Jossy Sayir

Efficient DSP implementation of an LDPC decoder

We present a high performance implementation of a belief propagation decoder for decoding low-density parity-check (LDPC) codes on a fixed point digital signal processor. A simplified decoding algorithm was used and a stopping criteria for the iterative decoder was implemented to reduce the average number of required iterations. This leads to an implementation with increased throughput compared to other implementations of LDPC codes or turbo codes. This decoder is able to decode at 5.4 Mbps on a Texas Instruments TMS320C64xx DSP running at 600 MHz.

Optimization of LDPC Codes for Receiver Frontends

The degree distribution of low-density parity-check (LDPC) codes is optimized for systems that iterate over the receiver frontend, e.g., soft detector, demodulator, equalizer, etc., and the LDPC decoder. The overall extrinsic information transfer (EXIT) function of an iterative LDPC decoder is computed, based on the codes own EXIT chart, under the Gaussian assumption. While the optimization of the variable node distribution is a nonlinear problem, the optimization of the check node distribution is shown to be a linear problem. This fact is exploited to design codes where both the variable and the check node distributions are optimized, resulting in more robust constructions. The technique presented requires only knowledge of the measured EXIT function of the receiver frontend

On the transport capacity of Gaussian multiple access and broadcast channels

We study the transport capacity of a Gaussian multiple access channel, which consists of a set of transmitters and a single receiver. The transport capacity is defined as the sum, over all transmitters, of the product of the transmission rate with a reward r(x), which is a function of the distance x between the transmitter and the receiver, and quantifies the usefulness of the transmitting information over a distance x. Assuming that the sum of the transmitter powers is upper bounded, we present in closed form the optimal power allocation among the transmitters, that maximizes the transport capacity. We then present simple expressions for the optimal power allocation and induced transport capacity, as the number of transmitters approaches infinity. We also study the transport capacity of a Gaussian broadcast channel, which consists of a single transmitter and multiple receivers. Here, the transport capacity is defined as the sum, over all receivers, of the product of the transmission rate with a reward r(x). We determine in closed form the maximum possible transport capacity and the distribution of the available transmitter power among the receivers that achieve it. Although this result has already been reported in the literature, our derivation is shorter, and leads to simpler expressions. Our results can be used to gain intuition and develop good design principles in a variety of settings. For example, they apply to the uplink and downlink channel of cellular networks, and also to sensor networks which consist of multiple sensors that communicate with a single central station.

Challenges and some new directions in channel coding

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, non-binary LDPC codes, and polar coding.

Implementation of an LDPC decoder on a vector signal processor

A parallel processor architecture-a vector signal processor (VSP), which consists of independent computation units is presented. This architecture is used to implement the sum-product algorithm to decode low-density parity-check codes. The VSP is well suited for this parallel decoding algorithm which results in a scalable decoder that allows a tradeoff between chip area and data throughput. With increasing number of computation units a data throughput of up to 36.1 MBit per second can be achieved which outperforms existing implementations on digital signal processors.

Capacity results for asymmetric wireless networks

In this paper, we study wireless ad hoc networks that consist of n source nodes and m destination nodes, placed randomly in a two dimensional area. Each source node is creating data traffic that must be delivered to one of the m destination nodes, chosen at random. When m is on the order of n/sup d/ with 0<d< 1/2 , the capacity of the network is affected by the formation of bottlenecks around the destinations, and the maximum aggregate throughput is on the order of n/sup d/. If, however, 1/2 <d<1, an aggregate throughput on the order of n/sup 1/2 / is achievable. The scheme that achieves this aggregate throughput does not suffer from the formation of bottlenecks. These results hold under a general model of channel fading, and with probability going to 1 as n/spl rarr//spl infin/.

Iterating the Arimoto-Blahut algorithm for faster convergence

The Arimoto-Blahut algorithm determines the capacity of a discrete memoryless channel through an iterative process in which the input probability distribution is adapted at each iteration. While it converges towards the capacity-achieving distribution for any discrete memoryless channel, the convergence can be slow when the channel has a large input alphabet. This is unfortunate when only a small number of the input letters are assigned non-zero probabilities in the capacity-achieving distribution. If we knew which input letters will end up with a probability of zero, we could eliminate these letters and operate the algorithm on a subset of the input alphabet. The algorithm would converge towards the same solution faster. We present an algorithm which makes use of this fact to speed up the convergence of the Arimoto-Blahut algorithm in such situations.

Capacity of an extension of cover's two-look gaussian channel

We extend Covers two-look Gaussian channel to dispersive, linear, time-invariant channels. An arbitrary number of colored, additive, stationary, Gaussian noise/interference sources is considered. Each noise/interference source may cause correlated or uncorrelated components observed by the two looks. The novelty of this work is a capacity formula derived using the asymptotic eigenvalue distribution of block-Toeplitz matrices as well as the application of this result to wireline communications.

On the transport capacity of a multiple access Gaussian channel

We address the problem of maximizing the transport capacity of a wireless network, defined as the sum, over all transmitters, of the products of the transmission rate with a reward r(x), which is a function of the distance x separating the transmitter and its receiver. When r(x) = x, this product is measured in bps /spl times/ meters, and is the natural measure of the usefulness of a transmission in a multihop wireless ad hoc network. We first consider a single transmitter-receiver pair, and determine the optimal distance between the two that maximizes the rate-reward product, for reward functions of the form r(x) = x/sup /spl rho// and when the signal power decays with distance according to a power law. We then calculate the scheme that maximizes the transport capacity in a multiple access network consisting of a single receiver and a number of transmitters, each placed at a fixed distance from the receiver, and each with a fixed power constraint. We conclude by showing that when the per-transmitter power constraints are substituted with a single constraint on the sum of the powers, the maximum transport capacity and the power allocation scheme that achieves it can be found by solving a convex optimization problem.

Density evolution for SUDOKU codes on the erasure channel

Codes based on SUDOKU puzzles are discussed, and belief propagation decoding introduced for the erasure channel. Despite the non-linearity of the code constraints, it is argued that density evolution can be used to analyse code performance due to the invariance of the code under alphabet permutation. The belief propagation decoder for erasure channels operates by exchanging messages containing sets of possible values. Accordingly, density evolution tracks the probability mass functions of the set cardinalities. The equations governing the mapping of those probability mass functions are derived and calculated for variable and constraint nodes, and decoding thresholds are computed for long SUDOKU codes with random interleavers.