Polar Decoder Cost Function Using CRC and Cross-Entropy
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Solution Overview
Problem
Current quantum annealing (QA) polar decoders face challenges in decoding codewords of lengths greater than 8 bits, exhibit poor performance in additive white Gaussian noise (AWGN) channels, and lack effective methods to utilize cyclic redundancy check (CRC) bits for improved error-correction, leading to computational inefficiencies and suboptimal decoding results.
Innovation Solution
A method and system that reformulates the decoding process as an optimization problem with an objective function incorporating node, frozen, and receiver constraints, using binary cross-entropy (BCE) for receiver constraints, removing frozen constraints, and representing CRC with XOR equations to simplify and enhance the decoding process, allowing for efficient decoding of longer codewords.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If quantum annealing (QA) polar decoding is used, then decoding speed is improved, but decoding accuracy deteriorates for codewords longer than 8 bits
Solution Approach 1:
The patent modifies the cost function parameters by incorporating binary cross-entropy instead of traditional distance metrics, and by adjusting the weighting of different constraint terms (node constraints, frozen constraints, receiver constraints) to optimize both speed and accuracy for longer codewords
Solution Approach 2:
The patent replaces the traditional QA Hamiltonian formulation with a simplified cost function that maintains quantum annealing speed advantages while correcting accuracy deficiencies through alternative mathematical formulations (binary cross-entropy, modified constraint aggregations)
2Device complexity
If traditional QA cost function is used, then computational simplicity is maintained, but error-correction performance deteriorates
Solution Approach 1:
The patent changes the functional form of the cost function from traditional distance-based metrics to binary cross-entropy, and modifies the aggregation of constraints with adjusted weighting parameters to improve error-correction performance while keeping the overall computational structure simple
Solution Approach 2:
The patent introduces ancillary variables as intermediary elements that help bridge the gap between simple QA computation and complex error-correction requirements, allowing the system to achieve better performance without proportionally increasing complexity
3Device complexity
If CRC bits are not utilized, then decoding complexity is reduced, but error-correction capability deteriorates
Solution Approach 1:
The patent performs preliminary incorporation of CRC constraints into the cost function formulation, so that CRC-based error detection and correction is integrated into the quantum annealing process itself, improving error-correction capability without requiring separate post-processing steps that would increase complexity
Data Source
AI summary
An optimization-based decoder with improved performance and cyclic redundancy check is provided. An optimization problem is generated and solved. The optimization problem includes a function implementing constraints on variables. Main variables correspond to nodes of the encoding graph, including input variables corresponding to output nodes and output variables corresponding to input nodes. Ancillary variables correspond to an additional output a logical operations in the encoding graph. Constraints are configured to generate cost penalties, for instance when the main and ancillary variables of a candidate solution disagree with conditions of the encoding graph, and to correspond with the cross-entropy between each codeword symbol and the corresponding input variable. A candidate solution is obtained by solving the optimization problem, wherein the output variables in the candidate solution correspond to decoded symbols.