Ldpc Decoding Algorithm

LDPC Code Constructions Note that a linear codes have a parity check matrix, and thus can be decoded using message-passing decoding. However, not all codes are well-suited for this decoding algorithm. Semi-random Construction Regular LDPC Codes 1962, Gallager Irregular LDPC Richardson and Urbanke, Luby et al. MacKay Codes Structured

LDPC decoding using one of these message-passing algorithms. Belief Propagation Decoding The implementation of the belief propagation algorithm is based on the decoding algorithm presented by Gallager 2.

Section 11.4 discusses a simple-minded decoding algorithm, which is shown to correct a nite fraction of errors. se Remember that a code is characterized by its codebook C, which is a subset of 0,1N. LDPC codes are linear codes, which means that the codebook is a linear subspace of 0,1N. In practice such a subspace can be specied

check LDPC decoding algorithms and corresponding VLSI implementations. Furthermore, decoders must fully support the wide range of all 5G NR blocklengths and code rates, which is a significant challenge. In this paper, we present a high-performance and low-complexity LDPC decoder, tailor-made to fulfill the 5G requirements.

decoding algorithm message -passing decoders and showed that using this type of decoder, one can come close to Shannon's bounds. In general, an LDPC coed is the null space of a sparse low-density matrix H , i.e., 0 Where is a low-density matrix in the following sense

5 31 07 LDPC Codes 14 Solution Long, structured, quotpseudorandomquot codes Practical, near-optimal decoding algorithms Examples Turbo codes 1993 Low-density parity-check LDPC codes 1960, 1999 State-of-the-art Turbo codes and LDPC codes have brought Shannon limits to within reach on a wide range of channels.

The message passing decoding algorithm for LDPC codes is an instantiation of a more general algorithm, known as belief propagation, that is used for inference in graphical models. In this section we describe the inference problem and describe the belief propagation BP algorithm. De nition 1. A factor graph is a collection of random variables

As with other codes, the maximum likelihood decoding of an LDPC code on the binary symmetric channel is an NP-complete problem, 25 shown by reduction from 3-dimensional matching.So assuming P ! NP, which is widely believed, then performing optimal decoding for an arbitrary code of any useful size is not practical.. However, sub-optimal techniques based on iterative belief propagation

also called message-passing or belief propagation algorithms for decoding LDPC codes. This is in itself a vast area with numerous technically sophisticated results. For a comprehensive discussion of this area, we point the reader to the upcoming book by Richardson and Urbanke 25, which is an excellent resource on this topic.

decoding algorithms of sparse codes perform very close to the optimal maximum likelihood decoder. 3 Decoding LDPC codes The algorithm used to decode LDPC codes was discovered indepen-dently several times and as a matter of fact comes under dierent names. The most common ones are the belief propagation algorithm