Polar Code Word Generation Using Reliability and Row Weight
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Solution Overview
Problem
Polar codes face performance limitations in decoding, especially for short or medium code lengths, where they do not exceed the performance of Turbo codes or LDPC codes, and suffer from error propagation due to hard decision decoding, necessitating improved decoding methods.
Innovation Solution
A hybrid Polar code is generated by selecting information bits and constructing encoding matrices based on bit reliability and weight, enhancing the code's minimum distance and decoding performance through SC or SC-List decoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional Polar code encoding is used, then the encoding achieves Shannon capacity with low complexity, but the decoding performance does not exceed Turbo codes or LDPC codes for short or medium code lengths
Solution Approach 1:
The patent transforms the fixed generating matrix GN into a configurable hybrid Polar code structure where information bit positions and frozen bit positions can be dynamically selected based on reliability metrics (such as Bhattacharyya parameters or capacity values). This parameter change allows the code to adapt to different channel conditions and code lengths, achieving superior decoding performance while maintaining polynomial-time encoding complexity through the use of selection rules rather than complex optimization algorithms.
2Productivity
If successive-cancellation decoding is used, then the complexity is O(N×log2 N) and approaches Shannon limit for large N, but error propagation occurs due to hard decision decoding
Solution Approach 1:
The patent performs preliminary selection of information bit positions and frozen bit positions based on reliability metrics before the actual encoding and decoding processes. By pre-determining which positions will carry information and which will be frozen based on channel reliability estimates, the system prepares the code structure in advance to minimize error propagation during successive-cancellation decoding, thereby improving decoding accuracy without sacrificing the O(N×log2 N) decoding speed.
3Reliability
If information bits are selected without considering row weight, then the encoding is simpler, but the minimum code distance is not optimized
Solution Approach 1:
The patent introduces row weight as an additional selection criterion alongside reliability metrics. Instead of selecting information bit positions based solely on reliability (such as capacity or Bhattacharyya parameters), the method incorporates the weight of rows in the generating matrix GN, where rows with higher weights contribute to larger minimum code distance. This parameter change enables the system to optimize error correction capability by selecting information positions that maximize the minimum distance between codewords, while the selection process remains computationally efficient through the use of predetermined selection rules.
Data Source
AI summary
Embodiments of the present application provide a method and an apparatus for generating a code word using a Polar code encoding manner. A sequence has N bits, in which K bits are information bits. A matrix of N rows×N columns is used for encoding the sequence. Each row of the matrix has a weight that equals to total number of non-zero elements in the row, and ith row of the matrix corresponds to ith bit position of the sequence, i=1, 2, . . . , N. Each bit position of the N-bit sequence has a reliability. The K bit positions of the sequence that are occupied by the K information bits are selected according to reliabilities of the bit positions of the sequence and weights of the rows of the matrix. The code word is generated by multiplying the sequence with the matrix.