LDPC Convolutional Encoding for Variable-Length Codewords
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Solution Overview
Problem
Current LDPC codes face challenges in adapting to variable-length communication systems, as they require fixed-length blocks, leading to difficulties in maintaining coding rate and preventing redundant sequences through padding or puncturing.
Innovation Solution
The development of a method for LDPC-CC with a time-varying period q, using parity check polynomials that allow for encoding and decoding of arbitrary-length information sequences, achieving a coding rate of (n−1)/n, where n is an integer greater than or equal to two, and q is a prime number greater than three, utilizing specific parity check polynomials and belief propagation for efficient error correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LDPC block code is used to achieve high error correction capability, then error correction performance is improved, but the coding rate cannot be maintained and redundant sequences are transmitted due to padding or puncturing processing
Solution Approach 1:
The patent transitions from static LDPC block codes with fixed block lengths to dynamic LDPC convolutional codes where the code can adapt to variable-length input sequences. The encoder processes information sequences of arbitrary length by using shift registers and mod 2 adders that dynamically adjust to the input length, eliminating the need for padding or puncturing while maintaining the desired coding rate.
2Length of moving object
If padding or puncturing processing is applied to adjust transmission information sequence length to LDPC block code block length, then the block length correspondence is achieved, but the coding rate changes and redundant sequences are transmitted
Solution Approach 1:
The patent extracts the core encoding functionality from the fixed-block LDPC structure and implements it in a convolutional framework. By removing the rigid block length constraint and using shift registers that can accommodate variable-length inputs, the system eliminates padding and puncturing operations while maintaining efficient coding rates.
3Reliability
If LDPC-CC with time-varying period q (prime number greater than three) is used, then error correction capability is improved and arbitrary-length sequences can be encoded, but the parity check polynomial complexity increases
Solution Approach 1:
The patent changes the time-varying period parameter q to a prime number greater than three, which optimizes the error correction capability of the LDPC-CC. This parameter selection creates a more favorable parity check matrix structure that improves decoding performance while the convolutional nature of the code keeps the encoder complexity manageable through its shift register implementation.
Data Source
AI summary
An encoding method generates an encoded sequence by performing encoding of a given coding rate according to a predetermined parity check matrix. The predetermined parity check matrix is a first parity check matrix or a second parity check matrix. The first parity check matrix corresponds to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials. The second parity check matrix is generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix. An eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressible by using a predetermined mathematical formula.