A Construction of Channel Code, Joint Source-Channel Code, and Universal Code for Arbitrary Stationary Memoryless Channels Using Sparse Matrices

A channel code is constructed using sparse matrices for stationary memoryless channels that do not necessarily have a symmetric property like a binary symmetric channel. It is also shown that the constructed code has the following remarkable properties. 1. Joint source-channel coding: Combining channel code with lossy source code, which is also constructed by sparse matrices, a simpler joint source-channel code can be constructed than that constructed by the ordinary block code. 2. Universal coding: The constructed channel code has a universal property under a specified condition.