Unidirectional error-correcting (UEC) codes are presented that are suitable for memory systems in which data are stored in blocks consisting of tracks. UEC codes are proposed that can correct any error pattern consisting of unidirectional errors confined to a single track. For two or more information tracks, a code exists for any given nontrivial length. It is shown that the codes can be constructed for any large track length and codes can have significantly higher information rates than other such UEC codes.>

t-random-error correcting and all-unidirectional-error detecting (t-EC/AUED) codes obtained by appending a suffix to each codeword of a linear block code are presented. Although this technique has been previously used to construct such codes, a different approach is proposed that involves starting with a nonoptimal t-EC linear code to obtain more efficient t-EC/AUED codes. Specifically, t-EC/AUED codes constructed from an even-weight t-EC linear code are shown to require a shorter suffix than when a general t-EC linear code is used. The t-EC/AUED codes obtained in this manner are thoroughly compared to the best known codes, and are shown to require fewer bits in almost all cases.>

The probabilities of the bits produced by an optimal binary source encoder for a memoryless source are analyzed. The class of sources for which the probability of zero must equal 1/2 for any such encoder is described. Procedures that minimize (maximize) the absolute difference of the bit probabilities are discussed. Corresponding upper bounds are derived and compared for the class of uniform sources.>

Decoding rules to minimize the probability of information bit errors in binary linear block codes are investigated. A novel decoding rule is proposed and compared to a recently proposed rule (see M. Elia and G. Prati, 1985) and to the standard rule, with respect to both the information bit error rate and the information word error rate. It is concluded that the proposed rule not only can be implemented much more efficiently that the standard rule, but also is superior with respect to either error rate. Some particular codes have been presented to show that the authors' rule can coincide or can differ from Elia and Prati's rule when applied to a given code.>

A new lower bound, which is the tightest possible, is obtained for the redundancy of optimal bimuy prefix-condition (OBPC) codes for a memoryless source for which the probability of the most likely source letter is known. It is shown that this bound, and upper bounds obtained by Gallager and Johnsen, hold for infinite as well as finite source alphabets. Also presented are bounds on the redundancy of OBPC codes for sources satisfying the condition that each of the first several probabilities in the list of source probabilities is sufficiently large relative to the sum of the remaining probabilities.

Although optimal binary source coding using symbol blocks of increasing length must eventually yield a code having an average codeword length arbitrarily close to the source entropy, it is known that the sequence of average codeword lengths need not be nonincreasing. The sequence is, however, bounded above by the average codeword length of the source, and certain subsequences must be nondecreasing. Sufficient conditions are obtained describing sources for which a decrease in average codeword length is achieved when coding pairs of symbols. A sufficient condition specifying sources for which no such decrease is possible is also obtained.

The problem of achieving synchronization for variable-length source codes is addressed through the use of self-synchronizing binary prefix-condition codes. Although our codes are suboptimal in the sense of minimum average codeword length, they have the advantages of being generated by an explicit constructive algorithm, having minimal additional redundancy compared with optimal codes-as little as one additional bit introduced into the least likely codeword for a large class of sources-and having statistical synchronizing performance that improves on that of the optimal code in many cases.