Information theoretic approach in detection and security codes

Signal detection plays a critical role in realizing reliable transmission through communication systems. With good detectors, transmission reliability can be enhanced. Maximum a posteriori (MAP) detector is taken as the optimal detector, which gives the detection result with maximum a posteriori value. Maximum-likelihood detector (MLD) and zero-forcing detector (ZFD) are the two classical detection schemes. MLD implements the statical method, maximum-likelihood estimation, to select the signal(information) with maximum-likelihood value. ZFD inverts the frequency response of the channel. But for some particular communication systems, both MAP and ML detection usually require high computation complexity, and sometime MAP and ML detection are even not applicable. This thesis first develops a novel and practical detection algorithm for two-dimensional (2-D) M-ary inter-symbol interferences (ISI) channel where MAP and MLD cannot be realized. Next, the thesis analyzes the fundamental performance of MLD and ZFD in multiple-input multiple-output (MIMO) systems from information theoretic point of view. The security code design to achieve physical layer communication security and reliability over wiretap channel is also studied.;Our work starts from developing a coding and detection algorithm for localized holographic data storage system. To deal with this problem, we model the whole storage system as a communication system with 2-D ISI channel and M-ary inputs. Since there is no existing efficient detection algorithm to detect the M-ary signals over 2-D ISI channel, we propose to implementing multi-level coding technology and detect the signal stage by stage. On each stage, to reduce the computation complexity, multi-strip BCJR with Gaussian approximation equalization algorithm is developed. The proposed equalization algorithm can hugely reduce the number of states for BCJR algorithm on each single data of the whole 2-D data page, which significantly reduces the computation complexity and makes the proposed equalization algorithm applicable. With the proposed detection scheme, we also compute the achievable information rate on each level. More over, the corresponding low-density parity-check (LDPC) component code is designed accordingly to achieve the achievable information rate with the proposed detection algorithm.;To numerically analyze the performance of ML and ZF detection technologies in a MIMO system, the mutual information (MI) is widely used as a metric. Existing results on fundamental limits of MIMO systems with ML or ZF detection are focused on the assumption of continuous signals at the receiver side and the effect of detectors has largely not been addressed. However, in practical digital communication systems, when the inputs are discrete, the continuous outputs given by the receivers have to be mapped to the alphabet of the transmitted signals, i.e. the final outputs should also have discrete values. In this dissertation we study the mutual information between the transmitted discrete signal and the quantized estimated signal given by maximum-likelihood or zero-forcing detector in a MIMO channel setting. To differentiate this from case of the mutual information without any assumption on the detector, we establish a new metric which is the post-detection mutual information (PMI). When phase-shift keying (PSK) constellations are adopted, easily computable asymptotically tight low bounds of the PMI with MLD or ZFD are derived. Furthermore, when quadrature amplitude modulation (QAM) constellations are adopted, a numerically closed form of the PMI with ZFD is provided. We show how much the mutual information is reduced by the presence of quantization of the detectors. The lower bounds provided in the dissertation tightly approach the simulation results in mid and high SNR region.;For the security problem in wiretap channel, we consider a commonly adopted wiretap model which has a noiseless main channel and a binary erasure eavesdropper’s channel. LDPC codes have been applied to achieve strong secrecy over such wiretap channel setting. However, it lacks design flexibility balancing on security and reliability, and cannot illustrate the fundamental tradeoffs among erasure rate, secrecy rate, and the security performance. We investigate a random complex field code (RCFC) design for such wiretap channels. The design of RCFCs is systematic and flexible for any code rate. Our analysis shows that RCFC can achieve the secrecy capacity as the code length goes to infinity. More strikingly, the presented design is the first one which provides a platform to tradeoff secrecy performance with the erasure rate of the eavesdropper’s channel and the secrecy rate.