A Separation Algorithm for Improved LP-Decoding of Linear Block Codes
TLDR
A new separation algorithm to improve the error-correcting performance of LP decoding for binary linear block codes using an IP formulation with indicator variables that help in detecting the violated parity checks and an efficient method of finding cuts induced by redundant parity checks.Abstract:
Maximum likelihood (ML) decoding is the optimal decoding algorithm for arbitrary linear block codes and can be written as an integer programming (IP) problem. Feldman relaxed this IP problem and presented linear programming (LP) based decoding. In this paper, we propose a new separation algorithm to improve the error-correcting performance of LP decoding for binary linear block codes. We use an IP formulation with indicator variables that help in detecting the violated parity checks. We derive Gomory cuts from the IP and use them in our separation algorithm. An efficient method of finding cuts induced by redundant parity checks (RPC) is also proposed. Under certain circumstances we can guarantee that these RPC cuts are valid and cut off the fractional optimal solutions of LP decoding. It is demonstrated on three LDPC codes and two BCH codes that our separation algorithm performs significantly better than LP decoding and belief propagation (BP) decoding.read more
Citations
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Journal ArticleDOI
Adaptive Cut Generation Algorithm for Improved Linear Programming Decoding of Binary Linear Codes
Xiaojie Zhang,Paul H. Siegel +1 more
TL;DR: A new and effective algorithm to generate parity inequalities derived from certain additional redundant parity check (RPC) constraints that can eliminate pseudocodewords produced by the LP decoder, often significantly improving the decoder error-rate performance.
Journal ArticleDOI
The ADMM Penalized Decoder for LDPC Codes
Xishuo Liu,Stark C. Draper +1 more
TL;DR: A new class of decoders obtained by applying the alternating direction method of multipliers (ADMM) algorithm to a set of non-convex optimization problems are constructed by adding a penalty term to the objective of LP decoding to make pseudocodewords, which are non-integer vertices of the LP relaxation, more costly.
Journal ArticleDOI
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
TL;DR: In this paper, a review and categorization of decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels is presented, including linear, integer and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory.
Journal ArticleDOI
Efficient ADMM Decoding of LDPC Codes Using Lookup Tables
TL;DR: Simulation results show that for both the regular and irregular LDPC codes, the ADMM decoding using LUT-based projection can substantially reduce the decoding time while maintaining the error rate performance at a comparatively large memory cost.
Proceedings ArticleDOI
Suppressing pseudocodewords by penalizing the objective of LP decoding
TL;DR: A new class of decoders for low density parity check (LDPC) codes is presented, based on the alternating direction method of multipliers (ADMM) decomposition technique for LP decoding, which achieves much better error performance compared to LP decoder at low SNRs.
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