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 degraded message sets. We design UEP codes based on knowledge of the channel quality for each user which means the transmitter knows the average number of correctly decoded sub-blocks for each receiver. However, we assume that there is no perfect channel state information at the transmitter. We assume K virtual users and order each user such that the i-th user intends to receive messages degraded from that received by the (i+1)-th user, where $1 \le i \le K-1$. We focus on constructing codes for K = 2 and K = 3 cases and present achievable rate regions for both cases. Our code construction can be applied to any values of K.
본 논문에서는 무선채널 통신에 적합한 레이트리스 특성을 가진 코드를 디자인하였다. 인터넷 같은 유선채널 통신과는 달리 무선채널 통신에는 노이즈가 존재하므로 좋은 성능을 가진 레이트리스 코드의 디자인이 어려워 지게 된다. 논문에서는 슈퍼포지션 코딩을 적용하여 노이즈 채널을 여러 개의 노이즈가 존재하지 않는 채널들로 전환시킴과 동시에 코드블록을 여러 개의 레벨로 나눈다. 그래서 채널상태가 좋을수록 수신단에서 더 많은 레벨들이 디코딩 될 수 있게 된다. 논문에서는 먼저 네트워크코딩과 연속적 간섭제거 과정을 적용하여 가우시안 채널에서 코드를 디자인하고 연속적 간섭제거 대신 결합 디코딩 방법을 적용하여 복잡도가 증가되지만 성능이 향상된 코드를 디자인한다. 논문 후반부에서는 페이팅 채널을 위해 레이트리스코드를 디자인한다.
