Prime-Period LDPC-CC Encoding for Stronger Error Correction
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Solution Overview
Problem
Current LDPC-CC technologies are limited in their time-varying periods, particularly for error correction capabilities beyond those described in Patent Literature 1, which restricts their application in achieving high error correction rates.
Innovation Solution
The development of an encoding and decoding method using LDPC-CC with a time-varying period of q, where q is a prime number greater than 3, employing a parity check polynomial of coding rate (n-1)/n, allowing for the generation of parity bits using specific equations and belief propagation for decoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LDPC-CC with time-varying period q (prime number > 3) is used, then error correction capability is improved, but device complexity increases
Solution Approach 1:
The patent changes the time-varying period parameter from conventional values (2, 3, 4) to prime numbers greater than 3 (5, 7, 11, 13, 17, 19, 23, 29, 31). This parameter change optimizes the error correction capability by creating more favorable parity check matrix structures with better distribution properties, while the modular encoder/decoder architecture keeps the implementation complexity manageable through reuse of computational components across different time steps.
2Adaptability or versatility
If padding or puncturing processing is applied to adjust sequence length, then compatibility with variable-length packets is improved, but coding rate changes or redundant sequences are transmitted
Solution Approach 1:
The patent employs a dynamic convolutional encoding approach where the encoder processes information sequences of any length without requiring fixed block boundaries. The time-varying parity check polynomial adapts dynamically to the input sequence length, eliminating the need for static padding or puncturing operations. This dynamic processing maintains the original coding rate while achieving full compatibility with variable-length Ethernet frames and other packet structures.
3Reliability
If LDPC-CC with prime number time-varying periods is implemented, then error correction performance is improved, but implementation complexity increases
Solution Approach 1:
The patent designs universal encoder and decoder structures that can handle any prime number time-varying period q > 3 through a single implementation framework. The encoder uses a generic algorithm that computes parity bits based on the current time step modulo q, while the decoder uses belief propagation that adapts to any q value. This universality allows the same hardware or software implementation to achieve optimal error correction performance for q=5, 7, 11, 13, 17, 19, 23, 29, or 31 without requiring separate dedicated circuits for each period value.
Data Source
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AI summary
An encoding method and encoder of a time-varying LDPC-CC with high error correction performance are provided. In an encoding method of performing low density parity check convolutional coding (LDPC-CC) of a time varying period of q using a parity check polynomial of a coding rate of (n-1)/n (where n is an integer equal to or greater than 2), the time varying period of q is a prime number greater than 3, the method receiving an information sequence as input and encoding the information sequence using equation 1 as a g-th (g=0, 1, ···, q-1) parity check polynomial to satisfy 0: Da#g,1,1+Da#g,1,2+Da#g,1,3X1D+Da#g,2,1+Da#g,2,2+Da#g,2,3X2D+⋯+Da#g,n−1,1+Da#g,n−1,2+Da#g,n−1,3Xn−1D+Da#g,1+Da#g,2+1PD=0 where, in equation 1: "%" represents a modulo and each coefficient satisfies the following with respect to k=1, 2, ... , n-1: a#0,k,1%q=a#1,k,1%q=a#2,k,1%q=a#3,k,1%q=⋯=a#g,k,1%q=⋯=a#q−2,k,1%q=a#q−1,k,1%q=vp=kvp=kfixed value; b#0,1%q=b#1,1%q=b#2,1%q=b#3,1%q=⋯=b#g,1%q=⋯=b#q−2,1%q=b#q−1,1%q=ww:fixed value; a#0,k,2%q=a#1,k,2%q=a#2,k,2%q=a#3,k,2%q=⋯=a#g,k,2%q=⋯=a#q−2,k,2%q=a#q−1,k,2%q=yp=kyp=k:fixed value; b#0,2%q=b#1,2%q=b#2,2%q=b#3,2%q=⋯=b#g,2%q=⋯=b#q−2,2%q=b#q−1,2%q=zz:fixed value; and a#0,k,3%q=a#1,k,3%q=a#2,k,3%q=a#3,k,3%q=⋯=a#g,k,3%q=⋯=a#q−2,k,3%q=a#q−1,k,3%q=sp=ksp=k:fixed value; a#g,k,1, a#g,k,2 and a#g,k,3 are natural numbers equal to or greater than 1 and a#g,k,1≠a#g,k,2, a#g,k,1≠a#g,k,3 and a#g,k,2≠a#g,k,3 hold true; b#g,1 and b#g,2 are natural numbers equal to or greater than 1 and b#g,1≠b#g,2 holds true; and vp=k and yp=k are natural numbers equal to or greater than 1.