Partition Information and its Transmission over Boolean Multi-Access Channels

In this paper, we propose a novel partition reservation system to study the partition information and its transmission over a noise-free Boolean multi-access channel. The objective of transmission is not message restoration, but to partition active users into distinct groups so that they can, subsequently, transmit their messages without collision. We first calculate (by mutual information) the amount of information needed for the partitioning without channel effects, and then propose two different coding schemes to obtain achievable transmission rates over the channel. The first one is the brute force method, where the codebook design is based on centralized source coding; the second method uses random coding where the codebook is generated randomly and optimal Bayesian decoding is employed to reconstruct the partition. Both methods shed light on the internal structure of the partition problem. A novel hypergraph formulation is proposed for the random coding scheme, which intuitively describes the information in terms of a strong coloring of a hypergraph induced by a sequence of channel operations and interactions between active users. An extended Fibonacci structure is found for a simple, but non-trivial, case with two active users. A comparison between these methods and group testing is conducted to demonstrate the uniqueness of our problem.Comment: Submitted to IEEE Transactions on Information Theory, major revisio

Design of information hiding algorithm for multi-link network transmission channel

Traditional channel information hiding algorithms based on m-sequence for multi-link network transmission, which apply m-sequence to channel coding information hiding system, do not analyze the upper limit of hiding capacity of multi-link network transmission channel system, and do not consider the hidden danger of overlapping secret information when embedding secret information is too large. It has the defects of low efficiency, poor accuracy and large storage cost. This paper designs an information hiding algorithm for multi-link network transmission channel based on secondary positioning, it uses RS code M public key cryptosystem to pre-process secret information and improve the security of information; calculates the upper limit of hiding capacity of multi-link network transmission channel system through information hiding capacity analysis model, and determines whether the hiding capacity exceeds the secret information. Secondary location and cyclic shift mechanism are introduced to improve the randomness of location selection and avoid overlapping of secret information. The experimental results show that the proposed algorithm has a great advantage in memory cost. When the channel SNR is 0 dB and 8 dB, the normalization coefficients are 0.87 and 1.04, respectively. This shows that the algorithm has a high accuracy in extracting secret information. The average time spent on hiding information is 2.04 s, indicating that the algorithm has high information hiding rate and storage efficiency

Asymptotic Error Free Partitioning over Noisy Boolean Multiaccess Channels

In this paper, we consider the problem of partitioning active users in a manner that facilitates multi-access without collision. The setting is of a noisy, synchronous, Boolean, multi-access channel where $K$ active users (out of a total of $N$ users) seek to access. A solution to the partition problem places each of the $N$ users in one of $K$ groups (or blocks) such that no two active nodes are in the same block. We consider a simple, but non-trivial and illustrative case of $K=2$ active users and study the number of steps $T$ used to solve the partition problem. By random coding and a suboptimal decoding scheme, we show that for any $T\geq (C_1 +\xi_1)\log N$, where $C_1$ and $\xi_1$ are positive constants (independent of $N$), and $\xi_1$ can be arbitrary small, the partition problem can be solved with error probability $P_e^{(N)} \to 0$, for large $N$. Under the same scheme, we also bound $T$ from the other direction, establishing that, for any $T \leq (C_2 - \xi_2) \log N$, the error probability $P_e^{(N)} \to 1$ for large $N$; again $C_2$ and $\xi_2$ are constants and $\xi_2$ can be arbitrarily small. These bounds on the number of steps are lower than the tight achievable lower-bound in terms of $T \geq (C_g +\xi)\log N$ for group testing (in which all active users are identified, rather than just partitioned). Thus, partitioning may prove to be a more efficient approach for multi-access than group testing.Comment: This paper was submitted in June 2014 to IEEE Transactions on Information Theory, and is under review no

Study of Fundamental Tradeoff Between Deliverable and Private Information in Statistical Inference

My primary objective in this dissertation is to establish a framework under which I launch a systematic study of the fundamental tradeoff between deliverable and private information in statistical inference. My research was partly motivated by arising and prevailing privacy concerns of users in many machine learning problems. In this dissertation, I begin by introducing examples where I am concerned of privacy leakage versus decision utility in statistical inference problems. I then go into further details about what I have achieved in formulating and solving such problems using information theory related metrics in a variety of settings. Both related works and my own results are later summarized in the first chapter. In the second chapter, I introduce a problem of detecting any subgraph using binary codeword queries. Furthermore, I seek and find limits imposed by the privacy of each graph which help me develop an understanding of privacy versus utility problems. In the third chapter, I shift my focus from the original graphical framework to a more general bin allocation problem motivated by addressing concerns on privacy leakage in regard to users’ web surfing patterns with usage of proxy or VPN services. After problem formulation, I deem it necessary to introduce submodular functions as a means of simplifying such problems and finding their solutions. In chapter four, I expand upon the concept introduced in chapter three by allowing uncertainty between hypotheses and find the relationship between distinguishability, privacy leakage and utility in a deterministic bin allocation framework. In chapters five and six, motivated by my previous works, I shift my focus to the problem of tradeoff between utility and leaked information when a randomization, rather than a deterministic mapping, is introduced as a privacy protecviii tion mechanism. In particular, I first seek solutions using a typical and widely accepted Information Bottleneck (IB) approach. I then detail how the original information bottleneck method does not necessarily provide an optimal solution to the proposed problem. I then offer my own novel approach based upon Augmented Lagrange Multipliers (ALM) and Alternating Direction Method of Multipliers (ADMM) with both theoretical justification and empirical evidence , as well as the inherent structures of both the objective function and privacy constraints. My approach has been shown to attain notable improvements than that under the IB framework, with well justified enhancement on efficiency of local convergence. Finally in chapter seven, I present plans to cope with issues of lacking true statistics, by exploiting a set of information theoretical measures which have been shown to be equipped with more benign properties in robustness against limited amount of training data than the regular mutual information measure