New Constructions of Codes for Asymmetric Channels via Concatenation

We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear single-error-correcting codes from ternary outer codes. We show that some of the Varshamov-Tenengol'ts-Constantin-Rao codes, a class of binary nonlinear codes for this channel, have a nice structure when viewed as ternary codes. In many cases, our ternary construction yields even better codes. For the nonbinary asymmetric channel, our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors

Concatenated Codes for Amplitude Damping

We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric errors, many new codes with good parameters are found, which are better than the amplitude damping codes obtained by any previously known construction.Comment: 5 page

Error suppression via complementary gauge choices in Reed-Muller codes

Concatenation of two quantum error correcting codes with complementary sets of transversal gates can provide a means towards universal fault-tolerant computation. We first show that it is generally preferable to choose the inner code with the higher pseudo-threshold in order to achieve lower logical failure rates. We then explore the threshold properties of a wide range of concatenation schemes. Notably, we demonstrate that the concatenation of complementary sets of Reed-Muller codes can increase the code capacity threshold under depolarizing noise when compared to extensions of previously proposed concatenation models. We also analyze the properties of logical errors under circuit level noise, showing that smaller codes perform better for all sampled physical error rates. Our work provides new insights into the performance of universal concatenated quantum codes for both code capacity and circuit level noise.Comment: 11 pages + 4 appendices, 6 figures. In v2, Fig.1 was added to conform to journal specification

Information-theoretic Physical Layer Security for Satellite Channels

Shannon introduced the classic model of a cryptosystem in 1949, where Eve has access to an identical copy of the cyphertext that Alice sends to Bob. Shannon defined perfect secrecy to be the case when the mutual information between the plaintext and the cyphertext is zero. Perfect secrecy is motivated by error-free transmission and requires that Bob and Alice share a secret key. Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the Shannon model assuming that the channels are noisy and proved that secrecy can be achieved without sharing a secret key. This model is called wiretap channel model and secrecy capacity is known when Eve's channel is noisier than Bob's channel. In this paper we review the concept of wiretap coding from the satellite channel viewpoint. We also review subsequently introduced stronger secrecy levels which can be numerically quantified and are keyless unconditionally secure under certain assumptions. We introduce the general construction of wiretap coding and analyse its applicability for a typical satellite channel. From our analysis we discuss the potential of keyless information theoretic physical layer security for satellite channels based on wiretap coding. We also identify system design implications for enabling simultaneous operation with additional information theoretic security protocols