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Krishna R. Narayanan

Publications and source records attributed to Krishna R. Narayanan.

65 records · Page 4Linked to original sources
arXiv2010

A Rate-Distortion Exponent Approach to Multiple Decoding Attempts for Reed-Solomon Codes

Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides the best performance-versus-complexity trade-off. In this paper, an analysis based on the rate-distortion exponent (RDE) is used to directly minimize the exponential decay rate of the error probability. This enables rigorous bounds on the error probability for finite-length RS codes and leads to modest performance gains. As a byproduct, a numerical method is derived that computes the rate-distortion exponent for independent non-identical sources. Analytical results are given for errors/erasures decoding.

cs.IT↗
arXiv2009

Can Iterative Decoding for Erasure Correlated Sources be Universal?

In this paper, we consider a few iterative decoding schemes for the joint source-channel coding of correlated sources. Specifically, we consider the joint source-channel coding of two erasure correlated sources with transmission over different erasure channels. Our main interest is in determining whether or not various code ensembles can achieve the capacity region universally over varying channel conditions. We consider two ensembles in the class of low-density generator-matrix (LDGM) codes known as Luby-Transform (LT) codes and one ensemble of low-density parity-check (LDPC) codes. We analyze them using density evolution and show that optimized LT codes can achieve the extremal symmetric point of the capacity region. We also show that LT codes are not universal under iterative decoding for this problem because they cannot simultaneously achieve the extremal symmetric point and a corner point of the capacity region. The sub-universality of iterative decoding is characterized by studying the density evolution for LT codes.

cs.IT↗
arXiv2009

A Rate-Distortion Perspective on Multiple Decoding Attempts for Reed-Solomon Codes

Recently, a number of authors have proposed decoding schemes for Reed-Solomon (RS) codes based on multiple trials of a simple RS decoding algorithm. In this paper, we present a rate-distortion (R-D) approach to analyze these multiple-decoding algorithms for RS codes. This approach is first used to understand the asymptotic performance-versus-complexity trade-off of multiple error-and-erasure decoding of RS codes. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the condition for a single error-and-erasure decoding to succeed reduces to a form where the distortion is compared to a fixed threshold. Finding the best set of erasure patterns for multiple decoding trials then turns out to be a covering problem which can be solved asymptotically by rate-distortion theory. Next, this approach is extended to analyze multiple algebraic soft-decision (ASD) decoding of RS codes. Both analytical and numerical computations of the R-D functions for the corresponding distortion measures are discussed. Simulation results show that proposed algorithms using this approach perform better than other algorithms with the same complexity.

cs.IT↗
arXiv2008

Algebraic Soft-Decision Decoding of Reed-Solomon Codes Using Bit-level Soft Information

The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied over erasure channels and the binary symmetric channel. The corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are derived. The multiplicity assignment strategy and the corresponding performance analysis are then generalized to characterize the decoding region of algebraic softdecision decoding over a mixed error and bit-level erasure channel. The bit-level decoding region of the proposed multiplicity assignment strategy is shown to be significantly larger than that of conventional Berlekamp-Massey decoding. As an application, a bit-level generalized minimum distance decoding algorithm is proposed. The proposed decoding compares favorably with many other Reed-Solomon soft-decision decoding algorithms over various channels. Moreover, owing to the simplicity of the proposed bit-level generalized minimum distance decoding, its performance can be tightly bounded using order statistics.

cs.IT↗
arXiv2007

On the Thermodynamic Temperature of a General Distribution

The concept of temperature is one of the key ideas in describing the thermodynamical properties of a physical system. In classical statistical mechanics of ideal gases, the notion of temperature can be described in two different ways, the kinetic temperature and the thermodynamic temperature. For the Boltzmann distribution, the two notions lead to the same result. However, for a general probability density function, while the kinetic temperature has been commonly used, there appears to be no corresponding general definition of thermodynamic temperature. In this paper, we propose such a definition and show that it is connected to the Fisher information associated with the distribution of the momenta.

cond-mat.stat-mech↗
arXiv2007

On the Distortion SNR Exponent of Some Layered Transmission Schemes

We consider the problem of joint source-channel coding for transmitting K samples of a complex Gaussian source over T = bK uses of a block-fading multiple input multiple output (MIMO) channel with M transmit and N receive antennas. We consider the case when we are allowed to code over L blocks. The channel gain is assumed to be constant over a block and channel gains for different blocks are assumed to be independent. The performance measure of interest is the rate of decay of the expected mean squared error with the signal-to-noise ratio (SNR), called the distortion SNR exponent. We first show that using a broadcast strategy of Gunduz and Erkip, but with a different power and rate allocation policy, the optimal distortion SNR exponent can be achieved for bandwidth efficiencies 0 < b < (|N-M|+1)/min(M,N). This is the first time the optimal exponent is characterized for 1/min(M,N) < b < (|N-M |+ 1)/ min(M, N). Also, for b > MNL^2, we show that the broadcast scheme achieves the optimal exponent of MNL. Special cases of this result have been derived for the L=1 case and for M=N=1 by Gunduz and Erkip. We then propose a digital layered transmission scheme that uses both time layering and superposition. This includes many previously known schemes as special cases. The proposed scheme is at least as good as the currently best known schemes for the entire range of bandwidth efficiencies, whereas at least for some M, N, and b, it is strictly better than the currently best known schemes.

cs.IT↗
arXiv2006

Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compare favorably with other popular soft decision decoding methods.

cs.IT↗
arXiv2006

Multilevel Coding for Channels with Non-uniform Inputs and Rateless Transmission over the BSC

We consider coding schemes for channels with non-uniform inputs (NUI), where standard linear block codes can not be applied directly. We show that multilevel coding (MLC) with a set of linear codes and a deterministic mapper can achieve the information rate of the channel with NUI. The mapper, however, does not have to be one-to-one. As an application of the proposed MLC scheme, we present a rateless transmission scheme over the binary symmetric channel (BSC).

cs.IT↗
arXiv2005

Performance Analysis of Algebraic Soft Decoding of Reed-Solomon Codes over Binary Symmetric and Erasure Channels

In this paper, we characterize the decoding region of algebraic soft decoding (ASD) of Reed-Solomon (RS) codes over erasure channels and binary symmetric channel (BSC). Optimal multiplicity assignment strategies (MAS) are investigated and tight bounds are derived to show the ASD can significantly outperform conventional Berlekamp Massey (BM) decoding over these channels for a wide code rate range. The analysis technique can also be extended to other channel models, e.g., RS coded modulation over erasure channels.

cs.IT↗
arXiv2005

Minimal Network Coding for Multicast

We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize the number of packets that undergo network coding. We also propose a decentralized algorithm to construct capacity achieving multicast codes when the processing at some nodes is restricted to routing. The proposed algorithms can be coupled with existing decentralized schemes to achieve minimum cost muticast.

cs.IT↗