Coding for Parallel Channels: Gallager Bounds for Binary Linear Codes with Applications to Repeat-Accumulate Codes and Variations

This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error probability are derived. These bounds are applied to various ensembles of turbo-like codes, focusing especially on repeat-accumulate codes and their recent variations which possess low encoding and decoding complexity and exhibit remarkable performance under iterative decoding. The framework of the second version of the Duman and Salehi (DS2) bounds is generalized to the case of parallel channels, along with the derivation of their optimized tilting measures. The connection between the generalized DS2 and the 1961 Gallager bounds, addressed by Divsalar and by Sason and Shamai for a single channel, is explored in the case of an arbitrary number of independent parallel channels. The generalization of the DS2 bound for parallel channels enables to re-derive specific bounds which were originally derived by Liu et al. as special cases of the Gallager bound. In the asymptotic case where we let the block length tend to infinity, the new bounds are used to obtain improved inner bounds on the attainable channel regions under ML decoding. The tightness of the new bounds for independent parallel channels is exemplified for structured ensembles of turbo-like codes. The improved bounds with their optimized tilting measures show, irrespectively of the block length of the codes, an improvement over the union bound and other previously reported bounds for independent parallel channels; this improvement is especially pronounced for moderate to large block lengths.Comment: Submitted to IEEE Trans. on Information Theory, June 2006 (57 pages, 9 figures

Analysis of coded OFDM system over frequency-selective fading channels

This thesis considers the analysis of system performance and resource allocation for a coded OFDM system over frequency selective fading channels. Due to the inseparable role taken by channel coding in a coded OFDM system, an information theoretical analysis is carried out and taken as the basis for the system performance and throughput. Based on the results of the information theoretical analysis, the optimal system BER performance of a coded OFDM system is first shown to converge to the outage probability for large OFDM block lengths. Instead of evaluating the outage probability numerically, we provide in this thesis a simple analytical closed form approximation of the outage probability for a coded OFDM system over frequency selective quasi-static fading channels. Simulation results of the turbo-coded OFDM systems further confirm the approximation of the outage probability. By taking the instantaneous channel capacity as the analytical building block, system throughput of a coded OFDM system is then provided. With the aim to compare the performance difference between adaptive and uniform resource allocation strategies, the system throughput of different allocation schemes under various channel conditions is analyzed. First, it is demonstrated that adaptive power allocation over OFDM sub-carriers at the transmitter achieves very little gain in terms of throughput over a uniform power distribution scheme. Theoretical analysis is then provided of the throughput increase of adaptive-rate schemes compared with fixed-rate schemes under various situations. Two practical OFDM systems implementing rate-compatible-punctured-turbo-code-based (RCPT-based) hybrid automatic-repeat-request (Hybrid-ARQ) and redundancy incremental Hybrid-ARQ protocols are also provided to verify the analytical results

LDPC code-based bandwidth efficient coding schemes for wireless communications

This dissertation deals with the design of bandwidth-efficient coding schemes with Low-Density Parity-Check (LDPC) for reliable wireless communications. Code design for wireless channels roughly falls into three categories: (1) when channel state information (CSI) is known only to the receiver (2) more practical case of partial CSI at the receiver when the channel has to be estimated (3) when CSI is known to the receiver as well as the transmitter. We consider coding schemes for all the above categories. For the first scenario, we describe a bandwidth efficient scheme which uses highorder constellations such as QAM over both AWGN as well as fading channels. We propose a simple design with LDPC codes which combines the good properties of Multi-level Coding (MLC) and bit-interleaved coded-modulation (BICM) schemes. Through simulations, we show that the proposed scheme performs better than MLC for short-medium lengths on AWGN and block-fading channels. For the first case, we also characterize the rate-diversity tradeoff of MIMO-OFDM and SISO-OFDM systems. We design optimal coding schemes which achieve this tradeoff when transmission is from a constrained constellation. Through simulations, we show that with a sub-optimal iterative decoder, the performance of this coding scheme is very close to the optimal limit for MIMO (flat quasi-static fading), MIMO-OFDM and SISO OFDM systems. For the second case, we design non-systematic Irregular Repeat Accumulate (IRA) codes, which are a special class of LDPC codes, for Inter-Symbol Interference (ISI) fading channels when CSI is estimated at the receiver. We use Orthogonal Frequency Division Multiplexing (OFDM) to convert the ISI fading channel into parallel flat fading subchannels. We use a simple receiver structure that performs iterative channel estimation and decoding and use non-systematic IRA codes that are optimized for this receiver. This combination is shown to perform very close to a receiver with perfect CSI and is also shown to be robust to change in the number of channel taps and Doppler. For the third case, we look at bandwidth efficient schemes for fading channels that perform close to capacity when the channel state information is known at the transmitter as well as the receiver. Schemes that achieve capacity with a Gaussian codebook for the above system are already known but not for constrained constellations. We derive the near-optimum scheme to achieve capacity with constrained constellations and then propose coding schemes which perform close to capacity. Through linear transformations, a MIMO system can be converted into non-interfering parallel subchannels and we further extend the proposed coding schemes to the MIMO case too

物理層に着目した産業用高信頼リアルタイム無線通信に関する研究

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 森川 博之, 東京大学准教授 中山 雅哉, 東京大学教授 相田 仁, 東京大学准教授 川原 圭博, 東京大学教授 廣瀬 明University of Tokyo(東京大学