522 research outputs found
Low-Complexity LP Decoding of Nonbinary Linear Codes
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has
attracted much attention in the research community in the past few years. LP
decoding has been derived for binary and nonbinary linear codes. However, the
most important problem with LP decoding for both binary and nonbinary linear
codes is that the complexity of standard LP solvers such as the simplex
algorithm remains prohibitively large for codes of moderate to large block
length. To address this problem, two low-complexity LP (LCLP) decoding
algorithms for binary linear codes have been proposed by Vontobel and Koetter,
henceforth called the basic LCLP decoding algorithm and the subgradient LCLP
decoding algorithm.
In this paper, we generalize these LCLP decoding algorithms to nonbinary
linear codes. The computational complexity per iteration of the proposed
nonbinary LCLP decoding algorithms scales linearly with the block length of the
code. A modified BCJR algorithm for efficient check-node calculations in the
nonbinary basic LCLP decoding algorithm is also proposed, which has complexity
linear in the check node degree.
Several simulation results are presented for nonbinary LDPC codes defined
over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and
8-phase-shift keying, respectively, over the AWGN channel. It is shown that for
some group-structured LDPC codes, the error-correcting performance of the
nonbinary LCLP decoding algorithms is similar to or better than that of the
min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201
Decoding Across the Quantum LDPC Code Landscape
We show that belief propagation combined with ordered statistics
post-processing is a general decoder for quantum low density parity check codes
constructed from the hypergraph product. To this end, we run numerical
simulations of the decoder applied to three families of hypergraph product
code: topological codes, fixed-rate random codes and a new class of codes that
we call semi-topological codes. Our new code families share properties of both
topological and random hypergraph product codes, with a construction that
allows for a finely-controlled trade-off between code threshold and stabilizer
locality. Our results indicate thresholds across all three families of
hypergraph product code, and provide evidence of exponential suppression in the
low error regime. For the Toric code, we observe a threshold in the range
. This result improves upon previous quantum decoders based on
belief propagation, and approaches the performance of the minimum weight
perfect matching algorithm. We expect semi-topological codes to have the same
threshold as Toric codes, as they are identical in the bulk, and we present
numerical evidence supporting this observation.Comment: The code for the BP+OSD decoder used in this work can be found on
Github: https://github.com/quantumgizmos/bp_os
VLSI Implementation of a Rate Decoder for Structural LDPC Channel Codes
AbstractThis paper proposes a low complexity low-density parity check decoder (LDPC) design. The design mainly accomplishes a message passing algorithm and systolic high throughput architecture. The typical mathematical calculations are based on the observation that nodes with high log likelihood ratio provide almost same information in every iteration and can be considered as stationary, we propose an algorithm in which the parity check matrix H is updated to a reduced complexity form every time a stationary node is encountered which results in lesser number of numerical computations in subsequent iterations. In this paper, we contemplately focuses on computational complexity and the decoder design significantly benefits from the high throughput point of view and the various improvisations introduced at various levels of abstraction in the decoder design. Threshold Controlled Min Sum Algorithm implements the LDPC decoder design for a code compliant with wired and wireless applications. A high performance LDPC decoder has been designed that achieves a throughput of 0.890 Gbps. The whole design of LDPC Decoder is designed, simulated and synthesized using Xilinx ISE 13.1 EDA Tool
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