The capacity region for W(write) U(unidirectional) M(memory) codes over an alphabet of size q for three of the cases as defined by G. Simonyi (1989) are derived. These are the cases where either the encoder, the decoder, or both know the old state of the WUM code. For the case where neither user knows the old state, an achievable rate region is derived. Also proved is a partial converse, showing that the achievable rate region may be equal to the capacity region. If one takes q=2, then the results obtained reduce to the known results for the binary WUM code.>

An achievable rate region for the binary multiplying channel is established such that block codes exist at all rate pairs within this region, with error probability that decreases exponentially with increasing block length. The result are generalized to asymmetrical rate pair.>

We have investigated the existence of some optimal burst-error-correcting codes. Several constructions and some nonexistence theorems are presented.

LetCbe the cyclic product code ofpsingle parity check codes of relatively prime lengthsn_{1}, n_{2},\cdots , n_{p} (n_{1} < n_{2} < \cdots < n_{p}). It is proven thatCcan correct2^{P-2}+2^{p-3}-1bursts of lengthn_{1}, andlfloor(\max\{p+1, \min\{2^{p-s}+s-1,2^{p-s}+2^{p-s-1}\}\}-1)/2\rfloorbursts of lengthn_{1}n_{2} \cdots n_{s} (2\leq s \leq p-2). Forp=3this means thatCis double-burst-n_{1}-correcting. An efficient decoding algorithm is presented for this code.