Systematic Polar Code Encoding for Short Code Distance Limits
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Solution Overview
Problem
Polar codes with short encoded bit sequences exhibit poor code spectrum performance due to short codeword distances, necessitating an improved encoding method to enhance reliability in data transmission.
Innovation Solution
The proposed encoding method involves performing sub-block column transformations on a polar code generation matrix using transformation matrices to form a target matrix, which reduces the number of codewords with minimum code distance and improves the code spectrum performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If systematic polar code is used for channel encoding, then bit error performance is improved, but code spectrum performance deteriorates due to short code distance
Solution Approach 1:
The invention segments the polar code generation matrix into multiple sub-matrices and applies different transformation operations to different segments. Specifically, the generation matrix is divided into first sub-matrix and second sub-matrix, with different encoding sequences applied to information bits and frozen bits respectively, thereby improving code spectrum performance while maintaining reliability
Solution Approach 2:
The invention changes the encoding parameters by introducing a transformation matrix that modifies the traditional systematic polar code encoding process. By applying column transformation to the generation matrix and using different encoding sequences for different bit types, the code distance and code spectrum performance are improved without sacrificing bit error performance
2Ease of operation
If conventional polar code generation matrix is used, then encoding process is simple, but code distance is short leading to poor code spectrum performance
Solution Approach 1:
The invention introduces a transformation matrix as an intermediary element between the conventional polar code generation matrix and the final encoding process. This transformation matrix serves as a mediator that enhances code distance and code spectrum performance while maintaining the systematic structure and relative simplicity of the encoding process
3Productivity
If encoding is performed with small bit sequence length, then transmission efficiency is maintained, but code distance becomes very short causing poor performance
Solution Approach 1:
The invention applies local quality improvement by treating information bits and frozen bits differently through distinct encoding sequences. For small bit sequences, this localized differentiation ensures that even though the overall code length is short, the code distance is maximized by optimizing the encoding of specific bit positions, thereby improving code spectrum performance without sacrificing transmission efficiency
Data Source
AI summary
The method includes: obtaining an input information bit sequence; determining a target matrix based on a first polar code generation matrix and a transformation matrix; encoding the input information bit sequence based on an inverse matrix of a first matrix, to obtain a first bit sequence, where the input information bit sequence is a bit sequence corresponding to an information bit, and the first matrix is a submatrix formed by a row, in the target matrix, corresponding to the information bit and a column, in the target matrix, corresponding to the information bit; and encoding the first bit sequence based on a second matrix, to obtain a second bit sequence, where the second matrix is a submatrix formed by the row, in the target matrix, corresponding to the information bit and a column, in the target matrix, corresponding to a frozen bit.