Polar Code Rate Matching with Piece-Wise Puncturing
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Solution Overview
Problem
Polar codes, particularly Arikan polar codes, face limitations in coding rate matching due to restrictions on codeword length, which can lead to suboptimal performance in error correction and transmission efficiency, especially when the required codeword length does not align with the power-of-two constraint.
Innovation Solution
The proposed solution involves a method for piece-wise rate matching using polar codes, where the transmitter determines an appropriate information sequence and punctures the codeword to match the desired coding rate, allowing for flexible codeword lengths by mapping bits to specific positions and using puncturing patterns to adjust the codeword length, enabling efficient transmission even when the required length does not align with traditional power-of-two constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If polar codes use traditional power-of-two codeword length constraints, then the encoding and decoding processes are simplified, but the coding rate matching flexibility is reduced and transmission efficiency deteriorates when required codeword length does not align with power-of-two constraints
Solution Approach 1:
The codeword is divided into multiple segments or parts, where each segment can be independently processed. The encoder generates a codeword of length Nb (power of two), then segments it into multiple sub-codewords of lengths that can be selectively transmitted. This allows the system to achieve flexible effective codeword lengths by transmitting different numbers of segments, resolving the contradiction between maintaining power-of-two encoding simplicity and achieving flexible rate matching.
Solution Approach 2:
The system dynamically adjusts the transmission length by selectively puncturing or shortening the codeword based on channel conditions and required coding rates. The encoder maintains the ability to generate full power-of-two length codewords, but the actual transmitted length becomes dynamic and adaptable to different requirements, thus achieving both encoding simplicity and rate matching flexibility.
2Adaptability or versatility
If polar codes transmit codewords with lengths that do not align with power-of-two constraints, then coding rate matching flexibility is improved, but error correction performance deteriorates due to suboptimal rate matching
Solution Approach 1:
The system changes the parameter of codeword length from fixed power-of-two values to flexible values that can be adjusted according to channel conditions and required coding rates. By using piece-wise rate matching, the system can select optimal codeword lengths from a range of possible values, maintaining error correction performance while achieving the desired flexibility in codeword length selection.
Solution Approach 2:
The encoder pre-generates codewords of power-of-two lengths with optimal error correction properties, then applies preliminary processing (puncturing, shortening, or concatenation) to achieve the desired flexible lengths. This preliminary action ensures that the base codewords have optimal error correction performance before being adjusted to match specific transmission requirements.
3Productivity
If polar codes use fixed power-of-two codeword lengths, then the encoding process is straightforward, but transmission efficiency is reduced due to inability to precisely match required coding rates
Solution Approach 1:
The system introduces an intermediary rate matching process between the power-of-two encoder and the channel. This intermediary layer handles the complexity of rate matching by using puncturing patterns, shortening, or concatenation operations on the base codewords, thereby improving transmission efficiency without requiring the encoder itself to be complex. The intermediary layer translates the simple power-of-two encoded output into flexible length transmissions that precisely match required coding rates.
Data Source
AI summary
Systems and methods are disclosed that relate to performing rate matching when using polar codes. In one embodiment, a plurality of bits are received at a polar encoder. A value is obtained that corresponds to at least one of: a coding rate to be used to transmit the plurality of bits, and a number of coded bits to be used to transmit the plurality of bits. It is determined which range of values the value falls within, and an information sequence is obtained that corresponds to the range the value falls within. The plurality of bits are mapped to a subset of positions of an input vector according to the information sequence. The remaining positions of the input vector are set as frozen values that are known by a decoder. The input vector is then encoded in the polar encoder to generate a codeword.