Non-Binary LDPC Encoding With Sub-Symbol Graph Decoding
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Solution Overview
Problem
Non-binary LDPC codes, which offer improved error correction performance, face challenges with increased decoding complexity and memory size requirements due to their definition on Galois fields of order greater than 2.
Innovation Solution
A new code structure is introduced where symbols from a Galois field of order q > 2 are projected into sub-symbols belonging to mathematical sets of order less than q, allowing for a reduced memory size decoder by subdividing symbol nodes into intermediate and sub-symbol nodes, while maintaining connectivity and using local recombinations for decoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-binary LDPC codes are used to improve error correction performance, then error correction capability is improved, but decoding complexity and memory size increase significantly
Solution Approach 1:
The patent segments each symbol from the Galois field GF(q) into multiple sub-symbols from smaller Galois fields GF(2^m). This segmentation allows the decoder to process smaller field elements instead of large q-ary symbols, reducing memory requirements and computational complexity while maintaining the error correction performance of the original non-binary code.
2Reliability
If symbols from Galois field of order q > 2 are directly decoded, then error correction performance is maximized, but memory size requirements increase significantly
Solution Approach 1:
Each symbol from GF(q) is divided into multiple sub-symbols from smaller Galois fields. The decoder stores and processes these smaller sub-symbols instead of entire large-field symbols, significantly reducing the memory size required for message passing operations while preserving the ability to correct errors in the original symbol.
Solution Approach 2:
The patent introduces intermediate nodes that represent the relationship between parent symbols and child sub-symbols. These intermediate nodes act as mediators during decoding, allowing the system to work with smaller field elements while maintaining the mathematical relationships necessary for error correction in the original larger field.
Data Source
AI summary
A string of K initial symbols is encoded with a code of the parity check type. The K initial symbols belong to a Galois field of order q strictly greater than 2. The code is defined by code characteristics representable by a graph (GRH) comprising N−K first nodes (NCi), each node satisfying a parity check equation defined on the Galois field of order q, N packets of intermediate nodes (NITi) and NI second nodes (NSSi), each intermediate node being linked to a single first node and to several second nodes by way of a connection scheme. The string of K initial symbols is encoded by using the said code characteristics and a string of N encoded symbols is obtained, respectively subdivided into NI sub-symbols belonging respectively to mathematical sets whose orders are less than q, according to a subdivision scheme representative of the connection scheme (Π).