate an encoding symbol in a rateless code, a degree d is chosen randomly from a given degree distribution. Then, d information symbols are selected randomly and their values are XORed. This encoded symbol is then transmitted. Decoding of rateless codes is bases on belief propagation, which is an iterative algorithm. A receiver can recover k information symbols if it receives k encoding symbol, where . We investigated rateless codes for the following applications: * UEP-Rateless Codes: We developed, for the first time, rateless codes that can provide UEP. We analyzed the proposed codes under both iterative decoding and maximum-likelihood decoding. Results are very promising and show the applicability of UEP-rateless codes in many important applications, such as transferring data frames or video/audio-on-demand streaming. * Maximum-likelihood Decoding of Rateless Codes: we derived upper and lower bounds on maximum-likelihood (ML) decoding bit error probabilities of finite-length rateless codes over the binary erasure channel. The bounds on ML decoding are of interest, as it provides an ultimate indication on the system performance. Simulation results depict that the bounds are tight. * Efficient Broadcast/Multicast Protocols via Rateless Coding: See our research section in SensorNets->Broadcast Protocols for details of these activities.
