25 research outputs found
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.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on
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Pruning Neural Belief Propagation Decoders
We consider near maximum-likelihood (ML) decoding of short linear block codes
based on neural belief propagation (BP) decoding recently introduced by
Nachmani et al.. While this method significantly outperforms conventional BP
decoding, the underlying parity-check matrix may still limit the overall
performance. In this paper, we introduce a method to tailor an overcomplete
parity-check matrix to (neural) BP decoding using machine learning. We consider
the weights in the Tanner graph as an indication of the importance of the
connected check nodes (CNs) to decoding and use them to prune unimportant CNs.
As the pruning is not tied over iterations, the final decoder uses a different
parity-check matrix in each iteration. For Reed-Muller and short low-density
parity-check codes, we achieve performance within 0.27 dB and 1.5 dB of the ML
performance while reducing the complexity of the decoder
Iterative Decoding on Multiple Tanner Graphs Using Random Edge Local Complementation
In this paper, we propose to enhance the performance of the sum-product
algorithm (SPA) by interleaving SPA iterations with a random local graph update
rule. This rule is known as edge local complementation (ELC), and has the
effect of modifying the Tanner graph while preserving the code. We have
previously shown how the ELC operation can be used to implement an iterative
permutation group decoder (SPA-PD)--one of the most successful iterative
soft-decision decoding strategies at small blocklengths. In this work, we
exploit the fact that ELC can also give structurally distinct parity-check
matrices for the same code. Our aim is to describe a simple iterative decoder,
running SPA-PD on distinct structures, based entirely on random usage of the
ELC operation. This is called SPA-ELC, and we focus on small blocklength codes
with strong algebraic structure. In particular, we look at the extended Golay
code and two extended quadratic residue codes. Both error rate performance and
average decoding complexity, measured by the average total number of messages
required in the decoding, significantly outperform those of the standard SPA,
and compares well with SPA-PD. However, in contrast to SPA-PD, which requires a
global action on the Tanner graph, we obtain a performance improvement via
local action alone. Such localized algorithms are of mathematical interest in
their own right, but are also suited to parallel/distributed realizations.Comment: 5 pages, to appear in proc. IEEE ISIT, June 200
A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes
In this paper, we study the impact of locality on the decoding of binary
cyclic codes under two approaches, namely ordered statistics decoding (OSD) and
trellis decoding. Given a binary cyclic code having locality or availability,
we suitably modify the OSD to obtain gains in terms of the Signal-To-Noise
ratio, for a given reliability and essentially the same level of decoder
complexity. With regard to trellis decoding, we show that careful introduction
of locality results in the creation of cyclic subcodes having lower maximum
state complexity. We also present a simple upper-bounding technique on the
state complexity profile, based on the zeros of the code. Finally, it is shown
how the decoding speed can be significantly increased in the presence of
locality, in the moderate-to-high SNR regime, by making use of a quick-look
decoder that often returns the ML codeword.Comment: Extended version of a paper submitted to ISIT 201
Decoding Reed-Muller Codes Using Minimum- Weight Parity Checks
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve near-ML performance in practice. The main idea is to apply iterative decoding to a highly-redundant parity-check (PC) matrix that contains only the minimum-weight dual codewords as rows. As examples, we consider the peeling decoder for the binary erasure channel, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gaussian noise channel, and bit-flipping and BP decoding for the binary symmetric channel. For short block lengths, it is shown that near-ML performance can indeed be achieved in many cases. We also propose a method to tailor the PC matrix to the received observation by selecting only a small fraction of useful minimum-weight PCs before decoding begins. This allows one to both improve performance and significantly reduce complexity compared to using the full set of minimum-weight PCs