This thesis focuses on error exponents for one-way channels with noisy feedback and two-way channels. Various coding techniques are proposed to obtain achievable error exponent regions for different rate-pair regimes. Both Discrete Memoryless Channels (DMC) and discrete time Additive White Gaussian Noise (AWGN) channels are considered, with a focus on zero-rate communication under block coding, and on positive-rate communication under variable length coding. While there exists a vast literature

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... on error exponents for one-way channels with noiseless feedback, there is little work on error exponents under noisy feedback, and no prior work on the characterization of two-way error exponent regions. The results derived from this work indicate that like in one-way channels, feedback (even noisy) cannot be used to increase the capacity of memoryless channels, but it can improve the error exponent region. The same holds for two-way parallel and AWGN channels. We provide initial characterizations of error exponent regions of two-way channels and shed some light on the challenges this problem presents.