Sequential decoding

About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.

On the iterative approximation of optimal joint source-channel decoding

Abstract: Joint source-channel decoding is formulated as an estimation problem. The optimal solution is stated and it is shown that it is not feasible in many practical systems due to its complexity. Therefore, a novel iterative procedure for the approximation of the optimal solution is introduced, which is based on the principle of iterative decoding of turbo codes. New analytical expressions for different types of information in the optimal algorithm are used to derive the iterative approximation. A direct comparison of the performance of the optimal algorithm and its iterative approximation is given for a simple transmission system with "short" channel codewords. Furthermore, the performance of iterative joint source-channel decoding is investigated for a more realistic system.

On information transmission over a finite buffer channel

Abstract: We study information transmission through a finite buffer queue. We model the channel as a finite-state channel whose state is given by the buffer occupancy upon packet arrival; a loss occurs when a packet arrives to a full queue. We study this problem in two contexts: one where the state of the buffer is known at the receiver, and the other where it is unknown. In the former case, we show that the capacity of the channel depends on the long-term loss probability of the buffer. Thus, even though the channel itself has memory, the capacity depends only on the stationary loss probability of the buffer. The main focus of this correspondence is on the latter case. When the receiver does not know the buffer state, this leads to the study of deletion channels, where symbols are randomly dropped and a subsequence of the transmitted symbols is received. In deletion channels, unlike erasure channels, there is no side-information about which symbols are dropped. We study the achievable rate for deletion channels, and focus our attention on simple (mismatched) decoding schemes. We show that even with simple decoding schemes, with independent and identically distributed (i.i.d.) input codebooks, the achievable rate in deletion channels differs from that of erasure channels by at most H0(pd)-pd logK/(K-1) bits, for pd<1-K-1, where p d is the deletion probability, K is the alphabet size, and H 0(middot) is the binary entropy function. Therefore, the difference in transmission rates between the erasure and deletion channels is not large for reasonable alphabet sizes. We also develop sharper lower bounds with the simple decoding framework for the deletion channel by analyzing it for Markovian codebooks. Here, it is shown that the difference between the deletion and erasure capacities is even smaller than that with i.i.d. input codebooks and for a larger range of deletion probabilities. We also examine the noisy deletion channel where a deletion channel is cascaded with a symmetric discrete memoryless channel (DMC). We derive a single letter expression for an achievable rate for such channels. For the binary case, we show that this result simplifies to max(0,1-[H0(thetas)+thetasH0(p e)]) where pe is the cross-over probability for the binary symmetric channel

Decoding one out of many

Abstract: Generic decoding of linear codes is the best known attack against most code-based cryptosystems. Understanding and measuring the complexity of the best decoding techniques is thus necessary to select secure parameters. We consider here the possibility that an attacker has access to many cryptograms and is satisfied by decrypting (i.e. decoding) only one of them. We show that, for the parameter range corresponding to the McEliece encryption scheme, a variant of Stern's collision decoding can be adapted to gain a factor almost $\sqrt{N}$ when N instances are given. If the attacker has access to an unlimited number of instances, we show that the attack complexity is significantly lower, in fact the number of security bits is divided by a number slightly smaller than 3/2 (but larger than 1). Finally we give indications on how to counter those attacks.

A Fast Polar Code List Decoder Architecture Based on Sphere Decoding

Abstract: Polar codes are a recently discovered family of capacity-achieving error-correcting codes. Among the proposed decoding algorithms, successive-cancellation list decoding guarantees the best error-correction performance with codes of moderate lengths, but it yields low throughput. Speed-up techniques have been proposed in the past: most of them rely on approximations that degrade the error-correction capability of the algorithm. We propose a speed-up technique for successive-cancellation list decoding of polar codes that is exact for list size of 2, while its approximations bring negligible error-correction performance degradation ( $3.16\times $ , at the cost of 14.2% in area occupation.

Quantum Serial Turbo Codes

Abstract: In this paper, we present a theory of quantum serial turbo codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum low-density parity-check (LDPC) codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Second, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular, its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoders have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be noncatastrophic and nonrecursive. While the resulting families of turbo codes have bounded minimum distance, from a pragmatic point of view, the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well-chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases.