Layered PAC Concatenated Coding for Low-FER High-Throughput Decoding
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Polarization adjusted convolutional (PAC) codes face challenges in practical utility due to variability in computational complexity, throughput bottlenecks, and the need for extreme low frame error rates (FER) in applications like fiber-optic data transmission and hard-disk storage, which existing technologies struggle to address effectively.
Innovation Solution
A concatenated coding scheme employing PAC codes as inner codes within a generalized concatenated coding (GCC) framework, utilizing layered polarization adjusted convolutional (LPAC) codes with customized outer Reed-Solomon codes to mitigate computational variability and enhance throughput, while leveraging the benefits of channel polarization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If sequential decoding is used for PAC codes, then near-optimal FER performance is achieved, but computational complexity becomes highly sensitive to noise severity
Solution Approach 1:
The patent segments the code into inner PAC codes and outer Reed-Solomon codes in a concatenated structure. The inner PAC codes handle the majority of error correction with low complexity sequential decoding, while the outer Reed-Solomon codes provide additional protection against residual errors. This segmentation allows the system to achieve extreme low FER values without requiring the inner decoder to handle all errors alone, thus controlling computational complexity while maintaining reliability.
2Reliability
If PAC codes are decoded sequentially to exploit channel polarization, then decoding accuracy is improved, but throughput is severely limited
Solution Approach 1:
The concatenated code structure segments the decoding task across multiple code layers. The inner PAC code decoding exploits channel polarization for high accuracy, while the outer Reed-Solomon code decoding handles remaining errors. This segmentation allows parallel processing of different code layers and enables pipeline implementation, thereby improving throughput without sacrificing the decoding accuracy benefits of sequential PAC code decoding.
Solution Approach 2:
The outer Reed-Solomon code acts as an intermediary that receives the output from the inner PAC code decoder and provides additional error correction. This intermediary layer allows the inner sequential decoder to operate at its optimal pace for accuracy while the outer decoder handles residual errors, effectively mediating between the accuracy requirements of sequential decoding and the throughput requirements of the overall system.
3Reliability
If multiple sequential decoders are used in parallel to circumvent cutoff rate barrier, then channel capacity is approached, but device complexity increases
Solution Approach 1:
The patent uses segmentation by dividing the error correction task across inner and outer code layers rather than using multiple parallel sequential decoders. The inner PAC code decoder handles the primary decoding task with controlled complexity, while the outer Reed-Solomon decoder provides additional protection. This layered segmentation achieves channel capacity approachability without the complexity of multiple parallel sequential decoding structures.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
An encoder 102 receives a concatenated encoder input block d, splits d into an outer code input array a, and encodes a using outer codes to generate an outer code output array b. The encoder generates, from b, a concatenated code output array x using a layered polarization adjusted convolutional (LPAC) code. A decoder 106 counts layers and carries out an inner decoding operation for a layered polarization adjusted convolutional (LPAC) code to generate an inner decoder decision b̃i from a concatenated decoder input array y and a cumulative decision feedback (b̂1,b̂2, ··· , b̂i-1). The decoder carries out an outer decoding operation to generate from b̃i an outer decoder decision âi, and carries out a reencoding operation to generate a decision feedback b̂i from âi, where the number of layers is an integer greater than one, with a concatenated decoder output block d̂ being generated from outer decoder decisions.