Staircase Polar Coding with Interleavers for Lower Decoding Latency
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Solution Overview
Problem
Conventional staircase encoding and decoding using polar codes in optical communications suffer from increased encoding and decoding latency, and the error rate performance of staircase polar codes can be improved by applying conventional techniques, but these improvements are not straightforward when implemented over a merge of staircase and polar codes.
Innovation Solution
The use of non-systematic polar codes as component codes in staircase codes, combined with specific interleavers that rotate and shift bit positions to ensure uniform error probabilities across codewords, thereby improving the error correction capability and reducing variations in decoding complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional staircase encoding and decoding using polar codes is used, then the system provides error correction capability, but the encoding and decoding latency is increased
Solution Approach 1:
The encoding process is divided into multiple stages: first encoding message bits into a first matrix, then encoding rows of this matrix into a second matrix. The decoding process is similarly segmented into multiple steps including propagating LLR values, interleaving, prepending, and iterative decoding. This segmentation allows for more manageable and optimized processing at each stage, reducing overall latency while maintaining error correction capability.
Solution Approach 2:
The decoder pre-calculates and stores LLR (log-likelihood ratio) values for all possible codewords before actual decoding occurs. During decoding, these pre-computed LLR values are retrieved and used to quickly determine the most likely transmitted codeword. This preliminary action eliminates the need for complex real-time calculations during the actual decoding process, significantly reducing decoding latency.
2Reliability
If conventional staircase polar codes are used, then error correction is provided, but variations in decoding complexity and error probabilities across codewords increase
Solution Approach 1:
The patent applies different processing treatments to different parts of the code structure. Specifically, systematic bits and non-systematic bits are handled differently during encoding and decoding. The interleaving operation also applies different permutations to different bit positions. This local differentiation ensures that bits with higher error probability receive more robust processing, while maintaining overall system efficiency and reducing complexity variations.
Solution Approach 2:
The patent transforms the decoding problem by changing the parameter representation from direct bit values to LLR (log-likelihood ratio) values. This parameter transformation allows for more uniform handling of different codewords and bit positions, stabilizing the decoding complexity across different input patterns. The LLR values provide a continuous domain that better represents the uncertainty and reliability of each bit, leading to more consistent decoding behavior.
Data Source
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AI summary
The present disclosure relates to data encoding and data decoding using polar codes. In particular, the disclosure proposes an apparatus for staircase polar code encoding, an apparatus for staircase polar code decoding, and corresponding methods. Thereby, a staircase code using non-systematic polar codes as component codes is proposed. Further, specific interleavers are proposed for interleaving matrices between row-encoding and column-encoding at the apparatus for encoding and also at the apparatus for decoding. Three different specific interleavers are presented, which lead to an improved performance of the apparatus for decoding, due to a better error correction probability.