Matrix-Based Polar Staircase Coding for Lower Encoding Latency
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Solution Overview
Problem
Existing polar code encoding and decoding methods are limited by their sequential nature and systematic construction, which can lead to increased latency and suboptimal error correction performance, especially in high-speed optical communications.
Innovation Solution
The proposed solution involves an apparatus and method for encoding data using non-systematic polar codes, where information bits are distributed across rows and columns of matrices, allowing for efficient polarization effects and simplified encoding processes. This approach enables the use of staircase construction with non-systematic polar codes, achieving the same error-correction performance as systematic polar codes but with reduced latency and increased speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If classical polar codes with systematic construction are used, then error correction performance is achieved, but encoding latency increases and encoding speed decreases
Solution Approach 1:
The patent inverts the traditional systematic polar code construction by using non-systematic code arrangement. Instead of placing information bits in fixed systematic positions, the invention distributes information bits across matrix rows and columns in a non-systematic manner, enabling parallel processing operations that reduce encoding latency while maintaining error correction performance.
Solution Approach 2:
The patent transitions from one-dimensional sequential encoding to two-dimensional matrix-based encoding. By organizing code bits in MxN matrices with rows and columns, the invention enables parallel encoding operations across multiple dimensions, significantly improving encoding speed and reducing latency while preserving the polarization effect for error correction.
2Reliability
If sequential SC decoding algorithm is used, then decoding is performed, but decoding speed is limited and latency increases
Solution Approach 1:
The patent segments the decoding process into independent row and column operations on matrix structures. By dividing the codeword into M rows and N columns, the decoding can be performed in parallel across different matrix dimensions, transforming the inherently sequential SC decoding into a parallelizable process that maintains accuracy while improving speed.
Solution Approach 2:
The patent applies two-dimensional matrix structure to enable parallel decoding operations. The MxN matrix organization allows simultaneous processing of multiple bit channels across rows and columns, breaking the sequential bottleneck of traditional SC decoding and achieving higher decoding throughput without sacrificing accuracy.
3Adaptability or versatility
If polar codes of length N=2^n are used, then classical construction is maintained, but code flexibility is limited and non-power-of-2 lengths cannot be achieved
Solution Approach 1:
The patent segments the code construction into smaller matrix blocks of size MxN where N=2^n. This block-based approach allows flexible concatenation and arrangement of multiple smaller polar code blocks to achieve various overall code lengths, providing adaptability while keeping each individual block's encoder structure simple and manageable.
Solution Approach 2:
The patent uses two-dimensional matrix arrangement to achieve code length flexibility. By organizing polar code blocks in M rows and N columns and allowing flexible repetition and concatenation patterns, the system can achieve various effective code lengths without requiring complete redesign of the encoder structure for each length.
Data Source
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AI summary
The present invention relates to an apparatus for encoding a sequence including information bits into a sequence of matrices. The apparatus is configured to generate a MxN matrix UNh, wherein M≤N/2, wherein in each row 0≤i<M of UNh each bit position 0≤j<M contains an information bit of the input sequence or a frozen bit depending on a set of frozen bit indices F of a polar code of length N associated with that row, wherein the bits xij, for 0≤i<M and 0≤j<N-M form a matrix Uh+1, while the bits xij for 0≤i<M and M≤j<N form a matrix Xh´, encode each row of UNh on the basis of the polar code of length N associated with that row, in order to obtain an encoded matrix XNh, wherein the bits xij of XNh for 0≤i<M and 0≤j<N-M form a matrix Xh+1´ while the bits xij for 0≤i<M and M≤j<N form a matrix Xh, transmit the matrix Xh.