15 research outputs found
On Pseudocodewords and Improved Union Bound of Linear Programming Decoding of HDPC Codes
In this paper, we present an improved union bound on the Linear Programming
(LP) decoding performance of the binary linear codes transmitted over an
additive white Gaussian noise channels. The bounding technique is based on the
second-order of Bonferroni-type inequality in probability theory, and it is
minimized by Prim's minimum spanning tree algorithm. The bound calculation
needs the fundamental cone generators of a given parity-check matrix rather
than only their weight spectrum, but involves relatively low computational
complexity. It is targeted to high-density parity-check codes, where the number
of their generators is extremely large and these generators are spread densely
in the Euclidean space. We explore the generator density and make a comparison
between different parity-check matrix representations. That density effects on
the improvement of the proposed bound over the conventional LP union bound. The
paper also presents a complete pseudo-weight distribution of the fundamental
cone generators for the BCH[31,21,5] code
Efficient Linear Programming Decoding of HDPC Codes
We propose several improvements for Linear Programming (LP) decoding
algorithms for High Density Parity Check (HDPC) codes. First, we use the
automorphism groups of a code to create parity check matrix diversity and to
generate valid cuts from redundant parity checks. Second, we propose an
efficient mixed integer decoder utilizing the branch and bound method. We
further enhance the proposed decoders by removing inactive constraints and by
adapting the parity check matrix prior to decoding according to the channel
observations. Based on simulation results the proposed decoders achieve near-ML
performance with reasonable complexity.Comment: Submitted to the IEEE Transactions on Communications, November 200
Deep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes
Tail-biting convolutional codes extend the classical zero-termination
convolutional codes: Both encoding schemes force the equality of start and end
states, but under the tail-biting each state is a valid termination. This paper
proposes a machine-learning approach to improve the state-of-the-art decoding
of tail-biting codes, focusing on the widely employed short length regime as in
the LTE standard. This standard also includes a CRC code.
First, we parameterize the circular Viterbi algorithm, a baseline decoder
that exploits the circular nature of the underlying trellis. An ensemble
combines multiple such weighted decoders, each decoder specializes in decoding
words from a specific region of the channel words' distribution. A region
corresponds to a subset of termination states; the ensemble covers the entire
states space. A non-learnable gating satisfies two goals: it filters easily
decoded words and mitigates the overhead of executing multiple weighted
decoders. The CRC criterion is employed to choose only a subset of experts for
decoding purpose. Our method achieves FER improvement of up to 0.75dB over the
CVA in the waterfall region for multiple code lengths, adding negligible
computational complexity compared to the circular Viterbi algorithm in high
SNRs