Marco Chiani

Lorenzo Valentini, Marco Chiani

We consider the transmission of data encoded into binary messages, with the goal of minimizing the Hamming distance, i.e., the number of bit-flips, between consecutive messages. This problem is relevant for enhancing the longevity of Non-Volatile Memories and reducing transition-induced energy consumption in data buses. Known as Write-Efficient Memory coding in the literature, this challenge has traditionally been addressed using optimal but complex schemes. In low-power computer systems the same topic is known as bus encoding. In this paper, we derive closed-form expressions to evaluate the average number of bit-flips for practical, sub-optimal encoding schemes, and propose two new schemes assisted by predefined random codebooks. We demonstrate that low-complexity solutions achieve performance very close to the optimal schemes, making them attractive for implementation in energy-sensitive and memory-critical applications. For instance, by adding 8 extra bits to 64-bits data, sub-optimal schemes can achieve a bit-flip reduction (related to energy saving) of approximately 24.7%, compared to the 26.4% reduction offered by the significantly more complex optimal scheme.

Andrea Mariani, Andrea Giorgetti, Marco Chiani

Information theoretic criteria (ITC) have been widely adopted in engineering and statistics for selecting, among an ordered set of candidate models, the one that better fits the observed sample data. The selected model minimizes a penalized likelihood metric, where the penalty is determined by the criterion adopted. While rules for choosing a penalty that guarantees a consistent estimate of the model order are known, theoretical tools for its design with finite samples have never been provided in a general setting. In this paper, we study model order selection for finite samples under a design perspective, focusing on the generalized information criterion (GIC), which embraces the most common ITC. The theory is general, and as case studies we consider: a) the problem of estimating the number of signals embedded in additive white Gaussian noise (AWGN) by using multiple sensors; b) model selection for the general linear model (GLM), which includes e.g. the problem of estimating the number of sinusoids in AWGN. The analysis reveals a trade-off between the probabilities of overestimating and underestimating the order of the model. We then propose to design the GIC penalty to minimize underestimation while keeping the overestimation probability below a specified level. For the considered problems, this method leads to analytical derivation of the optimal penalty for a given sample size. A performance comparison between the penalty optimized GIC and common AIC and BIC is provided, demonstrating the effectiveness of the proposed design strategy.