On BICM receivers for TCM transmission

Recent results have shown that the performance of bit-interleaved coded modulation (BICM) using convolutional codes in nonfading channels can be significantly improved when the interleaver takes a trivial form (BICM-T), i.e., when it does not interleave the bits at all. In this paper, we give a formal explanation for these results and show that BICM-T is in fact the combination of a TCM transmitter and a BICM receiver. To predict the performance of BICM-T, a new type of distance spectrum for convolutional codes is introduced, analytical bounds based on this spectrum are developed, and asymptotic approximations are also presented. It is shown that the minimum distance of the code is not the relevant optimization criterion for BICM-T. Optimal convolutional codes for different constrain lengths are tabulated and asymptotic gains of about 2 dB are obtained. These gains are found to be the same as those obtained by Ungerboeck's one-dimensional trellis coded modulation (1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be asymptotically as good as 1D-TCM.Comment: Submitted to the IEEE Transactions on Communication

Variations of the McEliece Cryptosystem

Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed

A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions

Low-density parity-check (LDPC) convolutional codes (or spatially-coupled codes) were recently shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular performance is now called threshold saturation via spatial coupling. This new phenomenon is characterized by the belief-propagation threshold of the spatially-coupled ensemble increasing to an intrinsic noise threshold defined by the uncoupled system. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled scalar recursions. Our approach is based on constructing potential functions for both the coupled and uncoupled recursions. Our results actually show that the fixed point of the coupled recursion is essentially determined by the minimum of the uncoupled potential function and we refer to this phenomenon as Maxwell saturation. A variety of examples are considered including the density-evolution equations for: irregular LDPC codes on the BEC, irregular low-density generator matrix codes on the BEC, a class of generalized LDPC codes with BCH component codes, the joint iterative decoding of LDPC codes on intersymbol-interference channels with erasure noise, and the compressed sensing of random vectors with i.i.d. components.Comment: This article is an extended journal version of arXiv:1204.5703 and has now been accepted to the IEEE Transactions on Information Theory. This version adds additional explanation for some details and also corrects a number of small typo

AG codes and AG quantum codes from the GGS curve

In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all $\mathbb F_{q^2}$-rational points of the curve is determined; the Feng-Rao designed minimum distance is computed for infinite families of such codes, as well as the automorphism group. As a result, some linear codes with better relative parameters with respect to one-point Hermitian codes are discovered. Classes of quantum and convolutional codes are provided relying on the constructed AG codes