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This chapter offers an overview of core topics in epilepsy research from a complex systems perspective, starting from single-node studies up to network theory analysis. In its first part, the chapter reviews the advances in EEG biomarkers for epileptic network mapping in both invasive and scalp EEG, including univariate epileptogenic indexes linear connectivity measures within the multivariate autoregressive model, non-linear correlation measures and graph-theoretical properties. In the second part, the chapter covers some of the initial contributions to characterize network dynamics in epilepsy. Particular attention is paid at the seizure prediction problem, using classic dynamical systems approaches as well as the most recent machine-learning prediction algorithms and network-science studies unraveling signatures of the transition from interictal to ictal activity.

Includes supplementary materials for the online appendix. Cognitive-relevant information is processed by different brain areas that cooperate to eventually produce a response. The relationship between local activity and global brain states during such processes, however, remains for the most part unexplored. To address this question, we designed a simple face-recognition task performed in patients with drug-resistant epilepsy and monitored with intracranial electroencephalography (EEG). Based on our observations, we developed a novel analytical framework (named “local–global” framework) to statistically correlate the brain activity in every recorded gray-matter region with the widespread connectivity fluctuations as proxy to identify concurrent local activations and global brain phenomena that may plausibly reflect a common functional network during cognition. The application of the local–global framework to the data from three subjects showed that similar connectivity fluctuations found across patients were mainly coupled to the local activity of brain areas involved in face information processing. In particular, our findings provide preliminary evidence that the reported global measures might be a novel signature of functional brain activity reorganization when a stimulus is processed in a task context regardless of the specific recorded areas. We thank all subjects for their participation in the study. We also thank Rodrigo Quian Quiroga and Hernán G. Rey for sharing some of their code to design the task paradigm. MVV was supported by a fellowship from “la Caixa” Foundation, Spain (ID 100010434, fellowship code LCF/BQ/DE17/11600022). MVV and ATC were supported by the Bial Foundation grant 106/18. GD, ATC and MVV were supported by the project “Clúster Emergent del Cervell Humà” (CECH, ref. 001-P-001682), within the framework of the European Research Development Fund Operational Program of Catalonia 2014–2020. ATC was supported by the Spanish National Research project (ref. PID2020-119072RA-I00/AEI/10.13039/501100011033) funded by the Spanish Ministry of Science, Innovation, and Universities (MCIU). GD was supported by a Spanish National Research project (ref. PID2019-105772GB-I00 MCIU AEI) funded by the Spanish Ministry of Science, Innovation, and Universities (MCIU), State Research Agency (AEI); HBP SGA3 Human Brain Project Specific Grant Agreement 3 (grant agreement no. 945539), funded by the EU H2020 FET Flagship programme; SGR Research Support Group support (ref. 2017 SGR 1545), funded by the Catalan Agency for Management of University and Research Grants (AGAUR); Neurotwin Digital twins for model-driven noninvasive electrical brain stimulation (grant agreement ID: 101017716) funded by the EU H2020 FET Proactive programme; euSNN European School of Network Neuroscience (grant agreement ID: 860563) funded by the EU H2020 MSCA-ITN Innovative Training Networks; Brain-Connects: Brain Connectivity during Stroke Recovery and Rehabilitation (ID 201725.33) funded by the Fundacio La Marato TV3; Corticity, FLAG-ERA JTC 2017 (ref. PCI2018-092891) funded by the Spanish Ministry of Science, Innovation and Universities (MCIU), State Research Agency (AEI). This research was also supported by “la Caixa” Foundation (CaixaImpulse Validate Program, project ref. CI20-00195).

The brain is hierarchically organized to process sensory signals. But, to what extent do functional connections within and across areas shape this hierarchical order? We addressed this problem in the thalamocortical network, while monkeys judged the presence or absence of a vibrotactile stimulus. We quantified the variability and a directed connectivity measure in simultaneously recorded neurons sharing the same cutaneous receptive field from the somatosensory thalamus (VPL) and areas 3b and 1 from the somatosensory cortex. During the stimulus presence, neuronal variability increased along the network VPL-3b-1. Furthermore, VPL and area 3b display fast dynamics with rapid feedforward interactions. In contrast, area 1 shows slower timescales with persistent intra-area interactions. Our results suggest that the lower variability of VPL and area 3b facilitates feedforward thalamocortical communication, while the higher variability of area 1 supports intra-cortical interactions during sensory processing. These results provide evidence of a hierarchical order along the thalamocortical network.

