Title :
Minimal Trellis Modules and Equivalent Convolutional Codes
Author :
Tang, Hung-Hua ; Lin, Mao-Chao ; Filho, Bartolomeu F Uchôa
Author_Institution :
Dept. of Electr. Eng., Univ. of Sci. & Technol., Taoyuan, Taiwan
Abstract :
In this correspondence, it is shown that some convolutional codes with distinct memory sizes of minimal encoders are equivalent in the sense that the minimal trellises of these codes are the shifted versions of one another. For an (n,k) binary convolutional code, the weight spectrum obtained from the minimal trellis may be slightly different from that obtained from the conventional code trellis with n-bit branches. Code search is conducted to find some good (n,n-1) binary convolutional codes. Bounds on the trellis complexity, measured by the number of states and the number of branches in the minimal trellis module, of any convolutional code and its equivalent codes are also derived.
Keywords :
binary codes; convolutional codes; trellis codes; binary convolutional code; distinct memory sizes; equivalent codes; minimal encoder; minimal trellis modules; weight spectrum; Block codes; Brazil Council; Convolutional codes; Decoding; Information theory; Materials science and technology; State-space methods; Error-correction coding; convolutional codes; minimal trellis; minimal trellis module; trellis complexity;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2006.878225