Shannon in his 1956 seminal paper introduced the concept of the zero error capacity, C0, of a noisy channel. This is defined as the least upper bound of rates, at which, it is possible to transmit information with zero probability of error. At present not many codes are known to achieve the zero error capacity. In this paper, some codes which achieve zero error capacities in limited magnitude error channels are described. The code lengths of these zero error capacity achieving codes can be of any finite length n=1,2,..., in contrast to the long lengths required for the known regular capacity achieving codes, such as turbo codes, LDPC codes, and polar codes. Both wrap around and non-wrap around limited magnitude error models are considered in this paper. For non-wrap around error model, the exact value of zero error capacities is derived, and optimal non-systematic and systematic codes are designed. The non-systematic codes achieve the zero error capacity with any finite length. The optimal systematic codes achieve the systematic zero error capacity of the channel, which is defined as the zero error capacity with the additional requirements that the communication must be carried out with a systematic code. It is also shown that the rates of the proposed systematic codes are equal to or approximately equal to the zero error capacity of the channel. For the wrap around model bounds are derived for the zero error capacity and in many cases the bounds give the exact value. In addition, optimal wrap around non-systematic and systematic codes are developed which either achieve or are close to achieving the zero error capacity with finite length.

Shannon in his 1956 seminal paper introduced the concept of the zero error capacity, Co, of a noisy channel. This is defined as the least upper bound of rates at which it is possible to transmit information with zero probability of error. At present not many codes are known to achieve the zero error capacity. In this paper, some codes which achieve zero error capacities in limited magnitude error channels are described. The code lengths of these zero error capacity achieving codes can be of any finite length n = 1, 2,..., in contrast to the long lengths required for the known regular capacity achieving codes such as turbo codes, LDPC codes and polar codes. Both non-systematic and systematic codes are described.

Gender inclusiveness in computing settings is receiving a lot of attention, but one potentially critical factor has mostly been overlooked -- software itself. To help close this gap, we recently created GenderMag, a systematic inspection method to enable software practitioners to evaluate their software for issues of gender-inclusiveness. In this paper, we present the first real-world investigation of software practitioners' ability to identify gender-inclusiveness issues in software they create/maintain using this method. Our investigation was a multiple-case field study of software teams at three major U.S. technology organizations. The results were that, using GenderMag to evaluate software, these software practitioners identified a surprisingly high number of gender-inclusiveness issues: 25% of the software features they evaluated had gender-inclusiveness issues.

The error detecting problem for limited magnitude errors over high radix channels is studied. In this error model, the error magnitude does not exceed a certain limited value and it is known beforehand. For asymmetric, unidirectional, and symmetric channels, both all and t error detecting codes are studied. In all these cases, close-to-optimal codes are proposed.

A relatively new model of error correction is the limited magnitude error model. That is, it is assumed that the absolute difference between the sent and received symbols is bounded above by a certain value$l$. In this paper, we propose systematic codes for asymmetric limited magnitude channels that are able to correct a single error. We also show how this construction can be slightly modified to design codes that can correct a single symmetric error of limited magnitude. The designed codes achieve higher code rates than single error correcting codes previously given in the literature.

This paper gives the theory and design of efficient codes capable of correcting errors caused by the insertion and deletion of a repeated symbol in the information sequence. Two efficient methods are described. For any fixed t+, t-∈ IN, one method gives a fixed length scheme to encode k information bits into a systematic code of length n = k + r, with r = (t++ t-) log2k + O(log log k), capable of correcting the insertion of t+repeated symbols and, simultaneously, correcting the deletion of t-repeated symbols in every codeword. The second method is a systematic variable length scheme which on average doubles the number of information bits k compared to the first method. The time complexity of the entire coding process for both schemes is T = O (k + (1+min{t-, t+})t) multiplication operations over a finite field containing k elements. The space complexity is S = O(k+t) field memory elements. The generalization to the m-ary case, m ≥ 2, is also given.

Systematic q-ary (q> 2) codes capable of correcting all asymmetric errors of maximum magnitudel, where l ¿ q - 2, are given. These codes are shown to be optimal. Further, simple encoding/decoding algorithms are described. The proposed code can be modified to design codes correcting all symmetric errors of maximum magnitudel, wherel¿ (q-2)/2.

Systematic q-ary (q > 2) codes capable of correcting all asymmetric errors of maximum magnitude l, where l ¿ q-2, are given. These codes are shown to be optimal. Further, simple encoding/decoding algorithms are described.

In diversity combining automatic repeat request (ARQ), erroneous packets are combined together forming a single, more reliable, packet. In this paper, we give a diversity combining scheme for the m-ary unidirectional channel. A system using the given scheme with a t-unidirectional error detecting code is able to correct up to Emax= [t/2] unidirectional errors. Simulation results show that the underlined diversity combining protocol significantly increases the channel throughput over plain ARQ. To use the given scheme, the decoder should be able to decide the error type (increasing or decreasing). Hence, we give simple techniques to make this decision for various unidirectional error detecting codes.