Publications by Shrinivas Kudekar

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Convolutional low-density parity-check (LDPC) ensembles, introduced by Felstrom 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 ...

We consider communication over a binary erasure channel with low density parity check codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code ensembles, in the asymptotic li ...

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 u ...

Recently the decay of correlations between bits of low density generator matrix (LDGM) codes have been investigated by using high temperature expansions from statistical physics \cite{KuMa07}. In this work we apply these ideas to a special class of low den ...

We consider communication over a binary input memoryless output symmetric channel with low density generator matrix codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code e ...

Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...

This thesis deals with the asymptotic analysis of coding systems based on sparse graph codes. The goal of this work is to analyze the decoder performance when transmitting over a general binary-input memoryless symmetric-output (BMS) channel. We consider t ...

Convolutional LDPC ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing as a function of the average degree. Several variations on the basic theme have been proposed to date, all of which s ...

Consider a binary linear code of length N, minimum distance d(min), transmission over the binary erasure channel with parameter 0 < epsilon < 1 or the binary symmetric channel with parameter 0 < epsilon < 1/2, and block-MAP decoding. It was shown by Tillic ...

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 ...

Consider a network of nodes where each node has a message to communicate to all other nodes. For this communication problem, we analyze a gossip based protocol where coded messages are exchanged. This problem was studied by Shah et al where a bound to the ...

Consider transmission over a binary additive white gaussian noise channel using a fixed low-density parity check code. We consider the posterior measure over the code bits and the corresponding correlation between two codebits, averaged over the noise real ...

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, ...

We consider communication over the binary erasure and the binary additive white gaussian noise channels using fixed linear block codes and also appropriate ensembles of such codes. We show concentration of the magnetization over the channel realizations an ...

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 distri ...

Shrinivas Kudekar

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Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC

Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel

Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

Decay of Correlations: An Application to Low-Density Parity Check codes

Proof of replica formulas in the high noise regime for communication using LDGM codes

Sharp Bounds for Optimal Decoding of Low Density Parity Check Codes

Statistical physics methods for sparse graph codes

Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC

Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels

Decay of correlations for sparse graph error correcting codes

Algebraic gossip on Arbitrary Networks

Decay of Correlations in Low Density Parity Check Codes: Low Noise Regime

Wave-Like Solutions of General 1-D Spatially Coupled Systems

Concentration of Magnetization for Linear Block Codes

Lower Bounds on the Rate-Distortion Function of Individual LDGM Codes

Sharp Bounds for MAP Decoding of General Irregular LDPC Codes