We propose that coding and decoding in the brain are achieved through digital computation using three principles: relative ordinal coding of inputs, random connections between neurons, and belief voting. Due to randomization and despite the coarseness of the relative codes, we show that these principles are sufficient for coding and decoding sequences with error-free reconstruction. In particular, the number of neurons needed grows linearly with the size of the input repertoire growing exponentially. We illustrate our model by reconstructing sequences with repertoires on the order of a billion items. From this, we derive the Shannon equations for the capacity limit to learn and transfer information in the neural population, which is then generalized to any type of neural network. Following the maximum entropy principle of efficient coding, we show that random connections serve to decorrelate redundant information in incoming signals, creating more compact codes for neurons and therefore, conveying a larger amount of information. Henceforth, despite the unreliability of the relative codes, few neurons become necessary to discriminate the original signal without error. Finally, we discuss the significance of this digital computation model regarding neurobiological findings in the brain and more generally with artificial intelligence algorithms, with a view toward a neural information theory and the design of digital neural networks.

In order to keep trace of information and grow up, the infant brain has to resolve the problem about where old information is located and how to index new ones. We propose that the immature prefrontal cortex (PFC) uses its primary functionality of detecting hierarchical patterns in temporal signals as a second feature to organize the spatial ordering of the cortical networks in the developing brain itself. Our hypothesis is that the PFC detects the hierarchical structure in temporal sequences in the shape of ordinal patterns and uses them to index information hierarchically in different parts of the brain. Henceforth, we propose that this mechanism for detecting ordinal patterns participates also in the hierarchical organization of the brain during development; i.e., the bootstrapping of the connectome. By doing so, it gives the tools to the language-ready brain for manipulating abstract knowledge and for planning temporally ordered information; i.e., the emergence of causality and symbolic thinking. In this position paper, we will review several neural models from the literature that support serial ordering and propose an original one. We will confront then our ideas with evidence from developmental, behavioral, and brain results.

Information-Centric Networking (ICN) is based on a recently proposed family of protocols in which contents are identified through names. ICN decouples the content to be retrieved from the specification of its location. It naturally supports the use of multiple paths; however, with multiple consumers and producers, coordination among the nodes is required to efficiently use the network resources. Network coding (NC) is a promising tool to address this issue. The challenge when using NC with ICN is to be able to get independent coded content in response to multiple parallel interests (i.e., requests) by one or several consumers. In this work, we propose a novel construction called MILIC (Multiple Interests for Linearly Independent Contents) that imposes constraints on how the replies to clients are network coded, intending to get linearly independent contents in response to multiple interests. Several protocol variants, called MICN (MILIC-ICN), built on top of NDN (Named Data Networking), are proposed to integrate these interest constraints and NC of data packets. Numerical analysis and simulations illustrate that MILIC performs well and that the MICN protocols reach close to optimal throughputs on some scenarios. MICN protocols compare favorably to existing protocols and show significant benefits when considering the total number of transmitted packets in the network, also in the case of high link loss rate.

This paper introduces a new formal mathematical problem initially motivated by an application of Network Coding (NC) to Information Centric Networks (ICN). It is of more limited scope but is remotely inspired by the well-known index coding problem. It is presented as follows: "given a vector space, can one construct several subsets of vectors, such that when drawing arbitrarily one vector from each subset, the selected vectors would be always linearly independent?". Answering this question is a step to construct an ICN efficient scheme with NC. We prove that our previously introduced construction is the only possible solution for a large family of constructions. This is an important result by itself. It also implies that any alternate solutions are outside this family and we propose one example.

Information Centric Networking (ICN) is a family of recent protocols based on a paradigm different from traditional IP networks. A natural and well-adapted extension to this type of networks is the use of network coding: this has been exploited in the previously proposed family of NetcodCCN/NetcodNDN protocols, which are capable of reaching network capacity. However, this has been observed with heuristics, and on a few examples of networks. We analyze more formally the properties of several variants of the protocol.

In order to keep trace of information and grow up, the infant brain has to resolve the problem about where old information is located and how to index new ones. We propose that the immature prefrontal cortex (PFC) use its primary functionality of detecting hierarchical patterns in temporal signals as a second purpose to organize the spatial ordering of the cortical networks in the developing brain itself. Our hypothesis is that the PFC detects the hierarchical structure in temporal sequences in the form of ordinal patterns and use them to index information hierarchically in different parts of the brain. Henceforth, we propose that this mechanism for detecting patterns participates in the ordinal organization development of the brain itself; i.e., the bootstrapping of the connectome. By doing so, it gives the tools to the language-ready brain for manipulating abstract knowledge and planning temporally ordered information; i.e., the emergence of symbolic thinking and language. We will review neural models that can support such mechanisms and propose new ones. We will confront then our ideas with evidence from developmental, behavioral and brain results and make some hypotheses, for instance, on the construction of the mirror neuron system, on embodied cognition, and on the capacity of learning-to-learn.

The use of Named Data Networking (NDN) for distributed multi-user applications, e.g. group messaging and file sharing, requires NDN synchronization protocols to maintain the same shared dataset (and its updates) among all nodes. ChronoSync [1], RoundSync [2], and PartialSync [3] are some proposals to address this issue, see [4]. Here we focus on the state-of-the-art protocol RoundSync [2]: we study its core features, that permit participating nodes to detect, propagate, and reconcile all changes. Particular attention is given to the case of multiple changes per round. We then propose an improved variant, iRoundSync, that exchanges fewer messages in the multiple-change case and is more resilient to packet losses. We quantify the performance gain of iRoundSync on a simple topology.

