the Transform Domain An LTI discrete-time system is completely characterized in the time-domain by its impulse response {h[n]} We consider now the use of the DTFT and the z-transform in developing the transform￾domain representations of an LTI system

Stability Condition in Terms of the Pole Locations A causal LTI digital filter is BIBO stable if and only if its impulse response h[n] is absolutely summable, i.e., We now develop a stability condition in terms of the pole locations of the transfer function H(z)

Later in the course we shall review various methods of designing frequency-selective filters satisfying prescribed specifications We now describe several low-order FIR and IIR digital filters with reasonable selective frequency responses that often are satisfactory in a number of applications

The simple filters discussed so far are characterized either by a single passband and/or a single stopband There are applications where filters with multiple passbands and stopbands are required The comb filter is an example of such filters

It is nearly impossible to design a linear￾phase IIR transfer function It is always possible to design an FIR transfer function with an exact linear-phase response Consider a causal FIR transfer function H(z) of length N+1, i.e., of order N:

The dtft provides a frequency-domain representation of discrete-time signals and lti discrete-time systems Because of the convergence condition, in many cases. the dtft of a sequence may not exist as a result. it is not possible to make use of such frequency-domain characterization in these cases Copyright C 2001, S K. Mitra

4.8.1 Definitions and Basic Concepts 4.8.2 Encoding of LDPC Codes 4.8.3 Decoding of LDPC codes 4.8.4 Density Evolution (Analysis of LDPC Codes on Symmetric Binary Input Channels) 4.8.6 Design and Construction of LDPC codes - Overview 4.8.8 Accumulator-Based LDPC Codes 4.8.9 Nonbinary LDPC codes 4.8.10 Performance Analysis of ML-Decoded LDPC Codes 4.8.11 More on Encoding 4.8.12 Applications of LDPC Codes

5.9 级联TCM 5.10 Multilevel Codes and Multistage Decoding 5.11 Bit-Interleaved Coded Modulation (BICM) with Iterative Decoding 5.13 Combined Coding and Shaping 5.14 Implementation Considerations and Application Examples

The research on wireless communications has received many attentions. The underlying physical channels may be characterized as time-varying fading channels. In this chapter, we will study communications over fading channels from an information-theoretic point of view. Many state-of-the-art coding and modulation schemes, including space-time codes, will be introduced

8.1 Introduction 8.2 MIMO System Model 8.3 Fundamental Capacity Limits of MIMO Channels 8.4 Capacity of MIMO Rayleigh Fading Channels (Random MIMO Channels) 8.5 Influence of Channel-State Information [Biglieri05] 8.6 Design of MIMO Systems