A technique is presented for constructing (d,k) block codes capable of detecting single bit errors and single peak-shift errors in consecutive two runs. This constrains the runlengths in the code sequences to odd numbers. The capacities and the cardinalities for finite code length of these codes are described. A technique is also proposed for constructing (d,k) block codes capable of correcting single peak-shift errors.

Runlength-limited block codes are investigated. These codes are useful for storing data in storage devices. Since most devices are not noiselss, the codes are often required to have some error-control capability. We consider runlength-limited codes that can correct or detect unidirectional byte errors. Some constructions of such codes are presented.

In this letter, we consider a magnetic or optical recording system employing a concatenated code that consists of a runlength-limited (d, k) block code as an inner code and a byte-error-correcting code as an outer code. (d, k) means that any two consecutive ones in the code bit stream are separated by at least d zeros and by at most k zeros. The minimum separation d and the maximum separation k are imposed in order to reduce intersymbol interference and extract clock control from the received bit stream, respectively. This letter recommends to use as the outer code a unidirectional-byte-error-correcting code instead of an ordinary byte-error-correcting code. If we devise the mapping of the code symbols of the outer code onto the codewords of the inner code, we may improve the error performance. Examples of the mappings are described.

We propose five classes of variable length codes for encoding positive integers: One is a class of codes having constant Hamming weight. The other four classes of codes have a prefix and a suffix in a codeword. The prefix indicates the weight or the length of the suffix and variable length constant weight codes are used for the prefixes and the suffixes of some of these codes. For encoding of these codes we can use Schalkwijk's algorithm. It is shown that some of the proposed codes are universal and asymptotically optimal in the meaning that P. Elias has defined. We compare them with other known codes from the viewpoints of the length of the codewords corresponding to integers 2M (M=0, 1, , 30) and the average codeword length for two sources: 26 letters in English sentences and the geometrically distributed positive integers. The results shows that some of the proposed codes which are universal and asymptotically optimal are more efficient than the known codes.

In this paper, a rate k/n punctured convolutional code is considered as a time-varying code with period k. The punctured convolutional codes with time-varying constraint length are studied. For these codes, new maximum likelihood decoding techniques are proposed. Not only for the binary symmetric channel but also for any discrete memoryless channel, these decoding techniques can periodically reduce the number of survivors and comparisons in the decoding process. On the basis of the proposed decoding techniques, new classes of punctured convolutional codes are introduced. Computer searches are perfermed to construct good codes from these classes.

Asymptotic bounds are considered for unidirectional byte error-correcting codes. Upper bounds are developed from the concepts of the Singleton, Plotkin, and Hamming bounds. Lower bounds are also derived from a combination of the generalized concatenated code construction and the Varshamov-Gilbert bound. As the result, we find that there exist codes of low rate better than those on the basis of Hamming distance with respect to unidirectional byte error-correction.