Q-Ary Polar Code Puncturing for Flexible Rate Matching
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Solution Overview
Problem
Existing error control coding methods, such as Arikan polar codes, are limited to binary symbol alphabets and restrict codeword lengths to powers of two, making it challenging to achieve flexible coding rates in communication systems.
Innovation Solution
The implementation of general polar codes that encode q-ary symbols, allowing for puncturing to adjust codeword lengths and achieve desired coding rates by using polar encoder kernels and puncturing patterns based on information sequences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Arikan polar codes are used for error control coding, then error detection and correction capability is improved, but coding rate flexibility deteriorates due to binary symbol alphabet limitation and power-of-two codeword length constraint
Solution Approach 1:
The patent changes the fundamental parameter of the symbol alphabet from binary (q=2) to q-ary (q≥2), enabling the encoder to process symbols from a larger alphabet. This parameter change allows the codeword length to be adjusted to match channel capacity requirements while maintaining the mathematical structure of polar codes, thus achieving both reliable error correction and flexible coding rates.
Solution Approach 2:
The patent introduces dynamic rate matching capability by allowing the codeword length to be adaptively adjusted according to channel conditions and coding rate requirements. The encoder can dynamically select the appropriate codeword length from available options, transforming the static power-of-two length constraint into a dynamic, adaptable system that responds to varying communication requirements.
2Ease of manufacture
If codeword length is fixed to power of two in Arikan polar codes, then encoding simplicity is improved, but rate matching capability deteriorates
Solution Approach 1:
The patent changes the codeword length parameter from fixed power-of-two values to variable lengths that can be adjusted to match the product of information bits and coding rate inverse. This parameter change enables the system to achieve exact rate matching while preserving the structured encoding approach of polar codes.
Solution Approach 2:
The patent segments the codeword into information bits and redundancy bits in a flexible manner, allowing the boundary between them to be adjusted according to the desired coding rate. This segmentation enables precise control over the coding rate while maintaining the systematic structure of the code.
3Device complexity
If binary symbol alphabet is used in polar codes, then implementation complexity is reduced, but coding rate adaptability deteriorates
Solution Approach 1:
The patent changes the alphabet size parameter from binary (2) to q-ary (q≥2), which increases the information density per symbol. This parameter change allows the system to achieve higher coding rates and better adaptability while the underlying encoding structure remains relatively simple, requiring only modification of the generator matrix and encoding algorithm to support the larger alphabet.
Data Source
AI summary
General polar codes are disclosed that encode symbols of a q-ary alphabet, where q≥2. Systems and methods are also disclosed for performing code rate matching when using general polar codes. In one embodiment, a method performed at a transmitter includes receiving a plurality of bits at a polar encoder. The plurality of bits represent a plurality of q-ary symbols, where q>2. The method further includes encoding the plurality of bits using the polar encoder to generate a codeword of q-ary symbols represented by bits. The method further includes puncturing the codeword according to a puncturing pattern to obtain a punctured codeword having a reduced bit length.