Ramji Venkataramanan

Source Coding With Feed-Forward: Rate-Distortion Theorems and Error Exponents for a General Source

In this work, we consider a source coding model with feed-forward. We analyze a system with a noiseless, feed-forward link where the decoder has knowledge of all previous source samples while reconstructing the present sample. The rate-distortion function for an arbitrary source with feed-forward is derived in terms of directed information, a variant of mutual information. We further investigate the nature of the rate-distortion function with feed-forward for two common types of sources- discrete memory- less sources and Gaussian sources. We then characterize the error exponent for a general source with feed-forward. The results are then extended to feed-forward with an arbitrary delay larger than the block length.

Capacity-achieving Sparse Regression Codes via approximate message passing decoding

Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. In this code, the codewords are sparse linear combinations of columns of a design matrix. In this paper, we propose an approximate message passing decoder for sparse superposition codes. The complexity of the decoder scales linearly with the size of the design matrix. The performance of the decoder is rigorously analyzed and it is shown to asymptotically achieve the AWGN capacity. We also provide simulation results to demonstrate the performance of the decoder at finite block lengths, and introduce a power allocation that significantly improves the empirical performance.

An Achievable Rate Region for the Broadcast Channel With Feedback

A single-letter achievable rate region is proposed for the two-receiver discrete memoryless broadcast channel with generalized feedback. The coding strategy involves block-Markov superposition coding using Martons coding scheme for the broadcast channel without feedback as the starting point. If the message rates in the Marton scheme are too high to be decoded at the end of a block, each receiver is left with a list of messages compatible with its output. Resolution information is sent in the following block to enable each receiver to resolve its list. The key observation is that the resolution information of the first receiver is correlated with that of the second. This correlated information is efficiently transmitted via joint source-channel coding, using ideas similar to the Han-Costa coding scheme. Using the result, we obtain an achievable rate region for the stochastically degraded additive white Gaussian noise broadcast channel with noisy feedback from only one receiver. It is shown that this region is strictly larger than the no-feedback capacity region.

Lossy compression via sparse linear regression: Computationally efficient encoding and decoding

We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. Codewords are structured linear combinations of columns of a design matrix. The proposed encoding algorithm sequentially chooses columns of the design matrix to successively approximate the source sequence. It is shown to achieve the optimal distortion-rate function for i.i.d Gaussian sources with squared-error distortion. For a given rate, the parameters of the design matrix can be varied to trade off distortion performance with encoding complexity. An example of such a trade-off is: computational resource (space or time) per source sample of O((n/ log n)2) and probability of excess distortion decaying exponentially in n/ log n, where n is the block length. The Sparse Regression Code is robust in the following sense: for any ergodic source, the proposed encoder achieves the optimal distortion-rate function of an i.i.d Gaussian source with the same variance. Simulations show that the encoder has very good empirical performance, especially at low and moderate rates.

Achievable rates for channels with deletions and insertions

Consider a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit added after it with probability i, or it is transmitted unmodified with probability 1 - d - i. We obtain a lower bound on the capacity of this channel. The transformation of the input sequence by the channel may be viewed in terms of runs as follows: some runs of the input sequence get shorter/longer, some runs get deleted, and some new runs are added. The capacity is difficult to compute mainly due to the last two phenomena: deleted runs, and new inserted runs. We consider a decoder which first decodes the positions of the deleted and inserted runs, and then the transmitted codeword. Analyzing the performance of such a decoder leads to a computable lower bound on the capacity.

Lossy Compression via Sparse Linear Regression: Computationally Efficient Encoding and Decoding

We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. Codewords are structured linear combinations of columns of a design matrix. The proposed encoding algorithm sequentially chooses columns of the design matrix to successively approximate the source sequence. It is shown to achieve the optimal distortion-rate function for i.i.d Gaussian sources with squared-error distortion. For a given rate, the parameters of the design matrix can be varied to trade off distortion performance with encoding complexity. An example of such a trade-off is: computational resource (space or time) per source sample of O((n/ log n)2) and probability of excess distortion decaying exponentially in n/ log n, where n is the block length. The Sparse Regression Code is robust in the following sense: for any ergodic source, the proposed encoder achieves the optimal distortion-rate function of an i.i.d Gaussian source with the same variance. Simulations show that the encoder has very good empirical performance, especially at low and moderate rates.

Interactive low-complexity codes for synchronization from deletions and insertions

We study the problem of synchronization of two remotely located data sources, which are mis-synchronized due to deletions and insertions. This is an important problem since a small number of synchronization errors can induce a large Hamming distance between the two sources. The goal is to effect synchronization with the rate-efficient use of lossless bidirectional links between the two sources. In this work, we focus on the following model. A binary sequence X of length n is edited to generate the sequence at the remote end, say Y, where the editing involves random deletions and insertions, possibly in small bursts. The problem is to synchronize Y with X with minimal exchange of information (in terms of both the average communication rate and the average number of interactive rounds of communication). We focus here on the case where the number of edits is much smaller than n, and propose an interactive algorithm which is computationally simple and has near-optimal communication complexity. Our algorithm works by efficiently splitting the source sequence into pieces containing either just a single deletion/insertion or a single burst deletion/insertion. Each of these pieces is then synchronized using an optimal one-way synchronization code, based on the single-deletion correcting channel codes of Varshamov and Tenengolts (VT codes).

Gaussian rate-distortion via sparse linear regression over compact dictionaries

We study a class of codes for compressing memoryless Gaussian sources, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a design matrix. With minimum-distance encoding we show that such a codebook can attain the rate-distortion function with the optimal error-exponent, for all distortions below a specified value. The structure of the codebook is motivated by an analogous construction proposed recently by Barron and Joseph for communication over an AWGN channel.

A New Achievable Rate Region for the Multiple-Access Channel With Noiseless Feedback

A new single-letter achievable rate region is proposed for the two-user discrete memoryless multiple-access channel(MAC) with noiseless feedback. The proposed region includes the Cover-Leung rate region , and it is shown that the inclusion is strict. The proof uses a block-Markov superposition strategy based on the observation that the messages of the two users are correlated given the feedback. The rates of transmission are too high for each encoder to decode the others message directly using the feedback, so they transmit correlated information in the next block to learn the message of one another. They then cooperate in the following block to resolve the residual uncertainty of the decoder. The coding scheme may be viewed as a natural generalization of the Cover-Leung scheme with a delay of one extra block and a pair of additional auxiliary random variables. We compute the proposed rate region for two different MACs and compare the results with other known rate regions for the MAC with feedback. Finally, we show how the coding scheme can be extended to obtain larger rate regions with more auxiliary random variables.

A new achievable rate region for the discrete memoryless multiple-access channel with feedback

A single-letter achievable rate region for the two-user discrete memoryless multiple-access channel is proposed. The rate region includes the Cover-Leung region [1], and it is shown that the inclusion is strict. The proof uses a block-Markov superposition strategy based on the observation that the messages of the two users are correlated given the feedback. The rates of transmission are too high for each encoder to decode the others message directly using the feedback, so they transmit correlated information in the next block in order to learn the message of one another. They then cooperate in the following block to resolve the residual uncertainty of the decoder. Our scheme may be viewed as a natural generalization of the Cover-Leung scheme with a delay of one extra block and a pair of additional auxiliary random variables. The scheme can also be extended to obtain larger rate-regions with more auxiliary random variables.