Neuroimaging techniques are now widely used to study human cognition. The functional associations between brain areas have become a standard proxy to describe how cognitive processes are distributed across the brain network. Among the many analysis tools available, dynamic models of brain activity have been developed to overcome the limitations of original connectivity measures such as functional connectivity. This goes in line with the many efforts devoted to the assessment of directional interactions between brain areas from the observed neuroimaging activity. This opinion article provides an overview of our model-based whole-brain effective connectivity to analyze fMRI data, while discussing the pros and cons of our approach with respect to other established approaches. Our framework relies on the multivariate Ornstein-Uhlenbeck (MOU) process and is thus referred to as MOU-EC. Once tuned, the model provides a directed connectivity estimate that reflects the dynamical state of BOLD activity, which can be used to explore cognition. We illustrate this approach using two applications on task-evoked fMRI data. First, as a connectivity measure, MOU-EC can be used to extract biomarkers for task-specific brain coordination, understood as the patterns of areas exchanging information. The multivariate nature of connectivity measures raises several challenges for whole-brain analysis, for which machine-learning tools present some advantages over statistical testing. Second, we show how to interpret changes in MOU-EC connections in a collective and model-based manner, bridging with network analysis. Our framework provides a comprehensive set of tools that open exciting perspectives to study distributed cognition, as well as neuropathologies., Author Summary Brain connectivity measures have been increasingly used to study cognition and neuropathologies with neuroimaging data. Many methods have been developed with particular objectives, in particular predictability to obtain biomarkers (i.e., which brain regions exhibit changes in their interactions across conditions) and interpretability (relating the connectivity measures back to the biology). In this article we present our framework for whole-brain effective connectivity that aims to find the equilibrium between these two desired properties, relying on a dynamic model that can be fitted to fMRI time series. Meanwhile, we compare it with previous work. Concretely, we show how machine learning can be used to extract biomarkers and how network-oriented analysis can be used to interpret the model estimates in terms of brain dynamics.

Movement-related theta oscillations in rodent hippocampus coordinate forward sweeps of location-specific neural activity that could be used to evaluate spatial trajectories online. This raises the possibility that increases in human hippocampal theta power accompany the evaluation of upcoming spatial choices. To test this hypothesis, we measured hippocampal oscillations during a spatial planning task that closely resembles a perceptual decision-making paradigm. In this task, female and male participants searched visually for the shortest path between a start and goal location in novel mazes that contained multiple choice points, and were subsequently asked to make a spatial decision at one of those choice points. During the search/planning period, we observed ~3-6 Hz hippocampal theta power increases that were negatively correlated with subsequent decision speed, where decision speed correlated with choice accuracy. Notably, hippocampal theta power increases were preferentially induced by planning in mazes containing a sequence of choices that were initially straightforward and subsequently ambiguous. These results implicate the hippocampal theta rhythm in the searches of deep decision trees, with a particular bottleneck form.

