Decoding cosets of first-order Reed-Muller code

Proper encoding of transmitted information can improve the performance of a communication system. To recover the information at the receiver it is necessary to decode the received signal. For many codes the complexity and slowness of the decoder is so severe that the code is not feasible for practical use. This thesis considers the decoding problem for one such class of codes, the comma-free codes related to the first-order Reed-Muller codes.

A factorization of the code matrix is found which leads to a simple, fast, minimum memory, decoder. The decoder is modular and only n modules are needed to decode a code of length 2ⁿ. The relevant factorization is extended to any code defined by a sequence of Kronecker products.

The problem of monitoring the correct synchronization position is also considered. A general answer seems to depend upon more detailed knowledge of the structure of comma-free codes. However, a technique is presented which gives useful results in many specific cases.