QPP Interleaver Coefficients for Contention-Free Turbo Decoding
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Solution Overview
Problem
The design of good quadratic permutation polynomial (QPP) interleavers for turbo codes is challenging due to the large number of potential coefficients, making it difficult to simulate and test individually, and existing guidelines do not always yield the best results, especially for long block lengths.
Innovation Solution
A QPP interleaver with the form Π(n) = f1n + f2n^2 mod K is implemented, which allows for simple hardware implementation and contention-free parallel decoding, using a search algorithm that considers algebraic-geometric properties to identify optimal coefficients, such as modified degrees of nonlinearity and spread factor, to improve error correction performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If pseudorandom interleavers are used for long block lengths, then good error correction performance is achieved, but large storage resources are required
Solution Approach 1:
The patent changes the fundamental parameter of the interleaver structure from pseudorandom to quadratic permutation polynomial form. This mathematical transformation allows the interleaver to achieve good error correction performance through the algebraic properties of QPP functions while requiring minimal storage resources, as the permutation can be computed directly from the polynomial formula without storing large lookup tables.
Solution Approach 2:
The patent replaces the mechanical storage-based pseudorandom interleaver with a computational algebraic system. Instead of storing pre-generated pseudorandom sequences in memory, the system uses direct computation of the QPP function Π(i) = (a1·i + a2·i²) mod N to generate the permutation sequence on-the-fly, substituting memory storage with mathematical computation.
2Reliability
If the number of QPP coefficients is increased to improve performance, then better error correction is achieved, but the complexity of simulation and testing increases significantly
Solution Approach 1:
The patent performs preliminary optimization of the QPP coefficients (a1, a2) using algebraic-geometric properties and theoretical analysis before deployment. By pre-determining optimal coefficient values based on mathematical properties rather than exhaustive simulation, the system achieves good error correction performance while avoiding the complex simulation and testing that would be required to evaluate all possible coefficient combinations.
Solution Approach 2:
The patent reduces the parameter search space by changing from evaluating all possible QPP coefficient combinations to selecting specific coefficients based on algebraic-geometric criteria. This parameter selection strategy transforms an intractable simulation problem into a manageable theoretical optimization problem.
3Productivity
If parallel decoders are implemented to improve decoding speed, then productivity increases, but contention for shared resources occurs
Solution Approach 1:
The patent changes the interleaver permutation structure to QPP form, which has specific mathematical properties that enable contention-free parallel access. The quadratic permutation polynomial structure creates a uniform distribution of memory access patterns that prevents multiple parallel decoders from simultaneously accessing the same memory locations, eliminating contention while maintaining high decoding speed.
Solution Approach 2:
The QPP interleaver creates equipotential access conditions for parallel decoders by ensuring that all decoders have equal and non-conflicting access to memory resources. The mathematical structure of the QPP function distributes memory accesses uniformly across all available resources, giving each parallel decoder equal access opportunities without creating hotspots or contention points.
Data Source
AI summary
A quadratic permutation polynomial (QPP) interleaver is described for turbo coding and decoding. The QPP interleaver has the form:Π(n)=f1n+f2n2 mod K, where the QPP coefficients f1 and f2. are designed to provide good error performance for a given block length K.