Existing quantum stabilizer codes constructed from the classic binary codes exclusively belong to the special subclass of Calderbank-Shor-Steane (CSS) codes. This paper fills in the gap by proposing five systematic constructions for non-CSS stabilizer codes, the first four of which are based on classic binary quasi-cyclic low-density parity-check (LDPC) codes and last on classic binary LDPC-convolutional codes. These new constructions exploit structured sparse graphs, make essential use of simple and powerful coding techniques including concatenation, rotation and scrambling, and generate rich classes of codes with a wide range of lengths and rates. We derive the sufficient, and in some cases also the necessary, conditions for each construction to satisfy the general symplectic inner product (SIP) condition, and develop practical decoder algorithms for these codes. The resulting codes are the first classes of non-CSS quantum LDPC codes and non-CSS quantum convolutional codes rooted from classic binary codes (rather than codes in GF(4)), and some of them perform as well as or better than the existing quantum codes.

This paper proposes a novel construction of analog codes based on nonlinear chaotic dynamical systems in general and the tent map in particular. In light of the importance of the symbolic coding in estimating tent chaos, the proposed construction exploit useful ideas of interleaving and parallel concatenation from classical coding theory to protect symbolic coding and subsequently chaotic states. The resultant new codes, dubbed chaotic analog turbo (CAT) codes, extend Chen-Wornell codes, in a spirit close to that of digital turbo codes extending digital convolutional codes. A new sequence detection method that improves the existing backward detection method is also developed. Through analysis and simulations, it is shown that CAT codes can noticeably outperform the existing analog ones.

This paper proposes efficient construction of new classes of quantum low-density parity-check (LDPC) codes through quasi-cyclic matrices, symmetric matrices and scrambling matrices. Unlike many of the existing quantum LDPC codes, the proposed construction is based on classic binary codes rather than quaternary codes, targets the general stabilizer formalism rather than the special CSS formalism, employs systematic approaches rather than computer search, and generates a rich class of codes of different rates and lengths rather than a single code. Simulations demonstrate that these new codes outperform the existing non-CSS LDPC stabilizer codes reported in literature.

Stabilizer codes are an important branch of quantum codes, but the existing stabilizer codes constructed from the classical binary codes almost exclusively belong to the special subclass of CSS codes. This paper develops simple and systematic constructions for two rich classes of non-CSS quantum stabilizer codes: quantum low density parity check (LDPC) codes based on classical quasi-cyclic LDPC codes and quantum convolutional codes based on classical LDPC-convolutional codes. Both classes enjoy a wide range of lengths and rates, and offer stronger error correction capability than the existing codes.

We investigate the self error resilience of practical distributed source coding (DSC) approaches at the presence of residual transmission errors. It is firstly shown that the existing asymmetric syndrome-former inverse-syndrome-former framework (ASIF), although simple, general and optimal for the noiseless-channel case, is not sustainable to transmission errors. The vulnerability stems from the underlying binning approach. Using ideas from channel coding, we illuminate a subtle relation between the binning approach and the parity approach, and demonstrate, through the examples of convolutional codes, how the former can be transformed to the latter for stronger self error resilience. Simulation results confirm that the new scheme is much more robust and less error-sensitive than the existing ASIF scheme