Layered PAC Decoding for Low-FER High-Throughput Concatenated Codes
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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 in applications like fiber-optic data transmission and hard-disk storage, which existing decoding methods 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 codes and a sequential decoder optimized for channel polarization effects, including a 'look-ahead' metric and 'time-out' rule to manage computational complexity.
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 channel noise and variability increases
Solution Approach 1:
The code is segmented into multiple layers (LPAC structure with L layers), where each layer handles a portion of the decoding task. This segmentation distributes the computational complexity across layers, reducing the variability and sensitivity to channel noise while maintaining near-optimal FER performance through coordinated layer decoding.
Solution Approach 2:
Outer codes are introduced as intermediary components between the channel and the inner PAC codes. These outer codes perform initial error correction, reducing the burden on the sequential decoder and stabilizing computational complexity by handling obvious errors before they propagate through the complex PAC decoding process.
2Reliability
If sequential decoding is used for PAC codes, then channel polarization benefits are exploited, but throughput is bottlenecked due to sequential processing requirements
Solution Approach 1:
The sequential decoding process is segmented into multiple parallel layers. Each layer can be processed independently or with minimal inter-layer dependency, enabling parallel execution across multiple processing units. This maintains the benefits of channel polarization while dramatically increasing throughput by eliminating the single-threaded sequential bottleneck.
Solution Approach 2:
The decoding architecture transitions from a single-dimensional sequential process to a multi-dimensional layered structure. This dimensional expansion allows simultaneous processing across layers, effectively adding a parallel processing dimension that preserves polarization benefits while overcoming throughput limitations.
3Productivity
If multi-core processors are used to increase throughput, then parallel decoding is enabled, but chip area and cost increase due to extra memory requirements
Solution Approach 1:
Multiple processing cores share common memory resources and control structures for the layered decoding process. Instead of each core having dedicated memory, the architecture merges memory resources into shared pools that serve multiple cores, reducing total chip area while maintaining parallel throughput capability through efficient memory arbitration and access protocols.
Data Source
AI summary
An encoder 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 counts layers and carries out an inner decoding operation for a layered polarization adjusted convolutional (LPAC) code to generate an inner decoder decision {tilde over (b)}i from a concatenated decoder input array y and a cumulative decision feedback ({circumflex over (b)}1, {circumflex over (b)}2, . . . , {circumflex over (b)}i−1). The decoder carries out an outer decoding operation to generate from {tilde over (b)}i an outer decoder decision âi, and carries out a reencoding operation to generate a decision feedback {circumflex over (b)}i from âi, where the number of layers is an integer greater than one, with a concatenated decoder output block {circumflex over (d)} being generated from outer decoder decisions.