New Rate Control and Bit Mapping Schemes for RA-Type LDPC Code

Abstract

In 1948, Shannon showed that arbitrarily reliable information transmission is possible through a noisy channel if the information rate in bits per channel use is less than the channel capacity of the channel. Since then, to achieve the Shannon limit, various channel coding schemes have been proposed. Recently, low-density parity-check (LDPC) codes were rediscovered and they are known as practically implementable codes to approach the channel capacity of various channels. In this dissertation, we concentrate on designing and analyzing the error correction schemes using LDPC codes, especially over the additive white Gaussian noise (AWGN) channel. Specifically, the following four error correction schemes based on LDPC codes are proposed.

First, a new rate-control scheme, called splitting, is proposed to construct low-rate codes from high-rate codes by splitting rows of the parity-check matrices of LDPC codes. The splitting can be used to build rate-compatible LDPC codes having good initial transmission performance. Since a high-degree check node is split into two low-degree check nodes to produce low-rate codes, splitting can generate good low-rate codes by making the number of distinct check node degrees as small as possible after splitting. Compared with puncturing and extending, the splitting not only shows faster decoding convergence speed but also has low decoding complexity. We also construct rate-compatible repeat accumulate-type LDPC (RA-Type LDPC) codes using splitting that cover the code rates from 1/3 to 4/5. It is shown that they outperform other rate-compatible RA-Type LDPC (RC RA-Type LDPC) codes for all rates.

Second, a bit mapping scheme is proposed to transmit the codeword bits over nonuniform parallel Gaussian channels. Contrary to the previously known mapping schemes such as mapping the codeword bits in consecutive order and mapping the information bits to more reliable channel, the proposed scheme flexibly transmits the information and parity bits of LDPC codewords by considering the characteristics of the code and channel such as degree distributions and channel difference. The proposed mapping scheme selects the best bit mapping for the given code and channel condition, while keeping the same overall computational complexity. For the various codes and nonuniform parallel Gaussian channels, the best mappings are derived and the validity of them is confirmed through the simulation.

Third, an adaptive bit-reliability mapping is proposed for the bit-level Chase combining in LDPC-coded high-order modulation systems. Contrary to the previously known bit-reliability mapping that assigns the information (or parity) bits to more (or less) reliable bit positions, the proposed mapping flexibly assigns codeword bits to the bit positions of various reliabilities by considering the characteristics of code and the protection levels. Compared with the symbol-level Chase combining and the constellation rearrangement bit mapping, the proposed mapping gives $0.7 dB$-$1.3 dB$ and $0.1 dB$-$1.0 dB$ gain at FER=$10^{-3}$ with no additional computational complexity, respectively. The adaptive bit-reliability mappings are derived for various environments and the validity of them is confirmed through the simulation.

Fourth, an adaptive decode-and-selective-forward scheme based on the code and channel characteristics is proposed. In this scheme, the relay node decodes the contaminated codewords received from the source, selects a part of codewords based on feedback information received from the destination, and forwards the selected part to the destination. The selected part is combined with the received codewords from the source at the destination. The proposed cooperative scheme selects the best portion of the codeword for the given environment at the relay node, while keeping the nearly same overall computational complexity. The convergence behavior of the proposed schemes is analyzed by employing the density evolution. In addition, the optimization of the time division parameter $\alpha$ is discussed. By choosing the suitable parameters and designing the codes accordingly, the system performance can be improved significantly.