Enumerative Coding Graph for DC-RLL Constraint Satisfaction
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Solution Overview
Problem
Existing enumerative coding techniques cannot generate codes that conform to complex constraints such as alternating RLL, interleaved RLL, or DC limited constraints, and are limited in encoding every possible dataword input.
Innovation Solution
The use of an enumerative coding graph with states and cardinalities that allow for encoding and decoding of constrained codes, including DC-RLL constraints, by selecting branches based on data comparisons and adjusting cardinalities to satisfy specific constraints, and employing precoders to further process codewords.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing enumerative coding techniques are used, then simple RLL constraints can be satisfied, but complex constraints such as alternating RLL, interleaved RLL, or DC limited constraints cannot be satisfied
Solution Approach 1:
The coding process is divided into multiple stages: a first enumerative encoder handles basic RLL constraints, followed by a precoder that applies additional transformations to satisfy complex constraints like alternating RLL, interleaved RLL, or DC limited constraints. This segmentation allows each stage to specialize in specific constraint types without requiring complete redesign of the entire coding system.
Solution Approach 2:
A precoder is introduced as an intermediary component between the enumerative encoder and the output. The precoder receives codewords from the enumerative encoder and applies additional processing to ensure compliance with complex constraints. This intermediary layer enables the system to satisfy diverse constraint requirements without complicating the core enumerative encoding logic.
2Reliability
If enumerative coding is used to satisfy complex constraints, then more codewords can conform to constraints, but the encoding graph size increases
Solution Approach 1:
The encoding system is segmented into a first enumerative encoder for basic constraints and a precoder for complex constraints. This allows the graph size to be managed in stages, where each encoder handles a subset of constraint requirements, preventing exponential growth of the overall encoding graph while maintaining reliability through multi-stage constraint satisfaction.
Solution Approach 2:
The precoder performs preliminary processing on codewords generated by the enumerative encoder before final output. By applying constraint-satisfying transformations in advance, the system ensures compliance with complex constraints without requiring the enumerative encoder itself to manage the full complexity, thus controlling graph size while maintaining error detection and correction capabilities.
3Adaptability or versatility
If a complete enumerative coding graph is used to encode all possible dataword inputs, then all datawords can be encoded, but the graph becomes too large to be practical
Solution Approach 1:
The encoding functionality is segmented across multiple encoders with specialized roles. The first enumerative encoder handles the primary encoding task with a manageable graph size, while the precoder handles additional constraint requirements. This segmentation allows the system to encode all possible dataword inputs without requiring a single excessively large graph, as the workload is distributed across multiple smaller, more practical encoding components.
Solution Approach 2:
The precoder serves multiple functions: it processes codewords from the enumerative encoder, applies transformations to satisfy complex constraints, and ensures compliance with various constraint types (alternating RLL, interleaved RLL, DC limited). This multi-functionality allows the system to maintain comprehensive dataword coverage while keeping individual graph sizes manageable, as the precoder handles diverse constraint requirements through a single versatile component.
Data Source
AI summary
Systems and methods are provided for encoding and decoding constrained codewords using an enumerative coding graph. The constrained codewords may contain run-length and DC level limits. The enumerative coding graph contains a series of states and each state has multiple branches that lead to other states. Each state in the enumerative coding graph is associated with at least two bits of an enumerative codeword. Configuring the structure of the graph and cardinalities associated with each state allows the encoder to generate a code that conforms to defined constraints.