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Alex Towell6d ago • 10 min read
Synthesis: Codecs as Structure
The series closes by restating the codes-as-priors thesis across all twelve instances and connecting...
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Alex Towell6d ago • 9 min read
McMillan's Converse
Any length vector satisfying Kraft has a prefix-free code. Here is the construction.
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Alex Towell6d ago • 7 min read
Rice / Golomb
Rice and Golomb codes are parametric: a single parameter k (or m) tunes the code to a specific geome...
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Alex Towell6d ago • 9 min read
Huffman Coding
Given a finite distribution, Huffman's algorithm builds the prefix-free code with minimum expected l...
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Alex Towell6d ago • 7 min read
VByte / Varint
VByte trades bit-level precision for byte-alignment, and that trade wins in practice. Most productio...
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Alex Towell6d ago • 7 min read
Fibonacci Coding
Fibonacci coding uses Zeckendorf's representation to produce self-synchronizing codewords. Every cod...
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Alex Towell6d ago • 7 min read
Elias Delta and Omega
Elias delta and omega extend Elias gamma by recursively encoding the length prefix. Each step yields...
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Alex Towell6d ago • 8 min read
Universal Codes as Priors
Every prefix-free code is a hypothesis about the source. The codeword lengths determine an implicit ...
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Alex Towell6d ago • 7 min read
Unary and Elias Gamma
Unary and Elias gamma are the two simplest universal codes. Unary encodes n in n bits; gamma in 2 lo...
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Alex Towell6d ago • 9 min read
Kraft's Inequality
Which codeword-length vectors are achievable by prefix-free codes? Kraft's inequality is the answer.
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Alex Towell6d ago • 7 min read
Arithmetic Coding
Arithmetic coding closes the gap between Huffman's per-symbol integer lengths and true entropy. A si...
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