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Laying out the message of the Aztec Code

The Aztec Code is a type of 2D barcode that uses a unique layout and encoding scheme to store information.

Here's a detailed description of laying out the message in an Aztec Code:

Core and Reference Grid

1.Core Structure:

The Aztec Code starts with a core, typically a 14x14 pixel square centered on a 2x2 white pixel area.

The core contains the most critical information about the code, including the number of layers and check words.

2.Layers and Symbol Expansion:

The symbol can have multiple layers, expanding outward from the core.

Each layer adds rows and columns of alternating black and white pixels (reference grid) to maintain alignment and readability of the code.

Layers increase by 2 pixels on each side, resulting in odd-numbered dimensions (e.g., 17x17, 21x21, etc.).

3.Grid Expansion:

Reference grid rows and columns are added at specific intervals (±16 pixels for layers 1-4, ±32 pixels for layers 5-12, and so on).

This grid helps readers maintain alignment and decode the symbol accurately.

Message Layout

1.Starting Point:

The message starts at the top-left corner of the core and wraps around it clockwise in a 1-bit thick layer.

For a compact Aztec Code (smaller capacity), the message is divided into four 7-bit pieces.

For a full Aztec Code (larger capacity), the message is divided into four 10-bit pieces.

2.Orientation and Encoding:

The bits are encoded such that 1s are represented by black squares and 0s by white squares.

Encoding begins with the most significant bit of the number of layers and ends with the check words.

3.Padding:

If the total capacity of the symbol does not divide evenly by the code words, the main message is padded with 0 bits at the beginning.

These padding bits are excluded from the check word calculation and are skipped during decoding.

4.Spiral Encoding:

The main message is laid out in a counterclockwise spiral pattern around the outermost layers of the symbol.

This spiral pattern is 2-bits thick, placing the bit-stuffed data words on the outer layers and check words closer to the core.

5.Bit Placement:

Starting from the outer top-left of the entire symbol, bits are placed sequentially in a 2-bit wide column left-to-right and top-to-bottom.

After reaching 2 rows from the bottom, the pattern rotates 90 degrees counterclockwise and continues in a 2-bit high row bottom-to-top and left-to-right.

This spiral pattern continues until the top-left corner of the next inner layer is reached, ending just above the top-left corner of the core.

Summary

The Aztec Code's layout and encoding scheme ensure efficient use of space while allowing for reliable decoding. The core and reference grid structure provide alignment and readability, while the spiral encoding of the message maximizes data capacity and error detection capabilities. The distinct pattern of black and white pixels not only encodes information but also facilitates robust error correction and data recovery, making Aztec Code suitable for various applications requiring compact and reliable data storage.

 

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