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• W4381199143 abstract "Huffman Codes are <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>optimal</i> Instantaneous Fixed-to-Variable (FV) codes in which every source symbol can only be encoded by one codeword. Relaxing these constraints permits constructing better FV codes. More specifically, recent work has shown that AIFV- <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> codes can beat Huffman coding. AIFV- <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> codes construct an <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> -tuple of different coding trees between which the code alternates and are only <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>almost instantaneous</i> (AI). This means that decoding a word might require a delay of a finite number of bits. Current algorithms for constructing optimal AIFV- <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> codes are iterative processes that construct progressively “better sets” of code trees. The processes have been proven to finitely converge to the optimal code but with no known bounds on the convergence rate. This paper derives a geometric interpretation of the space of binary AIFV-2 codes, permitting the development of the first polynomially time-bounded procedure for constructing optimal AIFV codes. This binary-search like procedure will run in <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>O</i> ( <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</i> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>3</sup> <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>b</i> ) time, where <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</i> is the number of symbols in the source alphabet and <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>b</i> is the maximum number of bits used to encode any one input probability." @default.
• W4381199143 created "2023-06-20" @default.
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• W4381199143 date "2023-10-01" @default.
• W4381199143 modified "2023-09-30" @default.
• W4381199143 title "A Polynomial Time Algorithm for Constructing Optimal Binary AIFV-2 Codes" @default.
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• W4381199143 doi "https://doi.org/10.1109/tit.2023.3287587" @default.
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