The direction of functional information flow in the sensory thalamocortical circuit may play a role in stimulus perception, but, surprisingly, this process is poorly understood. We addressed this problem by evaluating a directional information measure between simultaneously recorded neurons from somatosensory thalamus (ventral posterolateral nucleus, VPL) and somatosensory cortex (S1) sharing the same cutaneous receptive field while monkeys judged the presence or absence of a tactile stimulus. During stimulus presence, feed-forward information (VPL → S1) increased as a function of the stimulus amplitude, while pure feed-back information (S1 → VPL) was unaffected. In parallel, zero-lag interaction emerged with increasing stimulus amplitude, reflecting externally driven thalamocortical synchronization during stimulus processing. Furthermore, VPL → S1 information decreased during error trials. Also, VPL → S1 and zero-lag interaction decreased when monkeys were not required to report the stimulus presence. These findings provide evidence that both the direction of information flow and the instant synchronization in the sensory thalamocortical circuit play a role in stimulus perception. This work was supported by Dirección General de Asuntos del Personal Académico de la Universidad Nacional Autónoma de México Grants PAPIIT- IN202716 and PAPIIT-IN210819, Consejo Nacional de Ciencia y Tecnología Grant 240892 (to R.R.), Spanish Research Project PSI2016-75688-P [Agencia Estatal de Investigación/Fondo Europeo de Desarrollo Regional (AEI/FEDER), European Union] (to G.D.), by the European Union’s Horizon 2020 Research and Innovation Programme under Grants 720270 [Human Brain Project Specific Grant Agreement 1 (HBP SGA1)] and 785907 (HBP SGA2) (to G.D.), and by the Catalan Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) Programme 2017 Suport als Grups de Recerca (SGR) 1545 (to G.D.). Y.V. was supported by a Pew Latin American Fellowship and a Charles H. Revson Biomedical Science Fellowship.

We report a patient presenting drug-resistant, non-dominant temporal lobe epilepsy with ictal spitting and prosopometamorphopsia, both extremely rare semiologies. Second-phase pre-surgical monitoring was performed using SEEG due to lesion-negative imaging and the rare semiology. The seizure onset zone was delimited to the right anterior hippocampus and the temporobasal cortex, with the propagation zone within the entorhinal cortex. Interestingly, direct electrical stimulation to the entorhinal cortex, which was reproduced in a number of trials, evoked spitting without leading to seizures or post-discharges. After the resection of the epileptogenic zone, the patient remained seizure-free without AEDs for a follow-up period of five years (Engel Class 1a). The neuropathology revealed a focal cortical dysplasia type FCD-Ia. Spectral analysis of intracranial ictal EEG (iEEG) data suggested a possible role of the basal temporal and entorhinal cortex as a necessary node in ictal spitting. [Published with video sequences on www.epilepticdisorders.com].

Cardiac arrhythmias are a frequent complication related to seizures [1]. Most are benign although some, such as high-grade atrioventricular block, asystole, atrial fibrillation (AF), and ventricular fibrillation are potentially harmful. Indeed, several studies suggest that cardiac dysfunction may be the primary underlying cause of sudden unexpected death in epilepsy (SUDEP). Post-ictal atrial fibrillation (PIAF) is a very rare cardiac arrhythmia associated with seizures, and its relevance is currently unknown. AF characteristics include: 1) irregular R-R intervals, 2) absence of distinct repeating P waves, and 3) erratic atrial activity [2]. Atrial flutter is differentiated from AF because of the characteristic “saw tooth” waves on the ECG instead of the chaotic atrial rhythm of the AF. In fact, there are only four reported cases of PIAF diagnosed during video-EEG monitoring (VEM) [1], [3], [4]. We report a case of PIAF identified during long-term VEM, with recurrent episodes corroborated by Holter-ECG monitoring

The spatial mapping of localized events in brain activity critically depends on the correct identification of the pattern signatures associated with those events. For instance, in the context of epilepsy research, a number of different electrophysiological patterns have been associated with epileptogenic activity. Motivated by the need to define automated seizure focus detectors, we propose a novel data-driven algorithm for the spatial identification of localized events that is based on the following rationale: the distribution of emerging oscillations during confined events across all recording sites is highly non-uniform and can be mapped using a spatial entropy function. By applying this principle to EEG recording obtained from 67 distinct seizure epochs, our method successfully identified the seizure focus on a group of ten drug-resistant temporal lobe epilepsy patients (average sensitivity: 0.94, average specificity: 0.90) together with its characteristic electrophysiological pattern signature. Cross-validation of the method outputs with postresective information revealed the consistency of our findings in long follow-up seizure-free patients. Overall, our methodology provides a reliable computational procedure that might be used as in both experimental and clinical domains to identify the neural populations undergoing an emerging functional or pathological transition.Conflict of interestsThe authors declare no competing financial interests.