This paper studies the extension of the multiway relay channel (introduced by Gündüz et al.) by adding intra-cluster links. In this model, multiple clusters of users communicate with the help of one relay and the users within a cluster wish to exchange messages among themselves. Restricted encoders are considered; thus, the encoded messages of each user depend only on its own message, not on previously decoded ones. Cut-set bounds and achievable rates are given for the Gaussian case with and without time-sharing between clusters. Depending on the protocol considered, schemes based on random coding or nested lattice coding are proposed. The schemes are compared in terms of exchange capacity, that is the equal rate point in the capacity region of a symmetric multiway relay channel. It is shown that the gap between the cut-set bound and Compress-and-Forward, as well as Amplify-and-Forward, is independent of the transmit power constraints when time-sharing is used.

This paper investigates two classes of relay channels, the Gaussian relay channel and the Gaussian two-way relay channel, when additive noises at the relay and destination(s) are correlated. Lattice codes are used to achieve the rate region for Compress-and-Forward (relay channel) and Compress/Decodeand-Forward (two-way relay channel). Numerical calculations show that there exist particular values of the correlation coefficient such that the gap between the Cut-Set Bound (CSB) and the proposed schemes is minimal.

This paper studies the extension of the multiway relay channel model with restricted encoders (introduced by Gündüz et al.) by adding unit-gain intra-cluster links. In this model, multiple clusters of users communicate with the help of one relay and the users within a cluster wish to exchange messages among themselves. We obtain achievable rates and gaps to the cut-set bound as a function of the number of users and the cluster-to-relay gain g.

This paper analyzes a practical scheme for the binary coded side-information problem based on LDPC codes and trellis quantization. A recently proposed improved decoder is shown to be amenable to numerical density evolution and thus to LDPC code optimization. First results display significant gains compared to off-the-shelf codes, which could be further improved by refined modeling of the system.

Dans ce papier, nous proposons un nouvel algorithme de decodage iteratif pour le probleme de codage de source avec information adjacente compressee. L'information adjacente est compressee par un quantificateur qui genere un index. Plutot que d'utiliser un seul representant pour l'information adjacente (la reconstruction correspondante a l'index), nous allons projeter une solution intermediaire du decodage de la source sur la cellule de Voronoi correspondante a l'index recu. Grâce a cette projection, nous esperons rapprocher l'information adjacente du mot source recherche, accelerant ainsi le decodage iteratif de la source. Des simulations utilisant un code LDPC pour la branche principale et une quantification sur treillis pour l'information adjacente montrent que pour un nombre d'iterations de decodage fixe, notre algorithme permet d'augmenter le nombre de mots correctement decodes.

This paper presents a new iterative decoding algorithm for the source coding with coded side information problem. Side information (SI) is compressed to an index by a many-to-one (quantization) function. Instead of using the reconstruction corresponding to the quantization index as a single representative SI word to aid the main decoder, one can modify it by projecting an intermediate estimate of the source word onto the Voronoi cell associated to the SI index. The hope is that the projection brings the representative SI word closer to the source word, and thus accelerates iterative decoding. Simulations using LDPC syndrome coding in the main branch and trellis-coded quantization in the SI branch show that for a fixed number of decoder iterations, this method indeed increases the number of correctly decoded source words. In fact, the decoding threshold is shifted, which may be attributed to a partial compensation of the suboptimality of the quantizer.

The rate distortion behavior of sparse memoryless sources is studied. These serve as models of sparse signal representations and facilitate the performance analysis of “sparsifying” transforms like the wavelet transform and nonlinear approximation schemes. For strictly sparse binary sources with Hamming distortion, $R(D)$ is shown to be almost linear. For nonstrictly sparse continuous-valued sources, termed compressible, two measures of compressibility are introduced: incomplete moments and geometric mean. The former lead to low- and high-rate upper bounds on mean squared error $D(R)$, while the latter yields lower and upper bounds on source entropy, thereby characterizing asymptotic $R(D)$ behavior. Thus, the notion of compressibility is quantitatively connected with actual lossy compression. These bounding techniques are applied to two source models: Gaussian mixtures and power laws matching the approximately scale-invariant decay of wavelet coefficients. The former are versatile models for sparse data, which in particular allow to bound high-rate compression performance of a scalar mixture compared to a corresponding unmixed transform coding system. Such a comparison is interesting for transforms with known coefficient decay, but unknown coefficient ordering, e.g., when positions of highest-variance coefficients are unknown. The use of these models and results in distributed coding and compressed sensing scenarios are also discussed.

This paper revisits earlier work on the achievable rate-region for the coded side-information problem. For specific source distributions we provide computable extreme rate points. As opposed to previous works, we present short and concise proofs and additional rate points below the time-sharing line of previously known rate points. Our results are based on a formulation as an optimization problem.

This paper studies coding schemes for the q -ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet size q =2 m , m ∈N, thus complementing some recently proposed packet-based schemes requiring large q . First, theoretical optimality of a simple layered scheme is shown; then, a practical coding scheme based on a simple modification of standard binary LDPC decoding is proposed. The decoder is derived from first principles and using a factor-graph representation of a front end that maps q -ary symbols to groups of m bits connected to a binary code. The front end can be processed with a complexity that is linear in m =log 2 q . An extrinsic information transfer chart analysis is carried out and used for code optimization. Finally, it is shown how the same decoder structure can also be applied to a larger class of q -ary channels.

This paper proposes branch-and-prune algorithms for searching prefix-free joint source-channel codebooks with maximal free distance for given codeword lengths. For that purpose, it introduces improved techniques to bound the free distance of variable-length codes.