LDGM codes for wireless and quantum systems

In the last decade, helped by the increase in computing power, capacity approaching codes, such as turbo codes and low-density parity check (LDPC) codes, have been proposed. The common characteristics of these codes are their long length and their random-like codeword structure. However, the decoding complexity of turbo codes and the encoding complexity of LDPC codes are substantial. In order to alleviate this problem, we propose the use of low-density generator matrix (LDGM) codes, which are a special class of LDPC codes with low encoding and decoding complexity.; In this work, we explore different avenues to successfully apply LDGM codes in different communications environments such as quantum systems, realistic wireless channels with memory, and MIMO channels. In order to do so, it is necessary to generate LDGM codes for different rates. Thus, the first contribution of our work is showing that LDGM codes are very flexible and can be easily modified to achieve different rates. Then, we investigate the following topics: (1) In quantum environments, stabilizer codes are a special yet large class of quantum error-correcting codes, which introduce a connection between classical block codes and quantum codes. (2) We have proposed a modified algorithm for decoding of LDGM codes over hidden Markov channels. The proposed scheme clearly outperforms the system in which the channel statistics are not exploited at the decoder side. (3) In order to approach the capacity limit in MIMO systems, powerful channel codes have to be utilized. We compare schemes based on (i) the concatenation of space-time codes and powerful channel codes and (ii) systems based on just using channel coding (no space-time code) in the context of bit-interleaved coded modulation with an iterative process between the demapper and the code. (4) We compare different transmission schemes for multiple antenna transmission systems based on multilevel codes (MLC) in terms of the maximum rate that they can achieve. We introduce a new architecture that can provide nearly optimum performance without iterative demapping and has lower complexity than the full multilevel coding scheme. (5) We focus on the design of layered transmission schemes that can approach outage capacity in quasi-static fading channels in the high spectral efficiency regime without demapper iterations. (Abstract shortened by UMI.)...