1,962 research outputs found
Learned Belief-Propagation Decoding with Simple Scaling and SNR Adaptation
We consider the weighted belief-propagation (WBP) decoder recently proposed
by Nachmani et al. where different weights are introduced for each Tanner graph
edge and optimized using machine learning techniques. Our focus is on
simple-scaling models that use the same weights across certain edges to reduce
the storage and computational burden. The main contribution is to show that
simple scaling with few parameters often achieves the same gain as the full
parameterization. Moreover, several training improvements for WBP are proposed.
For example, it is shown that minimizing average binary cross-entropy is
suboptimal in general in terms of bit error rate (BER) and a new "soft-BER"
loss is proposed which can lead to better performance. We also investigate
parameter adapter networks (PANs) that learn the relation between the
signal-to-noise ratio and the WBP parameters. As an example, for the (32,16)
Reed-Muller code with a highly redundant parity-check matrix, training a PAN
with soft-BER loss gives near-maximum-likelihood performance assuming simple
scaling with only three parameters.Comment: 5 pages, 5 figures, submitted to ISIT 201
Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
We introduce the notion of the stopping redundancy hierarchy of a linear
block code as a measure of the trade-off between performance and complexity of
iterative decoding for the binary erasure channel. We derive lower and upper
bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and
Bonferroni-type inequalities, and specialize them for codes with cyclic
parity-check matrices. Based on the observed properties of parity-check
matrices with good stopping redundancy characteristics, we develop a novel
decoding technique, termed automorphism group decoding, that combines iterative
message passing and permutation decoding. We also present bounds on the
smallest number of permutations of an automorphism group decoder needed to
correct any set of erasures up to a prescribed size. Simulation results
demonstrate that for a large number of algebraic codes, the performance of the
new decoding method is close to that of maximum likelihood decoding.Comment: 40 pages, 6 figures, 10 tables, submitted to IEEE Transactions on
Information Theor
On the Decoding Complexity of Cyclic Codes Up to the BCH Bound
The standard algebraic decoding algorithm of cyclic codes up to the
BCH bound is very efficient and practical for relatively small while it
becomes unpractical for large as its computational complexity is .
Aim of this paper is to show how to make this algebraic decoding
computationally more efficient: in the case of binary codes, for example, the
complexity of the syndrome computation drops from to , and
that of the error location from to at most .Comment: accepted for publication in Proceedings ISIT 2011. IEEE copyrigh
Decoding Cyclic Codes up to a New Bound on the Minimum Distance
A new lower bound on the minimum distance of q-ary cyclic codes is proposed.
This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for
some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are
special cases of our bound. For some classes of codes the bound on the minimum
distance is refined. Furthermore, a quadratic-time decoding algorithm up to
this new bound is developed. The determination of the error locations is based
on the Euclidean Algorithm and a modified Chien search. The error evaluation is
done by solving a generalization of Forney's formula
Rewriting Flash Memories by Message Passing
This paper constructs WOM codes that combine rewriting and error correction
for mitigating the reliability and the endurance problems in flash memory. We
consider a rewriting model that is of practical interest to flash applications
where only the second write uses WOM codes. Our WOM code construction is based
on binary erasure quantization with LDGM codes, where the rewriting uses
message passing and has potential to share the efficient hardware
implementations with LDPC codes in practice. We show that the coding scheme
achieves the capacity of the rewriting model. Extensive simulations show that
the rewriting performance of our scheme compares favorably with that of polar
WOM code in the rate region where high rewriting success probability is
desired. We further augment our coding schemes with error correction
capability. By drawing a connection to the conjugate code pairs studied in the
context of quantum error correction, we develop a general framework for
constructing error-correction WOM codes. Under this framework, we give an
explicit construction of WOM codes whose codewords are contained in BCH codes.Comment: Submitted to ISIT 201
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