GC Code Soft-Input Decoding With Supercode Trellises
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Solution Overview
Problem
Current error correction decoding methods for flash memories, particularly those using generalized concatenated codes, face inefficiencies in decoding complexity and residual error rates, especially in achieving very low bit error rates required for reliable data storage, due to high computational complexity and memory requirements.
Innovation Solution
A soft input decoding method for generalized concatenated codes that employs trellis-based sequential stack decoding with supercodes and list-of-two decoding, iteratively decoding levels to achieve low residual error rates, utilizing supercodes to reduce memory usage and combining with list-of-two decoding to enhance code rates and reduce errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If algebraic hard input decoding is used for GC codes, then decoding complexity is low and hardware implementation is fast, but residual error rates remain high and reliability is insufficient
Solution Approach 1:
The decoding process is segmented into multiple levels corresponding to the nested structure of GC codes. Each level processes a specific subset of codewords, with the first level handling the most reliable codewords and subsequent levels handling progressively less reliable ones. This segmentation allows the system to achieve low residual error rates by distributing the decoding workload across multiple simplified stages rather than requiring a single complex decoder.
Solution Approach 2:
The decoding system dynamically adapts its behavior based on channel conditions and error patterns. The multi-level structure allows the decoder to activate only the necessary levels based on the observed error rates, making the complexity adaptive rather than fixed. When channel conditions are good, only the first level needs to be active; when conditions deteriorate, additional levels are activated to maintain reliability.
2Reliability
If soft input decoding algorithms like Chase decoding or ordered statistic decoding are used, then performance approaches maximum-likelihood decoding, but hardware implementation complexity increases and speed decreases
Solution Approach 1:
The soft input decoding problem is segmented into multiple independent levels, each handling a specific portion of the decoding task. This segmentation transforms a single complex soft input decoding problem into several simpler decoding problems that can be solved more quickly and with less computational overhead, while collectively achieving performance接近 maximum-likelihood decoding.
Solution Approach 2:
Instead of applying full soft input decoding to all codewords, the system applies decoding actions selectively at different levels. The first level processes the most reliable codewords with simpler algorithms, while subsequent levels handle progressively fewer and less reliable codewords. This partial action approach achieves near-ML performance for the critical codewords without incurring the full computational cost of applying complex soft input decoding universally.
3Device complexity
If sequential stack decoding with trellis representation is used, then low computational complexity is achieved for small noise levels, but memory requirements grow exponentially with the number of redundancy bits
Solution Approach 1:
The trellis-based sequential stack decoding is segmented across multiple levels, with each level operating on a reduced subset of the full code space. This segmentation prevents the exponential memory growth by limiting the trellis depth and state space at each level, while the collective effect of all levels provides the necessary error correction capability.
Solution Approach 2:
The problem is transformed from a single high-dimensional decoding challenge into multiple lower-dimensional subproblems. By organizing the decoding process across the additional dimension of decoding levels, the system reduces the memory requirements at each individual level while maintaining the overall error correction performance through the coordinated operation of all levels.
4Reliability
If channels with quantized output providing only 2 or 3 bits of soft information are used, then implementation is simpler, but reliability-based decoding algorithms have insufficient information to achieve low error rates
Solution Approach 1:
The limited soft information from quantized channels is segmented and processed at multiple decoding levels. Each level extracts and utilizes the available reliability information in a manner appropriate to its specific decoding task, accumulating error correction capability across levels rather than requiring all the information to be available at a single decoding stage.
Solution Approach 2:
The decoding system dynamically adapts to the limited information availability by adjusting its strategy at different levels. When soft information is scarce, the system relies more heavily on the structural properties of the GC codes and the cumulative effect of multiple levels. The multi-level architecture allows the system to optimize its use of limited information resources rather than requiring a fixed amount of information at each stage.
Data Source
AI summary
The invention relates to a soft input decoding method and a decoder for generalized concatenated (GC) codes. The GC codes are constructed from inner nested block codes, such as binary Bose-Chaudhuri-Hocquenghem, BCH, codes and outer codes, such as Reed-Solomon, RS, codes. In order to enable soft input decoding for the inner block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In one aspect, the present invention applies instead a representation of the block codes based on the trellises of supercodes in order to reduce the memory requirements for the representation of the inner codes. This enables an efficient hardware implementation. In another aspect, the present invention provides a soft input decoding method and device employing a sequential stack decoding algorithm in combination with list-of-two decoding which is particularly well suited for applications that require very low residual error rates.