Atypical antipsychotic drugs (APDs) used to treat positive and negative symptoms in schizophrenia block serotonin receptors 5-HT

Neuroimaging techniques are increasingly used to study brain cognition in humans. Beyond their individual activation, the functional associations between brain areas have become a standard proxy to describe how information is distributed across the brain network. Among the many analysis tools available, dynamic models of brain activity have been developed to overcome the limitations of original connectivity measures such as functional connectivity. In particular, much effort has been devoted to the assessment of directional interactions between brain areas from their observed activity. This paper summarizes our recent approach to analyze fMRI data based on our whole-brain effective connectivity referred to as MOU-EC, while discussing the pros and cons of its underlying assumptions with respect to other established approaches. Once tuned, the model provides a connectivity measure that reflects the dynamical state of BOLD activity obtained using fMRI, which can be used to explore the brain cognition. We focus on two important applications. First, as a connectivity measure, MOU-EC can be used to extract biomarkers for task-specific brain coordination, understood as the patterns of areas exchanging information. The multivariate nature of connectivity measures raises several challenges for whole-brain analysis, for which machine-learning tools presents some advantages over statistical testing. Second, we show how to interpret changes in MOU-EC connections in a collective and model-based manner, bridging with network analysis. To illustrate our framework, we use a dataset where subjects were recorded in two conditions, watching a movie and a black screen (referred to as rest). Our framework provides a comprehensive set of tools that open exciting perspectives for the study of distributed cognition, as well as neuropathologies.

Atypical antipsychotic drugs (APDs) used to treat positive and negative symptoms in schizophrenia block serotonin receptors 5-HT2AR and dopamine receptors D2R and stimulate 5-HT1AR directly or indirectly. However, the exact cellular mechanisms mediating their therapeutic actions remain unresolved. We recorded neural activity in the prefrontal cortex (PFC) and hippocampus (HPC) of freely-moving mice before and after acute administration of 5-HT1AR, 5-HT2AR and D2R selective agonists and antagonists and atypical APD risperidone. We then investigated the contribution of the three receptors to the actions of risperidone on brain activity via statistical modeling and pharmacological reversal (risperidone + 5-HT1AR antagonist WAY-100635, risperidone + 5-HT2A/2CR agonist DOI, risperidone + D2R agonist quinpirole). Risperidone, 5-HT1AR agonism with 8-OH-DPAT, 5-HT2AR antagonism with M100907, and D2R antagonism with haloperidol reduced locomotor activity of mice that correlated with a suppression of neural spiking, power of theta and gamma oscillations in PFC and HPC, and reduction of PFC-HPC theta phase synchronization. By contrast, activation of 5-HT2AR with DOI enhanced high-gamma oscillations in PFC and PFC-HPC high gamma functional connectivity, likely related to its hallucinogenic effects. Together, power changes, regression modeling and pharmacological reversals suggest an important role of 5-HT1AR agonism and 5-HT2AR antagonism in risperidone-induced alterations of delta, beta and gamma oscillations, while D2R antagonism may contribute to risperidone-mediated changes in delta oscillations. This study provides novel insight into the neural mechanisms for widely prescribed psychiatric medication targeting the serotonin and dopamine systems in two regions involved in the pathophysiology of schizophrenia. This work was supported by the Brain and Behavior Research Foundation (NARSAD Young Investigator Award 23014), SAF2013-49129-C2-2-R and SAF2016-80726-R (AEI / FEDER, UE) by the Spanish Ministry of Economy and Competitiveness (MINECO; to MVP). M.V. Puig is a Ramon y Cajal Investigator (RyC-2012-10042), M. Alemany a FPI predoctoral fellow (BES-2014-070429) from MINECO, and C. Delgado a FI predoctoral fellow (2018FI_B_00112)from the Generalitat de Catalunya (AGAUR)

Two alternative exact characterizations of the minimum error probability of Bayesian $M$ -ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al. ; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdu-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data- driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient. This work was funded by the EU via H2020 Marie SklodowskaCurie project COSMOS, grant no. 642563 (M.G.L., I.M., Z.L., and R.G.A). R.G.A. and C.G.B.M. acknowledge funding from the Spanish Ministry of Econ- omy and Competitiveness (Grant FIS2014-54177-R) and the CERCA Programme of the Generalitat de Catalunya. C.G.B.M. acknowledges the support by the Spanish Ministry of Economy and Competitiveness under the Maria de Maeztu Units of Excellence Programme (MDM-2015-0502). Z.L. acknowledges funding from the Slovenian Re- search Agency via program Complex Networks P1-0383 and project J5-8236.

