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Register a new userDecay of Correlations in Low Density Parity Check Codes: Low Noise Regime
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Added by
Shrinivas Kudekar Mr.
Publication date
2009
fields
Informatics Engineering
and research's language is
English
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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 realizations. We show that for low enough noise variance this average correlation decays exponentially fast with the graph distance between the code bits. One consequence of this result is that for low enough noise variance the GEXIT functions (further averaged over a standard code ensemble) of the belief propagation and optimal decoders are the same.
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We consider the effect of log-likelihood ratio saturation on belief propagation decoder low-density parity-check codes. Saturation is commonly done in practice and is known to have a significant effect on error floor performance. Our focus is on threshold analysis and stability of density evolution. We analyze the decoder for standard low-density parity-check code ensembles and show that belief propagation decoding generally degrades gracefully with saturation. Stability of density evolution is, on the other hand, rather strongly effected by saturation and the asymptotic qualitative effect of saturation is similar to reduction by one of variable node degree. We also show under what conditions the block threshold for the saturated belief propagation corresponds with the bit threshold.
In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively performance of Low-Density-Parity-Check (LDPC) codes decoded iteratively in the so-called error-floor regime. We discuss statistical properties of the numerical instanton-amoeba scheme focusing on detailed analysis and comparison of two regular LDPC codes: Tanners (155, 64, 20) and Margulis (672, 336, 16) codes. In the regime of moderate values of the signal-to-noise ratio we critically compare results of the instanton-amoeba evaluations against the standard Monte-Carlo calculations of the Frame-Error-Rate.
The concept and existence of sphere-bound-achieving and capacity-achieving lattices has been explained on AWGN channels by Forney. LDPC lattices, introduced by Sadeghi, perform very well under iterative decoding algorithm. In this work, we focus on an ensemble of regular LDPC lattices. We produce and investigate an ensemble of LDPC lattices with known properties. It is shown that these lattices are sphere-bound-achieving and capacity-achieving. As byproducts we find the minimum distance, coding gain, kissing number and an upper bound for probability of error for this special ensemble of regular LDPC lattices.
In this paper, two-user Gaussian interference channel(GIC) is revisited with the objective of developing implementable (explicit) channel codes. Specifically, low density parity check (LDPC) codes are adopted for use over these channels, and their benefits are studied. Different scenarios on the level of interference are considered. In particular, for strong interference channel examples with binary phase shift keying (BPSK), it is demonstrated that rates better than those offered by single user codes with time sharing are achievable. Promising results are also observed with quadrature-shift-keying (QPSK). Under general interference a Han-Kobayashi coding based scheme is employed splitting the information into public and private parts, and utilizing appropriate iterative decoders at the receivers. Using QPSK modulation at the two transmitters, it is shown that rate points higher than those achievable by time sharing are obtained.
We study the performance of low-density parity-check (LDPC) codes over finite integer rings, over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The second channel adds to each codeword an error vector of constant Lee weight, where the error vector is picked uniformly at random from the set of vectors of constant Lee weight. It is shown that the marginal conditional distribution of the two channels coincides, in the limit of large blocklengths. The performance of selected LDPC code ensembles is analyzed by means of density evolution and finite-length simulations, with belief propagation decoding and with a low-complexity symbol message passing algorithm.
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