Shrinivas Kudekar

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Convolutional low-density parity-check (LDPC) ensembles, introduced by Felström and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC(More)
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 threshold of the underlying component ensemble. This explains why convolutional LDPC ensembles, originally introduced by(More)
Recently, it was observed that spatially-coupled LDPC code ensembles approach the Shannon capacity for a class of binary-input memoryless symmetric (BMS) channels. The fundamental reason for this was attributed to a threshold saturation phenomena derived in [1]. In particular, it was shown that the belief propagation (BP) threshold of the spatially coupled(More)
We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a one-dimensional real-valued state. This is extended to a proof of the threshold saturation phenomenon for all such models, which includes spatially coupled irregular LDPC codes over the BEC, but also addresses(More)
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 the ensemble to the maximum a-priori threshold of the underlying component ensemble. We report on empirical evidence(More)
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 threshold of the ensemble to the maximum a-posteriori threshold of the underlying component ensemble. This paved the way(More)
We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a 1-D real-valued state. This is extended to a proof of the threshold saturation phenomenon for all such models, which includes spatially coupled irregular low-density parity-check codes over the binary erasure(More)
We consider lossy compression of a binary symmetric source by means of a low-density generator-matrix code. We derive two lower bounds on the rate distortion function which are valid for any low-density generator-matrix code with a given node degree distribution L(x) on the set of generators and for any encoding algorithm. These bounds show that, due to the(More)
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 coupling of individual code ensembles has the effect of increasing the belief propagation threshold of the coupled ensembles(More)
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 optimal (or ideal) decoder based on the posterior measure over the code bits, and its relationship to the sub-optimal(More)