Rate-compatible and unequal error protection codes

Abstract

The thesis is separated into two parts. In the first part of the thesis, we design practical codes having good rateless properties for the Gaussian channel using layered superposition and successive interference cancelation (SIC). Layered superposition converts the Gaussian channel into a set of layered noiseless channels so that sub-blocks in a layer are noiselessly delivered to the receiver as long as the channel gain is better than a threshold supportable by the layer. The message can be decoded as long as a certain number of sub-blocks are received regardless of which sub-blocks are received. We define this kind of codes as perfect rate-compatible codes. In this part of the thesis, we mainly discuss the case that all available received sub-blocks are in layers survived from a certain channel threshold which means the channel gain remains unchanged during one packet transmission. We construct asymptotically perfect rate-compatible codes for Gaussian channels under SIC applying network coding. In high SNR, asymptotically perfect codes possess optimal multiplexing gains instead of optimal exact rates. If we consider joint decoding instead of SIC, perfect rate-compatible codes can be constructed using Hadamard and Fourier transform matrices. We will extend some of our results to fading cases by simulations. In the other part of the thesis, we extend our results discussed in the first part of the thesis to more general cases. We will assume the channel gain can be changed from sub-packet to sub-packet during one packet transmission and additionally assume that more available received sub-blocks provide more decodable messages. Then, it can be thought as a problem of unequal error protection (UEP). We construct codes with good UEP properties for fading channels such that more information can be decoded when the channel condition is better. From another angle of view, we intend to deal with designing practical codes for a special case of broadcast channel with...