Capacity-Achieving Ensembles of Accumulate-Repeat-Accumulate Codes for the Erasure Channel with Bounded Complexity

The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with {\em bounded complexity}, per information bit, of encoding and decoding. It also introduces symmetry properties which play a central role in the construction of capacity-achieving ensembles for the BEC with bounded complexity. The results here improve on the tradeoff between performance and complexity provided by previous constructions of capacity-achieving ensembles of codes defined on graphs. The superiority of ARA codes with moderate to large block length is exemplified by computer simulations which compare their performance with those of previously reported capacity-achieving ensembles of LDPC and IRA codes. The ARA codes also have the advantage of being systematic.Comment: Submitted to IEEE Trans. on Information Theory, December 1st, 2005. Includes 50 pages and 13 figure

Investigation of Frame Alignments for GMM-based Digit-prompted Speaker Verification

Frame alignments can be computed by different methods in GMM-based speaker verification. By incorporating a phonetic Gaussian mixture model (PGMM), we are able to compare the performance using alignments extracted from the deep neural networks (DNN) and the conventional hidden Markov model (HMM) in digit-prompted speaker verification. Based on the different characteristics of these two alignments, we present a novel content verification method to improve the system security without much computational overhead. Our experiments on the RSR2015 Part-3 digit-prompted task show that, the DNN based alignment performs on par with the HMM alignment. The results also demonstrate the effectiveness of the proposed Kullback-Leibler (KL) divergence based scoring to reject speech with incorrect pass-phrases.Comment: accepted by APSIPA ASC 201

On Linear Operator Channels over Finite Fields

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size. Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant. The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated. Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.Comment: 53 pages, 3 figures, submitted to IEEE Transaction on Information Theor

Interference alignment for the MIMO interference channel

We study vector space interference alignment for the MIMO interference channel with no time or frequency diversity, and no symbol extensions. We prove both necessary and sufficient conditions for alignment. In particular, we characterize the feasibility of alignment for the symmetric three-user channel where all users transmit along d dimensions, all transmitters have M antennas and all receivers have N antennas, as well as feasibility of alignment for the fully symmetric (M=N) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a K-user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.Comment: 16 pages, 7 figures, final submitted versio

A General Framework for Transmission with Transceiver Distortion and Some Applications

A general theoretical framework is presented for analyzing information transmission over Gaussian channels with memoryless transceiver distortion, which encompasses various nonlinear distortion models including transmit-side clipping, receive-side analog-to-digital conversion, and others. The framework is based on the so-called generalized mutual information (GMI), and the analysis in particular benefits from the setup of Gaussian codebook ensemble and nearest-neighbor decoding, for which it is established that the GMI takes a general form analogous to the channel capacity of undistorted Gaussian channels, with a reduced "effective" signal-to-noise ratio (SNR) that depends on the nominal SNR and the distortion model. When applied to specific distortion models, an array of results of engineering relevance is obtained. For channels with transmit-side distortion only, it is shown that a conventional approach, which treats the distorted signal as the sum of the original signal part and a uncorrelated distortion part, achieves the GMI. For channels with output quantization, closed-form expressions are obtained for the effective SNR and the GMI, and related optimization problems are formulated and solved for quantizer design. Finally, super-Nyquist sampling is analyzed within the general framework, and it is shown that sampling beyond the Nyquist rate increases the GMI for all SNR. For example, with a binary symmetric output quantization, information rates exceeding one bit per channel use are achievable by sampling the output at four times the Nyquist rate.Comment: 32 pages (including 4 figures, 5 tables, and auxiliary materials); submitted to IEEE Transactions on Communication