Lossy joint source-channel coding in the finite blocklength regime

This paper finds new tight finite-blocklength bounds for the best achievable lossy joint source-channel code rate, and demonstrates that joint source-channel code design brings considerable performance advantage over a separate one in the non-asymptotic regime. A joint source-channel code maps a block of $k$ source symbols onto a length$-n$ channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability $\epsilon$ that the distortion exceeds a given threshold $d$. For memoryless sources and channels, it is demonstrated that the parameters of the best joint source-channel code must satisfy $nC - kR(d) \approx \sqrt{nV + k \mathcal V(d)} Q(\epsilon)$, where $C$ and $V$ are the channel capacity and channel dispersion, respectively; $R(d)$ and $\mathcal V(d)$ are the source rate-distortion and rate-dispersion functions; and $Q$ is the standard Gaussian complementary cdf. Symbol-by-symbol (uncoded) transmission is known to achieve the Shannon limit when the source and channel satisfy a certain probabilistic matching condition. In this paper we show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the non-asymptotic regime

Faulty Successive Cancellation Decoding of Polar Codes for the Binary Erasure Channel

In this paper, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under this model, polarization does not happen, meaning that fully reliable communication is not possible at any rate. Furthermore, a lower bound on the frame error rate of polar codes under faulty SC decoding is provided, which is then used, along with a well-known upper bound, in order to choose a blocklength that minimizes the erasure probability under faulty decoding. Finally, an unequal error protection scheme that can re-enable asymptotically erasure-free transmission at a small rate loss and by protecting only a constant fraction of the decoder is proposed. The same scheme is also shown to significantly improve the finite-length performance of the faulty successive cancellation decoder by protecting as little as 1.5% of the decoder.Comment: Accepted for publications in the IEEE Transactions on Communication

Erasure Multiple Descriptions

We consider a binary erasure version of the n-channel multiple descriptions problem with symmetric descriptions, i.e., the rates of the n descriptions are the same and the distortion constraint depends only on the number of messages received. We consider the case where there is no excess rate for every k out of n descriptions. Our goal is to characterize the achievable distortions D_1, D_2,...,D_n. We measure the fidelity of reconstruction using two distortion criteria: an average-case distortion criterion, under which distortion is measured by taking the average of the per-letter distortion over all source sequences, and a worst-case distortion criterion, under which distortion is measured by taking the maximum of the per-letter distortion over all source sequences. We present achievability schemes, based on random binning for average-case distortion and systematic MDS (maximum distance separable) codes for worst-case distortion, and prove optimality results for the corresponding achievable distortion regions. We then use the binary erasure multiple descriptions setup to propose a layered coding framework for multiple descriptions, which we then apply to vector Gaussian multiple descriptions and prove its optimality for symmetric scalar Gaussian multiple descriptions with two levels of receivers and no excess rate for the central receiver. We also prove a new outer bound for the general multi-terminal source coding problem and use it to prove an optimality result for the robust binary erasure CEO problem. For the latter, we provide a tight lower bound on the distortion for \ell messages for any coding scheme that achieves the minimum achievable distortion for k messages where k is less than or equal to \ell.Comment: 48 pages, 2 figures, submitted to IEEE Trans. Inf. Theor