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On linear structure and phase rotation invariant properties of block M-PSK modulation codes

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4 Author(s)
Kasami, T. ; Osaka Univ., Japan ; Takata, T. ; Fujiwara, T. ; Shu Lin

Two important structural properties of block M(=2' )-ary PSK modulation codes, linear structure and phase symmetry, are investigated. An M-ary modulation code is first represented as a code with symbols from the integer group SM-PSK=(0,1,2,---,M-1) under modulo-M addition. Then the linear structure of block M-PSK modulation codes over SM-PSK with respect to modulo- M vector addition is defined, and conditions are derived under which a block M-PSK modulation code is linear. Once the linear structure is developed, the phase symmetry of block M-PSK modulation codes is studied. In particular, a necessary and sufficient condition for a block M-PSK modulation code that is linear as a binary code to be invariant under 2h/180°M phase rotation, for 1⩽hl is derived. Finally, a list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 1 )