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We consider communication over memoryless channels using low-density parity-check code ensembles above the iterative (belief propagation) threshold. What is the computational complexity of decoding (i.e., of reconstructing all the typical…
There is a fundamental relationship between belief propagation and maximum a posteriori decoding. A decoding algorithm, which we call the Maxwell decoder, is introduced and provides a constructive description of this relationship. Both, the…
We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a-priori…
We consider spatially coupled code ensembles. A particular instance are convolutional LDPC ensembles. It was recently shown that, for transmission over the memoryless binary erasure channel, this coupling increases the belief propagation…
We consider transmission of two independent and separately encoded sources over a two-user binary-input Gaussian multiple-access channel. The channel gains are assumed to be unknown at the transmitter and the goal is to design an…
Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach capacity, as…
The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of…
We show that Reed-Muller codes achieve capacity under maximum a posteriori bit decoding for transmission over the binary erasure channel for all rates $0 < R < 1$. The proof is generic and applies to other codes with sufficient amount of…
The subject of this paper is transmission over a general class of binary-input memoryless symmetric channels using error correcting codes based on sparse graphs, namely low-density generator-matrix and low-density parity-check codes. The…
We consider spatially coupled code ensembles. A particular instance are convolutional LDPC ensembles. It was recently shown that, for transmission over the binary erasure channel, this coupling increases the belief propagation threshold of…
We consider spatially coupled code ensembles over a multiple access channel. Convolutional LDPC ensembles are one instance of spatially coupled codes. It was shown recently that, for transmission over the binary erasure channel, this…
Over binary input channels, uniform distribution is a universal prior, in the sense that it allows to maximize the worst case mutual information over all binary input channels, ensuring at least 94.2% of the capacity. In this paper, we…
We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
The generalized Poor-Verdu error lower bound established in [1] for multihypothesis testing is studied in the classical channel coding context. It is proved that for any sequence of block codes sent over the memoryless binary symmetric…
The posterior matching scheme, for feedback encoding of a message point lying on the unit interval over memoryless channels, maximizes mutual information for an arbitrary number of channel uses. However, it in general does not always…
We consider the discrete memoryless degraded broadcast channels with feedback. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this…
Belief propagation is a powerful tool in statistical physics, machine learning, and modern coding theory. As a decoding method, it is ubiquitous in classical error correction and has also been applied to stabilizer-based quantum error…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
A novel deep learning method for improving the belief propagation algorithm is proposed. The method generalizes the standard belief propagation algorithm by assigning weights to the edges of the Tanner graph. These edges are then trained…
The question whether RM codes are capacity-achieving is a long-standing open problem in coding theory that was recently answered in the affirmative for transmission over erasure channels [1], [2]. Remarkably, the proof does not rely on…