Epileptic seizures are known to follow specific changes in brain dynamics. While some algorithms can nowadays robustly detect these changes, a clear understanding of the mechanism by which these alterations occur and generate seizures is still lacking. Here, we provide crossvalidated evidence that such changes are initiated by an alteration of physiological network state dynamics. Specifically, our analysis of long intracranial electroencephalography (iEEG) recordings from a group of 10 patients identifies a critical phase of a few hours in which time-dependent network states become less variable ("degenerate"), and this phase is followed by a global functional connectivity reduction before seizure onset. This critical phase is characterized by an abnormal occurrence of highly correlated network instances and is shown to be particularly associated with the activity of the resected regions in patients with validated postsurgical outcome. Our approach characterizes preseizure network dynamics as a cascade of 2 sequential events providing new insights into seizure prediction and control., Author summary Understanding and predicting the generation of seizures in epileptic patients is fundamental to improving the quality of life of the more than 1% of the world population who suffer from this illness. Although seizure prediction has made important advances over the last decade, there is a lack of understanding of the common principles explaining the transitions that brain activity undergoes before a seizure. In this study, we characterized this transition from a novel perspective grounded on the mathematical analysis of continuous recordings inside the brains of epileptic patients over several days using depth electrodes. We show that the critical period preceding a seizure unfolds in a two-stage process. It begins with a phase of several hours when the highly correlated activity in the preceding days is altered, and it proceeds with a second, shorter phase of decrease in global connectivity before the seizure onset. Furthermore, our analysis reveals that these global alterations are more locally manifested in areas that are selected for surgical treatment. Our study suggests that preseizure activity might follow global stereotyped dynamics that could be targeted and modulated to prevent epileptic seizures.

Cognitive processing requires the ability to flexibly integrate and process information across large brain networks. How do brain networks dynamically reorganize to allow broad communication between many different brain regions in order to integrate information? We record neural activity from 12 epileptic patients using intracranial EEG while performing three cognitive tasks. We assess how the functional connectivity between different brain areas changes to facilitate communication across them. At the topological level, this facilitation is characterized by measures of integration and segregation. Across all patients, we found significant increases in integration and decreases in segregation during cognitive processing, especially in the gamma band (50–90 Hz). We also found higher levels of global synchronization and functional connectivity during task execution, again particularly in the gamma band. More importantly, functional connectivity modulations were not caused by changes in the level of the underlying oscillations. Instead, these modulations were caused by a rearrangement of the mutual synchronization between the different nodes as proposed by the “Communication Through Coherence” Theory. The authors would like to thank all patients for their participation and the IMIM-Hospital del Mar Epilepsy Unit staff for their technical assistance in collecting the data. This work was supported by Gustavo Deco's ERC Advanced Grant: DYSTRUCTURE (n. 295129), from the European Union's Horizon 2020 research and innovation programme under grant agreement No. (HBP SGA1) and by the Spanish Research Project PSI2013-42091-P. M.L.K. is supported by the ERC Consolidator Grant CAREGIVING (n. 615539) and the Center for Music in the Brain, funded by the Danish National Research Foundation (DNRF117).

