Semi-random forward error correction codes and space-time codes

Abstract

The fast development of wireless communications demands an ever-growing data rate and better quality of services. The forward-error-correction (FEC) code and space-time (ST) code are important means to meet these demands. Based on Shannon's theorem, a random code has a large probability to be good, but is very difficult to encode and decode. In this thesis, semi-random FEC codes and ST codes are designed to achieve both good-performance and low-complexity properties. This thesis is divided into two parts. In the first part, semi-random FEC codes are developed. The basic principle is to concatenate multiple simple recursive component codes in parallel via random interleavers. With recursive component codes and random interleavers, the resulting code has a nearly Gaussian weight distribution, which indicates its connection with the random code. Two FEC codes are proposed in this part: the concatenated tree (CT) code and the modified turbo-SPC code, suitable for coding rates R≧1/ 2 and 1/8 < R <1/2, respectively. Both codes have high-performance and low-complexity properties. The CT code employs tree codes as component codes, which allow very simple local decoding based on the belief-propagation algorithm. CT codes can be regarded as special low-density parity-check (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recursive/nonrecursive parts and multiple component codes. Compared with turbo codes, CT codes have similar (or better) performance, but with significantly lower decoding complexity. Compared with LDPC codes, CT codes have faster convergence speed, and better performance with short to medium code lengths (< 10000). CT codes are most suitable for coding rates R ≧1/2. For rates lower than 1/2, the relative gap between the performance of CT codes and the theoretical limit becomes large. To treat this problem, we develop the modified turbo-SPC code, which is an improvement of the turbo-SPC code with two states. The turbo-SPC code is closely related to the CT code. Turbo-SPC codes with two states are actually CT codes. With higher (than two) state numbers, the turbo-SPC code can achieve better performance than the CT code, but also with increased complexity. The modified turbo-SPC code is designed to provide better performance than the original two-state turbo-SPC code, i.e., the CT code, while still maintaining the low-complexity property. This code is most suitable for coding rates 1/8 < R<1/2. In the second part of this thesis, we develop a family of semi-random ST codes - the interleave-division-multiplexing space-time (IDM-ST) code. The basic principle is to employ multiple semi-random FEC codes, and transmit their randomly interleaved codewords simultaneously from all antennas. Signals from the same FEC encoder are referred to as a layer. On each transmit antenna, signals from all layers are superimposed and transmitted simultaneously. Assuming independent input sequences for different layers and independent random interleavers, signals transmitted from different antennas at different time instances can be approximately regarded as independent and identically distributed Gaussian random variables. This indicates a close connection between the IDM-ST code and the random ST code. The IDM-ST scheme is conceptually very simple and does not require any sophisticated methodology. It is flexible regarding the rate and the transmit antenna number. At the receiver side, a turbo-type iterative decoder is employed. Several simple iterative decoding algorithms are presented for different channel conditions. The related complexity is relatively low, and grows only linearly with the number of transmit antennas and quadratically with the path number of a multipath channel. A key property of the multi-layer IDM-ST code is the use of unequal power allocation among layers. The transmission power levels are designed carefully to optimize the system performance. To facilitate the search for optimal power levels, fast performance assessment techniques are proposed for the IDM-ST code over both fixed channels and quasi-static fading channels. These techniques are simple and relatively accurate. Using these techniques as searching tools, efficient power allocation strategies are developed to optimize the system performance. Simulation results show that the IDM-ST code can achieve near-capacity performance at high rates with relatively low decoding complexity. Compared with other existing ST codes, the IDM-ST code demonstrates better flexibility regarding the number of transmit antennas and the transmission rate. It provides a promising and unified solution to ST coding for high-rate applications with arbitrary numbers of transmit antennas.