Nearly optimal multiuser codes for the binary adder channel

Coding schemes for the T-user binary adder channel are investigated. Recursive constructions are given for two families of mixed-rate, multiuser codes. It is shown that these basic codes can be combined by time-sharing to yield codes approaching most rates in the T-user capacity region. In particular, the best codes constructed herein achieve a sum-rate, R/sub 1/+...+R/sub T/, which is higher than all previously reported codes for almost every T and is within 0.547-bit-per-channel use of the information-theoretic limit. Extensions to a T-user, Q-frequency adder channel are also discussed.

[1]  Eli Plotnik.  Code constructions for asynchronous random multiple-access to the adder channel , 1993, IEEE Trans. Inf. Theory.

[2]  Shih-Chun Chang,et al.  Further results on coding for T-user multiple-access channels , 1984, IEEE Trans. Inf. Theory.

[3]  Jack Keil Wolf.  Multi-User Communication Networks , 1978 .

[4]  Henk C. A. van Tilborg.  An upper bound for codes for the noisy two-access binary adder channel , 1986, IEEE Trans. Inf. Theory.

[5]  B. Rimoldi,et al.  Coding for the F-Adder Channel: Two Applications of Reed Solomon Codes , 1993, Proceedings. IEEE International Symposium on Information Theory.

[6]  Henk C. A. van Tilborg,et al.  A family of good uniquely decodable code pairs for the two-access binary adder channel , 1985, IEEE Trans. Inf. Theory.

[7]  Dusan B. Jevtic.  Disjoint uniquely decodable codebooks for noiseless synchronized multiple-access adder channels generated by integer sets , 1992, IEEE Trans. Inf. Theory.

[8]  James L. Massey,et al.  The collision channel without feedback , 1985, IEEE Trans. Inf. Theory.

[9]  John H. Wilson.  Error-correcting codes for a T-user binary adder channel , 1988, IEEE Trans. Inf. Theory.

[10]  Peter Mathys,et al.  A class of codes for a T active users out of N multiple-access communication system , 1990, IEEE Trans. Inf. Theory.

[11]  Thomas J. Ferguson.  Generalized T-user codes for multiple-access channels , 1982, IEEE Trans. Inf. Theory.

[12]  Jack K. Wolf,et al.  On the T-user M-frequency noiseless multiple-access channel with and without intensity information , 1981, IEEE Trans. Inf. Theory.

[13]  E. J. Weldon,et al.  Coding for T-user multiple-access channels , 1979, IEEE Trans. Inf. Theory.

[14]  Jack K. Wolf,et al.  The capacity region of a multiple-access discrete memoryless channel can increase with feedback (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[15]  Henk C. A. van Tilborg.  Upper bounds on |C2| for a uniquely decodable code pair (C1, C2) for a two-access binary adder channel , 1983, IEEE Trans. Inf. Theory.

[16]  Tadao Kasami,et al.  Graph theoretic approaches to the code construction for the two-user multiple- access binary adder channel , 1983, IEEE Trans. Inf. Theory.

[17]  Jack K. Wolf,et al.  Some very simple codes for the nonsynchronized two-user multiple-access adder channel with binary inputs (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[18]  Henry Herng-Jiunn Liao,et al.  Multiple access channels (Ph.D. Thesis abstr.) , 1973, IEEE Trans. Inf. Theory.

[19]  Thomas H. E. Ericson,et al.  The noncooperative binary adder channel , 1986, IEEE Trans. Inf. Theory.

[20]  Shu Lin,et al.  Nonhomogeneous Trellis codes for the Quasi-Synchronous Multiple-Access Binary adder channel with Two Users , 1986, IEEE Trans. Inf. Theory.

[21]  Toby Berger,et al.  Some families of zero- error block codes for the two-user binary adder channel with feedback , 1987, IEEE Trans. Inf. Theory.

[22]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[23]  László Györfi,et al.  Superimposed codes in Rn , 1988, IEEE Trans. Inf. Theory.