In this paper, we present structured message passing (SMP), a unifying framework for approximate inference algorithms that take advantage of structured representations such as algebraic decision diagrams and sparse hash tables. These representations can yield significant time and space savings over the conventional tabular representation when the message has several identical values (context-sp...

Belief propagation (BP) was only supposed to work for tree-like networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs. We show that BP can only converge to a stationary point of an approximate free energy, known as the...

• low density parity check (LDPC) codes are error correction codes • represented by two probability distributions λ and ρ • desired properties: – high code rate r ∈ R+ → fraction of redundancy present in the code – high noise threshold g ∈ R+ → the largest noise up to which the original code can be reconstructed from its noisy version without any loss of information • LDPC codes can be decoded ...

We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) on the conventional factor graph is equivariant to automorphisms and therefore prevents gains by AED. However, applying small modifications matrix at receiver side, we can break symmetry without changing code transmitter. This way, leverage a gain in error-correct...

This letter describes a practical Slepian-Wolf source coding scheme based on Low Density Parity Check (LDPC) codes. It considers the realistic setup where parameters of statistical model between and side information are unknown. A novel Self-Corrected Belief-Propagation (SC-BP) algorithm is proposed in order to make robust incorrect by introducing some memory inside LDPC decoder. Two Dimensiona...

We study the behavior of belief-propagation (BP) algorithm affected by erroneous data exchange in a wireless sensor network (WSN). The WSN conducts distributed multidimensional hypothesis test over binary random variables. joint statistical observations is modeled Markov field whose parameters are used to build BP messages exchanged between sensing nodes. Through linearization message-update ru...

We consider the problem of belief propagation in a network of communicating agents, modeled in the recently introduced Belief Revision Game (BRG) framework. In this setting, each agent expresses her belief through a propositional formula and revises her own belief at each step by considering the beliefs of her acquaintances, using belief change tools. In this paper, we investigate the extent to...

– We employ two different methods, based on belief propagation and TAP, for decoding corrupted messages encoded by employing Sourlas’s method, where the code word comprises products of K bits selected randomly from the original message. We show that the equations obtained by the two approaches are similar and provide the same solution as the one obtained by the replica approach in some cases (K...

Consider the inference problem of undirected graphical models[8, 9]. When the graph is tree, the Belief Propagation (BP) algorithm (J.Pearl[11]) is an efficient algorithm and the exact inference is computed. However, when the graph is “loopy,” and the loops are big, the exact inference becomes intractable. Besides sampling methods, such as MCMC, tractable approximate inference gives us one prac...

This paper is motivated by two applications, namely i) generalizations of cuckoo hashing,a computationally simple approach to assigning keys to objects, and ii) load balancing incontent distribution networks, where one is interested in determining the impact of contentreplication on performance. These two problems admit a common abstraction: in bothscenarios, performance is char...