Incremental Redundancy ECC Decoding with Partial Parity Checks
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Solution Overview
Problem
Incremental redundancy schemes in error correction coding face challenges in efficiently decoding code words due to insufficient error correction capability and increased complexity, latency, and power consumption, particularly when initial decoding attempts fail.
Innovation Solution
The method involves using a set of parity check equations defined such that any parity bit appears in multiple equations, with a partial subset of parity bits and equations used for initial decoding and all bits and equations for re-decoding, optimizing the parity check matrix to be nearly lower-triangular and ensuring each parity bit participates in multiple equations, thereby simplifying the decoding process and avoiding convergence to incorrect code words.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If incremental redundancy schemes increase error correcting capability according to channel state, then error correction reliability is improved, but device complexity and power consumption increase
Solution Approach 1:
The parity check equations are segmented into two subsets: a first subset used for initial decoding attempts and a second subset used when initial decoding fails. This segmentation allows the decoder to start with a simpler, smaller set of equations, reducing initial complexity while maintaining the capability to handle more complex error cases by activating the second subset only when needed.
Solution Approach 2:
The decoding process dynamically adapts its complexity based on the channel state and decoding success. The system transitions from using only the first subset of parity check equations to using both subsets when initial decoding fails, creating a dynamic complexity adjustment that matches the actual error conditions rather than always using maximum complexity.
2Reliability
If incremental redundancy schemes use more parity bits for re-decoding, then error correction reliability is improved, but latency and power consumption increase
Solution Approach 1:
The system performs preliminary decoding using only the first subset of parity check equations before attempting to use the full set. This preliminary action allows many decoding operations to complete quickly without invoking the more time-consuming full decoding process, thereby reducing average latency while maintaining the ability to achieve high reliability when errors are present.
Solution Approach 2:
Instead of always applying the full set of parity check equations, the system applies only a partial subset initially. This partial action is sufficient for many cases, and the full action is reserved for when the partial action fails, optimizing the balance between speed and reliability.
3Reliability
If all parity check equations are used for every decoding attempt, then error correction capability is maximized, but power consumption and complexity increase
Solution Approach 1:
The complete set of parity check equations is segmented into two subsets, allowing the decoder to consume less power by using only the first subset for initial attempts. The second subset is activated only when needed, creating a power-efficient segmented approach that maintains maximum error correction capability when required.
Solution Approach 2:
The decoding process uses periodic action by attempting decoding with the first subset, evaluating success, and only then periodically activating the second subset if needed. This periodic activation of the full equation set reduces average power consumption while maintaining the capability to achieve maximum error correction when errors occur.
Data Source
AI summary
A method includes accepting input including at least part of a codeword that has been encoded by an ECC defined by a set of parity check equations. The codeword includes data bits and parity bits. A decoding process is applied to the codeword using the data bits and only a first partial subset of parity bits in the input, and using only a second partial subset of equations. Upon a failure to decode the codeword using the partial subsets, the codeword is re-decoded using the data bits and all parity bits in the input, and using all equations. The set of parity check equations is defined such that any parity bit in the codeword appears in multiple equations, and any parity bit in the first partial subset of the parity bits appears in a plurality of equations in the second partial subset of the equations.