On the Construction of Multiply Constant-Weight Codes

Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, two methods of constructing MCWCs are presented following the concatenation methodology. In other words, MCWCs are constructed by concatenating approximate outer codes and inner codes. Besides, several classes of optimal MCWCs are derived from these methods. In the first method, the outer codes are [Formula: see text]-ary codes and the inner codes are constant-weight codes over [Formula: see text]. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves Johnson bound, then the resulting MCWC is optimal. In the second method, the outer codes are [Formula: see text]-ary codes and the inner codes are MCWCs. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves the Johnson bound, then the resulting MCWC is optimal.

Novel Approaches for Efficient Delay-Insensitive Communication

The increasing complexity and modularity of contemporary systems, paired with increasing parameter variabilities, makes the availability of flexible and robust, yet efficient, module-level interconnections instrumental. Delay-insensitive codes are very attractive in this context. There is considerable literature on this topic that classifies delay-insensitive communication channels according to the protocols (return-to-zero versus non-return-to-zero) and with respect to the codes (constant-weight versus systematic), with each solution having its specific pros and cons. From a higher abstraction, however, these protocols and codes represent corner cases of a more comprehensive solution space, and an exploration of this space promises to yield interesting new approaches. This is exactly what we do in this paper. More specifically, we present a novel coding scheme that combines the benefits of constant-weight codes, namely simple completion detection, with those of systematic codes, namely zero-effort decoding. We elaborate an approach for composing efficient “Partially Systematic Constant Weight” codes for a given data word length. In addition, we explore cost-efficient and orphan-free implementations of completion detectors for both, as well as suitable encoders and decoders. With respect to the protocols, we investigate the use of multiple spacers in return-to-zero protocols. We show that having a choice between multiple spacers can be beneficial with respect to energy efficiency. Alternatively, the freedom to choose one of multiple spacers can be leveraged to transfer information, thus turning the original return-to-zero protocol into a (very basic version of a) non-return-to-zero protocol. Again, this intermediate solution can combine benefits from both extremes. For all proposed solutions we provide quantitative comparisons that cover the whole relevant design space. In particular, we derive coding efficiency, power efficiency, as well as area effort for pipelined and non-pipelined communication channels. This not only gives evidence for the benefits and limitations of the presented novel schemes—our hope is that this paper can serve as a reference for designers seeking an optimized delay-insensitive code/protocol/implementation for their specific application.