Q-Ary LDPC Check-Node Decoding With Dynamic Trellis Pruning
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Solution Overview
Problem
Decoding q-ary low-density parity-check (LDPC) codes is hindered by complex check node processing, which requires significant computational resources and memory, particularly in setting up trellises to find likely combinations of q-ary levels for symbols involved in checks.
Innovation Solution
The implementation of a dynamic programming approach for check node processing, involving forward and backward trellis searches with state variables and metric computations to reduce complexity and memory requirements, includes truncating LLR vectors to fewer levels, rearranging symbols based on probability distributions, and using a time-varying trellis structure with a tail portion reflecting single or reduced levels, and applying scaling factors to restore performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional trellis search is used for check node processing, then decoding accuracy is maintained, but computational complexity and memory requirements increase significantly
Solution Approach 1:
The patent segments the q-ary symbols into multiple groups and processes them through separate trellises rather than using a single comprehensive trellis. This segmentation reduces the state space complexity from O(q^dc) to manageable segments, while still achieving accurate decoding by combining results from multiple smaller trellis searches.
Solution Approach 2:
The patent employs dynamic programming with forward and backward passes that adaptively compute metrics based on received signals and previous iterations. The trellis structure dynamically updates its metric computations to focus on most likely paths, reducing unnecessary computations while maintaining decoding accuracy.
2Measurement precision
If full trellis structure is used for check node processing, then accurate LLR computation is achieved, but memory space requirements increase
Solution Approach 1:
The patent extracts and processes only the necessary state variables and metrics required for accurate LLR computation, rather than storing complete trellis information. By extracting key metric values and discarding redundant state information after processing, memory requirements are significantly reduced while maintaining computation precision.
Solution Approach 2:
The patent applies different processing precision to different parts of the trellis based on their importance. Critical state transitions receive full precision computation, while less critical paths use reduced precision, optimizing the balance between memory usage and LLR accuracy.
3Reliability
If q-ary level combinations are exhaustively searched, then most likely symbol combinations are found, but processing time increases
Solution Approach 1:
The patent performs preliminary computations of metric values and probability distributions before the main decoding process. By pre-computing likelihood values and sorting symbols based on their probability distributions, the algorithm reduces the search space for exhaustive enumeration, finding most likely combinations faster without sacrificing accuracy.
Solution Approach 2:
The patent implements early termination and pruning mechanisms that allow the algorithm to skip unlikely q-ary level combinations and rush through the search process by focusing computational effort on promising paths. This selective approach maintains accuracy for likely combinations while dramatically reducing time spent on improbable possibilities.
Data Source
AI summary
f(x(sk−1, sk))=A(sk−1)+B(sk) is calculated for nm2 pairs of consecutive state variables {sk−1, sk} using A(sk)=mins<sub2>k−1</sub2>,x{A(sk−1)+Γ(xk=x)} and B(sk)=mins<sub2>k+1</sub2>,x{B(sk+1)+Γ(xk+1=x, sk+1)}, where Γ(xk=x) is a metric associated with a branch xk=x connecting consecutive state variables sk−1 and sk. The nm lowest values are selected from the nm2 calculated values of f(x(sk−1, sk))=A(sk−1)+B(sk) and log likelihood ratios (LLRs) are set to those lowest f(x(sk−1, sk)) values. The nm values of x that correspond to the nm lowest values are determined.