Vojin Senk

Expanding window fountain codes for unequal error protection

A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally.

Generalized ACE Constrained Progressive Edge-Growth LDPC Code Design

In this letter, we propose a generalization of the progressive edge-growth (PEG) algorithm with the aim of designing LDPC code graphs with substantially improved approximated cycle extrinsic message degree (ACE) properties. The proposed realization of generalized PEG algorithm outperforms original PEG algorithm and its subsequent modification proposed by Xiao and Banihashemi.

Expanding Window Fountain Codes for Unequal Error Protection

A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally.

Transactions papers evaluation and design of irregular LDPC codes using ACE spectrum

The construction of finite-length irregular LDPC codes with low error floors is currently an attractive research problem. In particular, for the binary erasure channel (BEC), the problem is to find the elements of selected irregular LDPC code ensembles with the size of their minimum stopping set being maximized. Due to the lack of analytical solutions to this problem, a simple but powerful heuristic design algorithm, the approximate cycle extrinsic message degree (ACE) constrained design algorithm, has recently been proposed. Building upon the ACE metric associated with a cycle in a code graph, we introduce the ACE spectrum of LDPC codes as a useful tool for evaluation of codes from selected irregular LDPC code ensembles. Using the ACE spectrum, we generalize the ACE constrained design algorithm, making it more flexible and efficient. We justify the ACE spectrum approach through examples and simulation results.

ACE Spectrum of LDPC Codes and Generalized ACE Design

The construction of good, finite-length, LDPC codes is currently an attractive research area. Reducing attention to the binary erasure channel (BEC), this problem translates into the problem of finding elements of selected (irregular) LDPC code ensemble with the size of the minimal stopping set being maximized. Faced with the lack of analytical solution to this problem, simple but powerful heuristic design algorithm, an ACE constrained design algorithm, was recently introduced. Building upon the ACE metric associated with every cycle in the code graph, we introduce the ACE spectrum of LDPC code as a useful measure of success in selection of the LDPC code from selected ensemble. Using ACE spectrum, we farther generalize ACE constrained design, making it more flexible and efficient.

On the entropy of couplings

Abstract In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be NP-hard, and their special cases are found to be essentially information-theoretic restatements of well-known computational problems, such as the Subset sum and the 3-Partition . The notion of minimum entropy coupling is introduced and its relevance is demonstrated in information-theoretic, computational, and statistical contexts. Finally, a family of pseudometrics (on the space of discrete probability distributions) defined by these couplings is studied, in particular their relation to the total variation distance, and a new characterization of the conditional entropy is given.

On the hardness of entropy minimization and related problems

We investigate certain optimization problems for Shannon information measures, namely, minimization of joint and conditional entropies H(X, Y), H(X|Y), H(Y|X), and maximization of mutual information I(X; Y), over convex regions. When restricted to the so-called transportation polytopes (sets of distributions with fixed marginals), very simple proofs of NP-hardness are obtained for these problems because in that case they are all equivalent, and their connection to the well-known SUBSET SUM and PARTITION problems is revealed. The computational intractability of the more general problems over arbitrary polytopes is then a simple consequence. Further, a simple class of polytopes is shown over which the above problems are not equivalent and their complexity differs sharply, namely, minimization of H(X, Y) and H(Y|X) is trivial, while minimization of H(X|Y) and maximization of I(X; Y) are strongly NP-hard problems. Finally, two new (pseudo)metrics on the space of discrete probability distributions are introduced, based on the so-called variation of information quantity, and NP-hardness of their computation is shown.

Methods for the Soft-Decision Decoding of MTR Codes in Multiple-Head Magnetic Recording Systems

Two different methods for the soft-decision decoding of the maximum-transition-run (MTR) codes have been considered in this paper. The first one, the maximum a posteriori (MAP) algorithm, is based on the Bayesian algorithm, computing a posteriori log-likelihood ratios (LLR) using MTR codewords. The second one, the soft-decision implementation in Boolean logic circuits has been used to propagate the soft-values through the MTR decoder. The MTR code performs as an inner encoding code, in a simple concatenation of the low-density parity-check (LDPC) and the MTR. The special case of two-track two-head E2PR4 channel model was used, assuming the low level of inter-track interference (ITI) and the AWGN noise presence. The soft-decision decoding results with nearly 1.7dB coding gain, using the MAP algorithm, while nearly 1.9dB, using the second one approach.

On the Optimized Patent-Free LDPC Code Design for Content Distribution Systems

In this paper, we analyze the application of asymptotic and finite-length analysis and design of low-density parity-check (LDPC) codes for the large scale content distribution systems over packet based networks, such as MBMS or DVB-H. We show connections of the classical coding theory performance measure, the bit error rate (BER) performance, and the measure called the overhead factor which is of interest in the content distribution systems. We point out to LDPC codes design methods that can provide an excellent overhead factor performance. Particularly, we are interested in performance limits of the class of patent-free LDPC codes.

Some properties of Rényi entropy over countably infinite alphabets

We study certain properties of Rényi entropy functionals