Theserotonergic system plays a crucial role in cognition and is a target of many psychiatric treatments. In particular, serotonin 5-HT1A receptors (5-HT1AR) in the prefrontal cortex and hippocampus play key roles in learning, memory, behavioral flexibility, and response inhibition. Here, we investigated how 5-HT1A receptors influence neural network dynamics in the prefrontal cortex and hippocampus and prefronto-hippocampal functional connectivity in alert mice. We found that pharmacological stimulation of 5-HT1AR with 8-OH-DPAT markedly reduces theta, beta, and high gamma oscillations in both areas and weakens prefronto-hippocampal phase synchronization at theta and beta frequencies. Pharmacological inhibition of 5-HT1A receptors with WAY-100635 reduces theta and high gamma oscillatory activity but increases beta and delta oscillations. It also weakens prefronto-hippocampal phase synchronization at theta frequencies. These results reveal that prefronto-hippocampal neurodynamics are highly sensitive to 5-HT1A manipulation and may be relevant for understanding the actions of psychiatric medication targeting the serotonergic system.

We investigated whether it is possible to study the network dynamics and the anatomical regions involved in the earliest moments of picture naming by using invasive electroencephalogram (EEG) traces to predict naming errors. Four right-handed participants with focal epilepsy explored with extensive stereotactic implant montages that recorded temporal, parietal and occipital regions -in two patients of both hemispheres-named a total of 228 black and white pictures in three different sessions recorded in different days. The subjects made errors that involved anomia and semantic dysphasia, which related to word frequency and not to visual complexity. Using different modalities of spectrum analysis and classification with a support vector machine (SVM) we could predict errors with rates that ranged from slightly above chance level to 100%, even in the preconscious phase, i.e., 100 msec after stimulus presentation. The highest rates were obtained using the gamma bands of all contact spectra without averaging, which implies a fine modulation of the neuronal activity at a network level. Despite no subset of nodes could match the whole set, rates close to the best prediction scores were obtained through the spectra of the temporal-parietal and temporal-occipital junction along with the temporal pole and hippocampus. When both hemispheres were explored nodes from the left side dominated in the best subsets. We argue that posterior temporal regions, especially of the dominant side, are involved very early, even in the preconscious phase (100 msec), in language production.

A source-channel coding scheme in which source messages are assigned to two classes and encoded using a channel code that depends on the class index is studied. A low-complexity implementation with two quasi-cyclic LDPC codes with belief-propagation decoding achieves a better frame error rate than optimized separate coding. The coding gain obtained by simulation is consistent with the theoretical gain.

Specifically, during the passive stimulation task there is an abrupt decrease in the number of causal correlations after the first stimulation, which is shown to be independent of the spike-train variability of each area. Conclusions Neuronal causal correlation paths that are specific to the discriminations task are ubiquitous, bidirectional and remain approximately constant along the task in both sensory and motor areas. These findings are robust to the stimulation pair under study and the spike-train variability of each area.

We study a source-channel coding scheme in which source messages are assigned to classes and encoded using a channel code that depends on the class index. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding as the number of classes increases. The performance of this scheme is studied by means of random-coding bounds and validated by simulation of a low-complexity implementation using existing source and channel codes. © 2014 IEEE.

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight., Comment: Submitted to IEEE Transactions on Information Theory

Neural correlations during a cognitive task are central to study brain information processing and computation. However, they have been poorly analyzed due to the difficulty of recording simultaneous single neurons during task performance. In the present work, we quantified neural directional correlations using spike trains that were simultaneously recorded in sensory, premotor, and motor cortical areas of two monkeys during a somatosensory discrimination task. Upon modeling spike trains as binary time series, we used a nonparametric Bayesian method to estimate pairwise directional correlations between many pairs of neurons throughout different stages of the task, namely, perception, working memory, decision making, and motor report. We find that solving the task involves feedforward and feedback correlation paths linking sensory and motor areas during certain task intervals. Specifically, information is communicated by task-driven neural correlations that are significantly delayed across secondary somatosensory cortex, premotor, and motor areas when decision making takes place. Crucially, when sensory comparison is no longer requested for task performance, a major proportion of directional correlations consistently vanish across all cortical areas., Comment: Article and Supplementary Information

Based on the hypothesis-testing method, we derive lower bounds on the average error probability of finite-length joint source-channel coding. The extension of the meta-converse bound of channel coding to joint source-channel coding depends on the codebook and the decoding rule and thus, it is a priori computationally challenging. Weaker versions of this general bound recover known converses in the literature and provide computationally feasible expressions.

