Quasi-cyclic unit memory convolutional codes

Unit memory convolutional codes with generator matrices, which are composed of circulant submatrices, are introduced. This structure facilitates the analysis of efficient search for good codes. Equivalences among such codes and some of the basic structural properties are discussed. In particular, catastrophic encoders and minimal encoders are characterized and dual codes treated. Further, various distance measures are discussed, and a number of good codes, some of which result from efficient computer search and some of which result from known block codes, are presented. >

[1]  Gregory S. Lauer Some optimal partial-unit-memory codes (Corresp.) , 1979, IEEE Trans. Inf. Theory.

[2]  Tom Verhoeff,et al.  An updated table of minimum-distance bounds for binary linear codes , 1987, IEEE Trans. Inf. Theory.

[3]  Rolf Johannesson,et al.  Further results on binary convolutional codes with an optimum distance profile (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[4]  G. Solomon,et al.  A Connection Between Block and Convolutional Codes , 1979 .

[5]  Knud J. Larsen Comments on 'An efficient algorithm for computing free distance' by Bahl, L., et al , 1973, IEEE Trans. Inf. Theory.

[6]  Jørn Justesen,et al.  Bounds on distances and error exponents of unit memory codes , 1983, IEEE Trans. Inf. Theory.

[7]  P. Piret,et al.  Structure and constructions of cyclic convolutional codes , 1976, IEEE Trans. Inf. Theory.

[8]  Rolf Johannesson,et al.  Robustly optimal rate one-half binary convolutional codes (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[9]  Solomon W. Golomb,et al.  Shift Register Sequences , 1981 .

[10]  G. David Forney,et al.  Convolutional codes I: Algebraic structure , 1970, IEEE Trans. Inf. Theory.

[11]  Daniel J. Costello,et al.  Distance and computation in sequential decoding , 1976, IEEE Transactions on Communications.

[12]  Daniel J. Costello,et al.  Asymptotically catastrophic convolutional codes , 1980, IEEE Trans. Inf. Theory.

[13]  Lin-nan Lee,et al.  Short unit-memory byte-oriented binary convolutional codes having maximal free distance (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[14]  Sudhakar M. Reddy,et al.  Circulant bases for cyclic codes (Corresp.) , 1970, IEEE Trans. Inf. Theory.

[15]  Lalit R. Bahl,et al.  An efficient algorithm for computing free distance (Corresp.) , 1972, IEEE Trans. Inf. Theory.

[16]  Charles L. Weber,et al.  Minimum weight convolutional codewords of finite length (Corresp.) , 1976, IEEE Trans. Inf. Theory.