GEL Codeword Structure with SPC-Aided Flexible Decoding
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Solution Overview
Problem
The existing Generalized Error-Locating (GEL) codeword structure is inflexible and has high implementation complexity and overheads due to exact division constraints between row and column codes, which complicates decoding and increases power consumption in data center interconnects.
Innovation Solution
The proposed method involves obtaining a target check matrix through elementary transformation of the original check matrix, using the parity bit of the column code for Reed-Solomon RS coding of the row code, and adding a Single Parity Check (SPC) parity bit to facilitate error location checking at the first layer, allowing for improved decoding efficiency without exact division constraints between the finite fields of the row and column codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exact division constraint is imposed between row code and column code bit widths, then decoding can be performed, but device complexity and codeword overheads increase
Solution Approach 1:
The patent extracts the exact division constraint from the GEL codeword structure, allowing row code and column code to be defined in different finite fields without requiring l1 to be exactly divisible by l2. This removal of the constraint simplifies the system while maintaining decoding capability through modified decoding procedures.
Solution Approach 2:
The patent changes the parameters of the finite fields by allowing l1 and l2 to be any positive integers without the division constraint. This parameter change enables greater flexibility in code design while the modified decoding algorithm compensates for the relaxed constraints to maintain reliability.
2Reliability
If exact division constraint is imposed between row code and column code bit widths, then decoding can be performed, but power consumption increases
Solution Approach 1:
The patent removes the exact division constraint that causes increased power consumption, allowing more efficient code configurations. The relaxed constraints enable optimization of finite field parameters to reduce computational complexity and power consumption while maintaining decoding capability.
3Reliability
If exact division constraint is imposed between row code and column code bit widths, then decoding can be performed, but codeword overheads increase
Solution Approach 1:
The patent extracts and removes the exact division constraint that leads to increased codeword overheads. By allowing independent selection of finite field parameters l1 and l2, the system can optimize codeword structure to reduce overhead while maintaining necessary decoding capability.
4Productivity
If decoding is performed at the first layer without prior information, then decoding process can start, but decoding success rate decreases
Solution Approach 1:
The patent applies preliminary action by pre-defining the SPC parity bit and its relationship with the first layer code before decoding begins. This preliminary setup provides the decoding algorithm with necessary initial information, improving success rate while maintaining efficient decoding process initiation.
Data Source
AI summary
An HC of a code B is first transformed into an HB. A parity bit of the code B is obtained by performing an operation on the HB and an information bit of the code B. The parity bit is used to perform RS coding on a code A, to obtain a parity bit of the code A. A check code of a GEL code is obtained by performing an operation on the parity bits of the code B and the code A. Finally, a single bit parity check bit is added. The code A is defined in a finite field GF (2l1), the code B is defined in a finite field GF (2l2), and l1 and l2 are positive integers. A success rate of decoding the code A in the first row can be improved using this method.