Efficient Coding Techniques for Networks & Channels with Transmission Errors

Doctoral thesis, 2007

This thesis consists of two parts, both of which investigate coding techniques for information transmission through channels in the presence of errors. Part I discusses topics of network coding and rateless codes. Part~II considers channel codes for continuous phase modulation. These two parts are clearly different, but they are also related. In Part I, we first discuss the bit error probability (BEP) in the sinks. We develop algorithms to calculate the sink BEP for both binary codes and nonbinary codes. The results can be exact or approximate, with different computational complexity. Then, we discuss optimal sink decoding problems. We show that the statistical information of upstream channels is critical to the decoders. We propose analysis bounds for the different decoding schemes. Then, we investigate the binary coding approach for combination networks. Our codes are deterministic, and achieve min-cut capacities with only cyclic shifting and XOR operations. We propose a binary rateless coding scheme for general (in topology) networks with erasure networks. The codes have merits of small block magnitude and very small overheads (near maximum distance separable). Finally, we investigate cross-layer design approaches for random rateless network codes. For Part II, we first investigate serially concatenated continuous phase modulation (SCCPM) with convolutional codes (CC) over rings. The properties for systems with both infinite and finite block lengths are investigated. Compared to previous SCCPM with a binary CC, the proposed system shows an improvement concerning the convergence threshold or error floors. Then, we investigate the analysis and design of low density generator matrix codes for CPM. We discuss systems with a finite block length. We also consider a rate-adaptive system for slowly fading channels. A significant energy saving is found from non-adaptive schemes.