Lossless Channel is a #Discrete Memoryless Channel (DMC) that has only one non-zero element in each column as shown in Channel Matrix# :
$$ P = \left[ \begin{array}{ccccc} \frac{3}{4} & \frac{1}{4} & 0 & 0 & 0\\ 0 & 0 & \frac{1}{3} & \frac{2}{3} & 0\\ 0 & 0 & 0 & 0 & 1 \end{array} \right] $$
Noiseless Channel is a #Discrete Memoryless Channel (DMC) if it satisfies both characteristics of #Deterministic Channel and #Lossless Channel. It has only one non-zero element for each row and column, which also means that the sizes for both input alphabet and output alphabet are the same, i.e., \(j-1 = k-1\).