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.

 

 

Rate-compatible coding via puncturing of LDPC codes

 

In designing an error correcting system for a time-invariant channel, we choose a code with a fixed rate and correction capability that adapts to the worst channel condition. However, in a mobile adaptive network the channel is time-varying, and different types of data require different error protection needs. Therefore, to maintain an acceptable quality of service, we need to change the coding rate during transmission. A natural solution to such a problem is the usage of a class of codes instead of a single code, depending on the quality of the channel. It is not practical to switch between multiple encoders and decoders, but we want to have one `good' code whose encoder and decoder are modified according to the rate without losing the good properties of the code. An interesting solution to this is the technique of puncturing. In this method, to change the rate of a code to a higher rate, we puncture (delete) a subset of the codeword bits. We study punctured LDPC codes over BEC and extend it to other MBIOS channels. We intend to derive bounds on the degradation of performance of punctured LDPC ensembles as a function of puncturing fraction. Using which, we plan to arrive at criteria for good puncturing patterns and degree distributions. We then intend to investigate the effect of puncturing on finite-length LDPC codes. We analyze this over BEC using a graph-theoretic approach and extend this analysis to random puncturing over other MBIOS channels. Finally, we plan to optimize the puncturing patterns to minimize the loss of performance due to puncturing in finite length cases.