Yonatan Kaspi

Error Exponents for Broadcast Channels With Degraded Message Sets

We consider a broadcast channel with a degraded message set, in which a single transmitter sends a common message to two receivers and a private message to one of the receivers only. The main goal of this work is to find new lower bounds to the error exponents of the strong user, the one that should decode both messages, and of the weak user, that should decode only the common message. Unlike previous works, where suboptimal decoders were used, the exponents we derive in this work pertain to optimal decoding and depend on both rates. We take two different approaches. The first approach is based, in part, on variations of Gallager-type bounding techniques that were presented in a much earlier work on error exponents for erasure/list decoding. The resulting lower bounds are quite simple to understand and to compute. The second approach is based on a technique that is rooted in statistical physics, and it is exponentially tight from the initial step and onward. This technique is based on analyzing the statistics of certain enumerators. Numerical results show that the bounds obtained by this technique are tighter than those obtained by the first approach and previous results. The derivation, however, is more complex than the first approach and the retrieved exponents are harder to compute.

Structure Theorems for Real-Time Variable Rate Coding With and Without Side Information

The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate. Structure theorems, pertaining to the encoder and next-state functions, are derived for every given finite-state decoder, which can have access to side information.

Zero-Delay and Causal Single-User and Multi-User Lossy Source Coding with Decoder Side Information

We consider zero-delay, single-user, and multi-user source coding with an average distortion constraint and decoder side information. The zero-delay constraint translates into causal (sequential) encoder and decoder pairs as well as the use of instantaneous codes. For the single-user setting, we show that optimal performance is attained by time sharing at most two scalar encoder-decoder pairs, that use zero-error side information codes. Side information look-ahead is shown to be useless in this setting. Furthermore, we show that even without delay constraints, if either the encoder or decoder are restricted a priori to be scalar, the performance loss cannot be compensated by the other component, which can be scalar as well without further loss. Finally, we show that the multi-terminal source coding problem can be solved in the zero-delay regime and the rate-distortion region is provided.

Zero-Delay and Causal Secure Source Coding

We investigate the combination between causal/zero-delay source coding and information-theoretic secrecy. Two source coding models with secrecy constraints are considered. We start by considering zero-delay perfectly secret lossless transmission of a memoryless source. We derive bounds on the key rate and coding rate needed for perfect zero-delay secrecy. In this setting, we consider two models that differ by the ability of the eavesdropper to parse the bit-stream passing from the encoder to the legitimate decoder into separate messages. We also consider causal source coding with a fidelity criterion and side information at the decoder and the eavesdropper. Unlike the zero-delay setting where variable-length coding is traditionally used but might leak information on the source through the length of the codewords, in this setting, since delay is allowed, block coding is possible. We show that in this setting, a separation of encryption and causal source coding is optimal.

Error exponents of optimum decoding for the degraded broadcast channel using moments of type class enumerators

The analysis of random coding error exponents pertaining to optimal decoding in a degraded broadcast with degraded message sets is revisited. Instead of using Jensens inequality as well as some other inequalities in the derivation, we demonstrate that, after an initial step, an exponentially tight analysis can be carried out by assessing the relevant moments of a certain type class enumerator.

Error exponents for degraded broadcast channels with degraded message sets

We consider a degraded broadcast channel with maximum likelihood decoders and derive lower bounds on the error exponent of each user. Unlike earlier results, our exponents pertain to optimal decoding and include both rates.

Error exponents for optimum decoding of the degraded broadcast channel using moments of type class enumerators

The analysis of random coding error exponents pertaining to optimal decoding in a degraded broadcast with degraded message sets is revisited. Instead of using Jensens inequality as well as some other inequalities in the derivation, we demonstrate that, after an initial step, an exponentially tight analysis can be carried out by assessing the relevant moments of a certain type class enumerator.

On real-time and causal secure source coding

We investigate two source coding problems with secrecy constraints. In the first problem we consider real-time fully secure transmission of a memoryless source. We show that although classical variable-rate coding is not an option since the lengths of the codewords leak information on the source, the key rate can be as low as the average Huffman codeword length of the source. In the second problem we consider causal source coding with a fidelity criterion and side information at the decoder and the eavesdropper. We show that when the eavesdropper has degraded side information, it is optimal to first use a causal rate distortion code and then encrypt its output with a key.

The zero-delay Wyner-Ziv problem

We consider the zero-delay version of the Wyner-Ziv problem. The zero-delay constraint translates into causal (sequential) encoder and decoder pairs as well as the use of instantaneous codes. We show that optimal performance is attained by time sharing at most two scalar encoder-decoder pairs, that use zero-error side information codes. Side information lookahead is shown to be useless in this setting. We show that the restriction to causal encoding functions is the one that causes the performance degradation, compared to unrestricted systems, and not the sequential decoders or instantaneous codes.

On zero-delay lossy source coding with side information at the decoder

We consider real-time, variable-rate lossy source coding in the presence of side information (SI) at the decoder. We show that time-sharing at most two scalar encoder-decoder pairs achieves optimal performance. We further demonstrate that in this setting, increasing the number of quantization levels can reduce the minimum average rate. Finally, two structure theorems, pertaining to source- or SI look-ahead are given.