Whenever companies plan to enter new geographical areas, they need disaggregated sales in each location. To make such predictions, sales time series or final customers' data in geographical disaggregation are necessary. However, for most companies, such datasets are unavailable or impractical. The manuscript has two main goals. One focal problem is how to disaggregate an aggregate sales prediction with no historical proportions. The other is how to improve spatial models using Point of Interest (POI) data. To solve these problems, we combine two literature streams — spatial marketing and sales forecasting — and propose a new hybrid probabilistic approach: Gravitational Sales Prediction (GSP). Our approach uses POI data to estimate area attraction, customer stocks, and flows to predict sales proportions. We later use these proportions to disaggregate an aggregate forecast. GSP is validated using sales data from two countries and more than ten economic segments. When compared to a strong benchmark that relies on past sales proportions, GSP exceeded expectations by achieving not only a similar performance to the benchmark but also outperforming it in some locations. It showed the most promising results in the middle level of aggregation. The result is a powerful and flexible approach that can be embedded in any decision support system.

In this paper, we present a deliberate bit flipping (DBF) coding scheme for binary two-dimensional (2-D) channels, where specific patterns in channel inputs are the significant cause of errors. The idea is to eliminate a constrained encoder and, instead, embed a constraint into an error correction codeword that is arranged into a 2-D array by deliberately flipping the bits that violate the constraint. The DBF method relies on the error correction capability of the code being used so that it should be able to correct both deliberate errors and channel errors. Therefore, it is crucial to flip minimum number of bits in order not to overburden the error correction decoder. We devise a constrained combinatorial formulation for minimizing the number of flipped bits for a given set of harmful patterns. The generalized belief propagation algorithm is used to find an approximate solution for the problem. We evaluate the performance gain of our proposed approach on a data-dependent 2-D channel, where 2-D isolated-bits patterns are the harmful patterns for the channel. Furthermore, the performance of the DBF method is compared with classical 2-D constrained coding schemes for the 2-D no isolated-bits constraint on a memoryless binary symmetric channel.

Quantum low-density parity check (QLDPC) codes are promising in realization of scalable, fault tolerant quantum memory for computation. Many of the QLDPC codes constructions suffer from unavoidable short cycles in their Tanner graph which degrade the decoding performance of the belief propagation (BP) algorithm. In this paper, we propose a syndrome based generalized belief propagation (GBP) algorithm for decoding of quantum LDPC codes and analyze how the proposed algorithm escapes from short cycle trapping sets effectively compared to the BP algorithm. Simulation results show improved decoding performance of the GBP algorithm over BP for the dual containing Calderbank, Shor and Steane (CSS) codes when cycles of length 4 are considered in the region based approach.

We propose a novel approach to modulation coding using the Generalized Belief Propagation (GBP) algorithm. The idea is to completely eliminate a constrained encoder and, instead, embed a constraint into an error correction codeword by deliberately flipping the bits that violate the constraint. The GBP algorithm is used to keep the number of flipped bits small in order not to overburden the decoder. We incorporate our method to impose the two-dimensional (2D) no isolated bit constraint on a low-density parity check (LDPC) coded 2D data array. Furthermore, we show that the number of flipped bits can be optimized so that it is not beyond the error correcting capability of the code. Applied to Two Dimensional Magnetic Recording (TDMR) systems, our approach results in an order of magnitude gain in the frame error rate.

Two dimensional magnetic recording (TDMR) achieves high areal densities by reducing the size of a bit comparable to the size of the magnetic grains resulting in two dimensional (2D) inter symbol interference (ISI) and very high media noise. Therefore, it is critical to handle the media noise along with the 2D ISI detection. In this paper, we tune the generalized belief propagation (GBP) algorithm to handle the media noise seen in TDMR. We also provide an intuition into the nature of hard decisions provided by the GBP algorithm. The performance of the GBP algorithm is evaluated over a Voronoi based TDMR channel model where the soft outputs from the GBP algorithm are used by a belief propagation (BP) algorithm to decode low-density parity check (LDPC) codes.

In this paper, we estimate the Mutual Information Rate (MIR) for Two-Dimensional Magnetic Recording (TDMR) channel with input constraints by using the Generalized Belief Propagation (GBP) algorithm. The Voronoi channel model is considered in this paper. Since the main source of media noise in the TDMR channel is the boundary distortion of the bit area which is manifested in presence of transitions of the input data, the constraints utilized for TDMR systems limit the number of transitions in the input patterns. In [1], we showed that constrained coding can provide performance gain in the bit error rate (BER). However, BER is not a proper figure of merit to compare various input distributions for a fixed channel since the rate loss due to using constrained input is not accounted for. On the other hand, computing MIR for different input distributions can lead us to the limits of the channel capacity.

In this paper, we propose a method for estimating the Symmetric Information Rate (SIR) for Two Dimensional Magnetic Recording (TDMR) channel by using the Generalized Belief Propagation (GBP) algorithm. We consider the Voronoi model as the channel model of a TDMR system. The dominant component of noise in TDMR caused by the imperfections of the medium is called “media noise”. The nature of the media noise is data-dependent, however, the media noise can be closely approximated by additive white Gaussian noise (AWGN) with variance and mean dependent on channel bits written on the magnetic medium. Lower and upper bounds on the SIR are obtained by using the GBP algorithm. In addition, it is shown that the accuracy of the SIR estimation can be adjusted for sufficient size of the magnetic medium. Finally, the bit aspect ratio of a TDMR system is optimized by maximizing the SIR per unit area.

In this paper, we investigate the problem of the empirical coordination in a triangular multiterminal network. A triangular multiterminal network consists of three terminals where two terminals observe two external i.i.d correlated sequences. The third terminal wishes to generate a sequence with desired empirical joint distribution. For this problem, we derive inner and outer bounds on the empirical coordination capacity region. It is shown that the capacity region of the degraded source network and the inner and outer bounds on the capacity region of the cascade multiterminal network can be directly obtained from our inner and outer bounds. For a cipher system, we establish key distribution over a network with a reliable terminal, using the results of the empirical coordination. As another example, the problem of rate distortion in the triangular multiterminal network is discussed in which a distributed doubly symmetric binary source is available.