Tail-Biting TLDPC Trellis Encoding With Lower Memory Complexity
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing error correction codes, such as LDPC codes, face complexity in encoding and high memory requirements due to the need for Gaussian elimination and dense parity check matrices, which increases computational load and costs, especially for small block sizes and low-density parity check codes.
Innovation Solution
The method involves associating redundancy data bits with information data bits using a tail-biting trellis low-density parity check encoding scheme, where the base code is represented by a two-state trellis with pre-determined permutation rules, eliminating the need for storing the H matrix and reducing connectivity, thereby decreasing memory and computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Gaussian elimination is used to encode LDPC codes, then encoding can be performed, but computational complexity and memory requirements increase significantly
Solution Approach 1:
The parity check matrix H is segmented into multiple blocks, where each block corresponds to a subset of parity check equations. The encoding process is divided into multiple steps, where each step solves a portion of the system using Gaussian elimination, rather than solving the entire system at once. This segmentation reduces the computational complexity of each individual Gaussian elimination operation while maintaining the ability to encode LDPC codes effectively.
2Reliability
If dense parity check matrices are used to ensure code performance, then minimum distance is improved, but memory requirements and connectivity increase
Solution Approach 1:
The dense parity check matrix H is divided into multiple smaller blocks, each containing a subset of the parity check equations. This segmentation allows the system to work with smaller matrix subsets during encoding, reducing the memory required to store and process the matrix at any given time, while the overall code structure maintains the necessary minimum distance properties through the combined effect of all blocks.
Solution Approach 2:
The parity check matrix is pre-organized into a blocked structure before encoding begins. This preliminary arrangement groups parity check equations in a way that facilitates efficient processing in subsequent encoding steps, allowing the system to maintain high minimum distance properties while reducing the operational memory requirements during the actual encoding process.
3Productivity
If high-rate codes are used to increase throughput, then data transmission efficiency is improved, but error correction capability may be reduced
Solution Approach 1:
The encoding process is segmented into multiple steps, with each step handling a specific block of parity check equations. This segmentation allows for systematic generation of parity bits that maintains error correction capability even as the code rate increases, by ensuring that each segment contributes to the overall code structure in a controlled manner.
Data Source
AI summary
Encoding method (1) and device associating p redundancy data bits with k information data bits to determine code words with a block length of n=p+k data bits. The code words are of tail-biting trellis low density parity check type. The method and the device implement a degree distribution profile of the n data bits defining a base code word including multiple replicas of the n data bits with respect to the degree distribution. This base code is represented by a two-states trellis formed of sections with positions accommodating data bits of the base code whereby the number of positions of a section is denoted as the degree of the section. The method and the device makes (2) a partition of the base code trellis into p intersecting regular parts of triple sections representing p parity check equations.