We derive a random-coding upper bound on the average probability of error of joint source-channel coding that recovers Csiszar's error exponent when used with product distributions over the channel inputs. Our proof technique for the error probability analysis employs a code construction for which source messages are assigned to subsets and codewords are generated with a distribution that depends on the subset.

This paper presents a random-coding upper bound on the average error probability of joint source-channel coding that attains Csiszar's error exponent. The bound is based on a code construction for which source messages are assigned to disjoint subsets (classes), and codewords are generated according to a distribution that depends on the class of the source message. For a single class, the bound recovers Gallager's exponent; identifying the classes with source type classes, it recovers Csiszar's exponent. Moreover, it is shown that as a two appropriately designed classes are sufficient to attain Csiszar's exponent.

Random-coding exact characterizations and bounds to the error probability of joint source-channel coding are presented. In particular, upper bounds using maximum-a-posteriori and threshold decoding are derived as well as a lower bound motivated by Verdu-Han's lemma.

We study iterative multiuser joint decoding in large randomly spread code division multiple access systems under the assumption that the number of users accessing the channel is unknown by the receiver. In particular, we focus on the factor graph representation and iterative algorithms based on belief propagation. We study a suboptimal iterative scheme that jointly detects the encoded data and the users' activity. By using the replica method from statistical physics, we analyze the performance of the iterative detector. Using density evolution, we provide a fixed-point equation of the overall iterative system where the probability messages depend on the users' activity. Finally, when the scaling between the log number of users and the block length is below a threshold, we show that in the large-system limit a simple structure on the users' codes yields a multiuser efficiency fixed-point equation that is equivalent to the case of all-active users with a system load scaled by the activity rate.

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service (specified by error probability)., Comment: to appear in IEEE Transactions on Information Theory

Comunicació presentada al IEEE International Symposium on Information Theory (ISIT '08), celebrat a Toronto (Ontario, Canadà) els dies 6, 7, 8, 9, 10 i 11 de juliol de 2008, organitzat per l'Institute of Electrical and Electronics Engineers (IEEE). We study the minimum mean square error (MMSE) and the multiuser efficiency η of large dynamic multiple access communication systems in which optimal multiuser detection is performed at the receiver as the number and the identities of active users is allowed to change at each transmission time. The system dynamics are ruled by a Markov model describing the evolution of the channel occupancy and a large-system analysis is performed when the number of observations grow large. Starting on the equivalent scalar channel and the fixed-point equation tying multiuser efficiency and MMSE, we extend it to the case of a dynamic channel, and derive lower and upper bounds for the MMSE (and, thus, for η as well) holding true in the limit of large signal–to–noise ratios and increasingly large observation time T. This work was supported by the Spanish Ministry of Education and Science/nunder Project TEC2006- 01428/TCM, and by the STREP project No. IST-/n026905 (MASCOT) within the 6th framework program of the European/nCommission.

We present a study of large multiple-access communication systems in which multiuser detection is performed without knowledge of the number of interferers. When the number of users increases without bound, optimum detectors can be analyzed asymptotically. A statistical physics approach based on spin glass theory provides analytical tools to deal with large systems in which the performance parameters to be analyzed (error probabilities, etc) are self-averaging in the limit. Of particular interest is the replica method that is used as a key technique to compute the free-energy function and the macroscopic parameters that determine the multiuser efficiency and the bit error probability in the large system limit.

Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required sources. One of the main theoretical motivations for random network codes stems from the lower bound on the probability of successful decoding reported by Ho et. al. (2003). This result demonstrates that all sinks in a linearly solvable network can successfully decode all sources provided that the random code field size is large enough. This paper develops a new bound on the probability of successful decoding., Comment: 5 pages, 4 figures. Submitted to 2007 IEEE International Symposium on Information Theory

This paper studies an almost-lossless source-channel coding scheme in which source messages are assigned to different classes and encoded with a channel code that depends on the class index. The code performance is analyzed by means of random-coding error exponents and validated by simulation of a low-complexity implementation using existing source and channel codes. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding when the number of classes increases., Published in the IEEE Transactions on Information Theory