Coding for the multiple-access adder channel

• Authors: B. Laczay
• Venue: General Theory of Information Transfer and Combinatorics
• Year: 2006

The coding problem for the multiple-access adder channel is considered, both for the case of permanent user activity and partial user activity. For permanent user activity, Khachatrian [10] has written an excellent survey for general, symmetric and non-symmetric rates. In this survey, we only deal with the special symmetric rate case, where all users have two codewords. The length of the shortest possible code is characterized, and amongst others, we present the code construction of Chang and Weldon [5]. We also deal with the case of signature coding (where we mean that one of the codewords for each user is the zero vector). As a code construction of this kind, we show Lindström's one [12]. We also consider partial user activity. For this case, the resulting upper and lower bounds on the length of the shortest possible code differs by a factor of two. There are some constructions for suboptimal codes, but we do not know about constructions with length approaching the upper bound. The signature code is similar to the Bm code examined by D'yachkov and Rykov [7]. It is interesting, that the upper and lower bounds for the length of Bm codes are the same as for signature codes.