Mismatched Decoding Reliability Function at Zero Rate

We derive an upper bound on the reliability function of mismatched decoding for zero-rate codes. The bound is based on a result by Koml ́os that shows the existence of a subcode with certain symmetry properties. The bound is shown to coincide with the expurgated exponent at rate zero for a broad family of channel-decoding metric pairs.ERC grant ITU

MIMO block-fading channels with mismatched CSI

YesWe study transmission over multiple-input multiple-output (MIMO) block-fading channels with imperfect channel state information (CSI) at both the transmitter and receiver. Specifically, based on mismatched decoding theory for a fixed channel realization, we investigate the largest achievable rates with independent and identically distributed inputs and a nearest neighbor decoder. We then study the corresponding information outage probability in the high signal-to-noise ratio (SNR) regime and analyze the interplay between estimation error variances at the transmitter and at the receiver to determine the optimal outage exponent, defined as the high-SNR slope of the outage probability plotted in a logarithmic-logarithmic scale against the SNR. We demonstrate that despite operating with imperfect CSI, power adaptation can offer substantial gains in terms of outage exponent.A. T. Asyhari was supported in part by the Yousef Jameel Scholarship, University of Cambridge, Cambridge, U.K., and the National Science Council of Taiwan under grant NSC 102-2218-E-009-001. A. Guillén i Fàbregas was supported in part by the European Research Council under ERC grant agreement 259663 and the Spanish Ministry of Economy and Competitiveness under grant TEC2012-38800-C03-03

Mismatched decoding: Error exponents, second-order rates and saddlepoint approximations

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error exponents and second-order coding rates matching those of constant-composition random coding, while being directly applicable to channels with infinite or continuous alphabets. The number of auxiliary costs required to match the error exponents and second-order rates of constant-composition coding is studied, and is shown to be at most two. For independent identically distributed random coding, asymptotic estimates of two well-known non-asymptotic bounds are given using saddlepoint approximations. Each expression is shown to characterize the asymptotic behavior of the corresponding random-coding bound at both fixed and varying rates, thus unifying the regimes characterized by error exponents, second-order rates, and moderate deviations. For fixed rates, novel exact asymptotics expressions are obtained to within a multiplicative 1+o(1) term. Using numerical examples, it is shown that the saddlepoint approximations are highly accurate even at short block lengths.This work was supported in part by the European Research Council under Grant 259663, in part by the European Union’s 7th Framework Programme under Grant 303633, and in part by the Spanish Ministry of Economy and Competitiveness under Grants RYC-2011-08150 and TEC2012-38800-C03-03

Mismatched Multi-Letter Successive Decoding for the Multiple-Access Channel

This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is considered, and achievable rate regions and error exponents are derived both for the standard MAC (independent codebooks), and for the cognitive MAC (one user knows both messages) with superposition coding. In the cognitive case, the rate region and error exponent are shown to be tight with respect to the ensemble average. The rate regions are compared with those of the commonly considered decoder that chooses the message pair maximizing the decoding metric, and numerical examples are given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions.This work was supported in part by the European Research Council through ERC under Grant 259663 and Grant 725411, in part by the European Union’s 7th Framework Programme under Grant 303633, and in part by the Spanish Ministry of Economy and Competitiveness under Grant RYC-2011-08150, Grant TEC2012-38800-C03- 03, and Grant TEC2016-78434-C3-1-R

An achievable error exponent for the mismatched multiple-access channel

This paper considers channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. Using constant-composition random coding, an achievable error exponent is obtained which is tight with respect to the ensemble average, and positive for all rate pairs in the interior of Lapidoth's achievable rate region. © 2012 IEEE

MIMO block-fading channels with mismatched CSI

We study transmission over multiple-input multiple-output block-fading channels with imperfect channel state information (CSI) at both the transmitter and receiver. In particular, based on mismatched decoding theory for a fixed channel realization, we investigate the largest achievable rates with independent and identically distributed inputs and the nearest neighbor decoder. We then study the corresponding information outage probability in the high signal-to-noise ratio (SNR) regime and analyze the interplay between estimation error variances at the transmitter and receiver to determine the optimal outage exponent, defined as the high-SNR slope of the outage probability plotted in a logarithmic-logarithmic scale against the SNR. We demonstrate that despite operating with imperfect CSI, power adaptation can offer substantial gains in terms of outage exponent

Shaping Bits

The performance of bit-interleaved coded modulation (BICM) with bit shaping (i.e., non-equiprobable bit probabilities in the underlying binary code) is studied. For the Gaussian channel, the rates achievable with BICM and bit shaping are practically identical to those of coded modulation or multilevel coding. This identity holds for the whole range of values of signal-to-noise ratio. Moreover, the random coding error exponent of BICM significantly exceeds that of multilevel coding and is very close to that of coded modulation

Efficient Systematic Encoding of Non-binary VT Codes

This paper addresses the problem of efficient encoding of non-binary Varshamov-Tenengolts (VT) codes. We propose a linear-time encoding method to systematically map binary message sequences onto VT codewords. The method provides a new lower bound on the size of q-ary VT codes of length n

Multilayer Codes for Synchronization from Deletions and Insertions

Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence X differs from the decoder's sequence Y by a small number of edits (deletions and insertions). The goal is to construct a message M, to be sent via a one-way error free link, such that the decoder can reconstruct X using M and Y. In this paper, we devise a coding scheme for this one-way synchronization model. The scheme is based on multiple layers of Varshamov-Tenengolts (VT) codes combined with off-the-shelf linear error-correcting codes, and uses a list decoder. We bound the expected list size of the decoder under certain assumptions, and validate its performance via numerical simulations. We also consider an alternative decoder that uses only the constraints from the VT codes (i.e., does not require a linear code), and has a smaller redundancy at the expense of a slightly larger average list size

Coding for Segmented Edit Channels.

We consider insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. No segment markers are available in the received sequence. We propose code constructions for the segmented deletion, segmented insertion, and segmented insertion-deletion channels based on subsets of Varshamov-Tenengolts codes chosen with pre-determined prefixes and/or suffixes. The proposed codes, constructed for any finite alphabet, are zero-error and can be decoded segment-by-segment. We also derive an upper bound on the rate of any zero-error code for the segmented edit channel, in terms of the segment length. This upper bound shows that the rate scaling of the proposed codes as the segment length increases is the same as that of the maximal code