Master of Science / We are in an ever-increasing demand for computing power to sustain our technological advancements. A significant driving factor of our progress is the size and speed of memory we possess. Modern computer architectures use DDR4-based DRAM (Dynamic Random Access Memory) to hold all the immediate information for processing needs. Each bit in a DRAM memory module is implemented with a tiny capacitor and a transistor. Since the capacitors are prone to charge leakage, each bit must be frequently rewritten with its old value. A dedicated memory controller handles the periodic refreshes. If the cells aren't refreshed, the bits lose their charge and lose the information stored by flipping to either 0 or 1 (depending upon the design). Due to manufacturing variations, every tiny capacitor fabricated will have different physical characteristics. Charge leakage depends upon capacitance and other such physical properties. Hence, no two DRAM modules can have the same properties and decay pattern and cannot be reproduced again accurately. This DRAM attribute can be considered a source of 'Physically Unclonable Functions' and is sought after in the Cryptography domain. This thesis aims to characterize the decay patterns of commercial DDR4 DRAM modules. I implemented a custom System On Chip on AMD/Xilinx's ZCU104 FPGA platform to interface different DDR4 modules with a primitive memory controller (without refreshes). Additionally, I introduced electric and magnetic fields close to the DRAM module to investigate their effects on the decay characteristics.

<p dir="ltr">We study the communication model with perfect feedback considered by Berlekamp (PhD Thesis, 1964), in which Alice wishes to communicate a binary message to Bob through a noisy adversarial channel, and has the ability to receive feedback from Bob via an additional noiseless channel. Berlekamp showed that in this model one can tolerate 1/3 fraction of errors (a.k.a., bit-flips or substitutions) with non-vanishing communication rate, which strictly improves upon the 1/4 error rate that is tolerable in the classical one-way communication setting without feedback. In the case when the channel is corrupted by erasures, it is easy to show that a fraction of erasures tending to 1 can be tolerated in the noiseless feedback setting, which also beats the 1/2 fraction that is maximally correctable in the no-feedback setting. In this thesis, we consider a more general perfect feedback channel that may introduce both errors and erasures. We show the following results:</p><p dir="ltr">1. If α, β ∈ [0, 1) are such that 3α + β < 1, then there exists a code that achieves a positive communication rate tolerating α fraction of errors and β fraction of erasures. Furthermore, no code can achieve a positive-rate in this channel when 3α + β ≥ 1.</p><p dir="ltr">2. For the case when 3α + β < 1, we compute the maximal asymptotic communication rate achievable in this setting.</p>