Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes

Abstract

Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially-coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.

Corrected typos in degree distributions νand μof MN and HA codes

References in corpus (3)

• Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
• Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform so well over the BEC
• Capacity-Achieving Ensembles of Accumulate-Repeat-Accumulate Codes for the Erasure Channel with Bounded Complexity

Cited by in corpus (11)

• A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions
• Performance Improvement of Iterative Multiuser Detection for Large Sparsely-Spread CDMA Systems by Spatial Coupling
• Design of Spatially Coupled LDPC Codes over GF(q) for Windowed Decoding
• Spatially-Coupled Precoded Rateless Codes with Bounded Degree Achieve the Capacity of BEC under BP decoding
• Spatially-Coupled Precoded Rateless Codes
• Spatially-Coupled MacKay-Neal Codes with No Bit Nodes of Degree Two Achieve the Capacity of BEC
• A Potential Theory of General Spatially-Coupled Systems via a Continuum Approximation
• Spatially-Coupled Binary MacKay-Neal Codes for Channels with Non-Binary Inputs and Affine Subspace Outputs
• Spatially-Coupled MacKay-Neal Codes Universally Achieve the Symmetric Information Rate of Arbitrary Generalized Erasure Channels with Memory
• Iterative LMMSE Channel Estimation, Multiuser Detection, and Decoding via Spatial Coupling
• Design of Irregular SC-LDPC Codes With Non-Uniform Degree Distributions by Linear Programing