Phase-Invariant Codewords for Long Message Encoding
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Solution Overview
Problem
Current data encoding techniques require excessive storage and computational resources for encoding and decoding longer messages, as the resources needed grow exponentially with the length of the codeword, making it difficult to represent messages with longer bit strings.
Innovation Solution
The system divides a message into substrings and associates each substring with a phase invariant codeword, using a lookup table to encode a composite codeword on a data-bearing medium, allowing for longer messages to be encoded with reduced storage requirements by using a structured array of bits with circular shifting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If conventional encoding techniques are used to represent longer messages, then the message length increases, but the storage and computational resources required grow exponentially
Solution Approach 1:
The patent divides a long message into multiple substrings, where each substring is encoded using a separate phase invariant codeword. This segmentation allows the system to handle longer messages by breaking them into manageable chunks, avoiding the exponential resource growth that would occur with a single codeword for the entire message.
Solution Approach 2:
The patent changes the parameter of codeword phase by applying circular shifts to create phase invariant codewords. This parameter transformation allows the decoder to correctly interpret messages regardless of synchronization position, enabling more flexible and efficient encoding of longer messages without requiring additional storage resources.
2Loss of information
If conventional encoding techniques are used to represent longer messages, then the message length increases, but the computational resources required for encoding and decoding grow exponentially
Solution Approach 1:
By segmenting the message into substrings that can be independently encoded with phase invariant codewords, the computational complexity for each encoding operation remains manageable. The segmentation approach allows parallel processing of substrings and simplifies the decoding process by enabling independent phase correction for each codeword.
Solution Approach 2:
The patent performs preliminary encoding of substrings into phase invariant codewords using lookup tables before transmission or storage. This preliminary action prepares the data in a format that requires minimal computational resources during decoding, as the phase invariant property allows for simple correlation-based synchronization and decoding operations.
3Adaptability or versatility
If phase invariant codewords are used with circular shifting, then synchronization flexibility improves, but codeword structure complexity increases
Solution Approach 1:
The patent applies circular shifts to change the phase parameter of codewords, creating phase invariant representations. This parameter transformation provides synchronization flexibility because the decoded message remains correct regardless of the starting position. The structure complexity is managed by using systematic circular shift operations and lookup tables rather than completely new codeword designs.
Data Source
AI summary
Disclosed herein are a system, non-transitory computer-readable medium, and method for encoding and decoding information on a data bearing medium. A message comprising a bit string is read. A plurality of substrings in the message may be associated with a phase invariant codeword.