A NEW H-ARQ SCHEME USING BCH CODES WITH UNEQUAL DATA AND PARITY FRAMES

Size: px

Start display at page:

Download "A NEW H-ARQ SCHEME USING BCH CODES WITH UNEQUAL DATA AND PARITY FRAMES"

Janel Skinner
5 years ago
Views:

1 A NEW H-ARQ SCHEME USING BCH CODES WITH UNEQUAL DATA AND ARITY FRAMES K.D.R. JAGATH-KUMARA Institute of Information Sciences & Technology, College of Sciences Massey University, RC2.56, Riddet Building, B 222, almerston North, New Zealand Abstract In this paper, a type of hybrid-arq protocol, which uses short parity frames for error correction in received data frames, is discussed. The new scheme exploits the low frame error rate suffered by short parity frames and the error correction capability of poweul BCH codes. The throughput of the new protocol is found using theoretical analysis and compared with normal ARQ protocols. Key-Words: Link rotocols, H-ARQ Schemes, BCH Codes. Introduction The general methods of error control in data communication links are forward error correction (FEC), overlaying an automatic repeat request (ARQ) scheme or using a combination of both which is referred to as hybrid-arq (H-ARQ). In both ARQ and HARQ, presence of errors is detected by using an error detecting code. In case of ARQ, upon detection of errors, a retransmission request or a negative acknowledgment (NAck) is sent back to the transmitter. The transmitter then will retransmit the same data frame. Broadly speaking, various H-ARQ schemes, transmits either a small amount of parity bits with the data frame for error correction or an equal size parity frame generated by a ½- rate code. In the later case, data frame can be recovered by inverting the parity frame or by normal error correction procedure, []. In the generalized version explained in [2] and [3], the code rate is continually varied to suit the channel condition by using punctured convolutional codes. The author proposes a new H-ARQ scheme which is different from Type and 2 explained in the previous publications. Here, the input data stream is first encoded by using a systematic error control code such as a BCH code. Next, the data frame consisting of only data bits are transmitted after appending CRC error detection overhead bits. The receiver will send back a NAck_ indicating that it needs parity bits if it detects errors in this data frame. The transmitter will then transmit only the parity frame generated during BCH encoding which is of much shorter length. Unlike in other types of H- ARQ, in this new scheme the parity frames are much shorter compared to the data frame and it is not included with a CRC error detection overhead. The receiver then will combine the parity frame with the original data frame and peorms the normal forward error correction. If the total number of errors in both frames is within the error correction capability of the code, the data frame will be corrected of errors. An Ack will be issued and the transmitter can send a new frame. Otherwise, the receiver can request either a copy of the same parity frame a few more times (NAck_) or a copy of the original data frame after only one attempt of error correction (NAck_D). In this paper, the second option is considered where a new data frame or the corresponding parity frame is transmitted alternatively in case of errors. The advantage of this method is that the parity frame consumes much less channel capacity than a full data frame and the error correction in the reconstructed codeword is likely to be successful even in only reasonably good channels. This will in turn improve the throughput because now the average number of bits transmitted per single correct bit is reduced. Further, the short frames are less likely to suffer from channel errors and the frame error rate of parity frames is very small compared to that of long data frames. This decreases the probability of large number of errors occurring in the parity frame and increases the chance of error correction in the data frame after combining. Therefore, the new scheme gains on throughput in two ways.

2 2. Theoretical Analysis The main tasks of the new protocol are error detection or error correction and generating NAck_s, NAck_Ds or Acks at the receiver, and BCH and CRC parity generation and transmission of data or parity frames at the transmitter. During the normal operation, the receiver can mainly be in one of the three states shown below. F: It has just received a new frame or a retransmission and errors are being detected using CRC : It has just received a parity frame and errors are being corrected using BCH E: The end state, i.e. the frame was either error free or errors were just corrected and waiting for the new frame F E - - robability that a parity frame is requested, (Nack_) robability that a retransmission of a data frame is requested, (Nack_D) Fig. : State Diagram The theoretical analysis of the new scheme takes into account the fact that a peect reverse channel is not available and acknowledgements may reach the transmitter with errors. Therefore, in this protocol, a reliable reverse channel is obtained by sending multiple but not excessive number of acknowledgements. For this either a separate control frame or an outgoing data frame can be used. To distinguish between NAck_s and NAck_Ds an additional -bit field is sufficient. By ensuring that the number of repeated acknowledgements are optimum, the average time delay associated with the transmission of a successful data frame, can be minimized. Normally, to keep the frame error rate (FER) below a certain limit, say 5%, the link is operated over given region of channel error probabilities only. The data transmission rate is usually reduced whenever the channel bit error probability rises to a certain threshold. Therefore, at a maximum FER of 5%, it is expected that only one out of two acknowledgements are lost and a reliable reverse channel can be obtained by repeating a given acknowledgement in more than two data or control frames. The BCH H-ARQ protocol described in this paper uses following control fields. C 32 bits, -byte for control and sequence number and 3-bytes for multiple acknowledgements C2 8 bits, for control and sequence number CRC 6-bits, CRC parity bits D Data field BCH arity field Therefore, the total length of a data frame, L D+CRC+C and the total length of a parity frame, L p +C2. Here, (D+C) and is made equal to k and (n-k) bits respectively as in BCH (n,k,t) codes. In case the control field is in error or the parity portion has excessive number of errors, the data frame will not be corrected and a retransmission of a copy of the data frame will be requested. An 8-bit field is used as the starting delimeter for all frames. Using the state diagram above, it is possible to derive an expression for the error-free throughput of the new H-ARQ protocol. The results are presented for different BCH codes where L is between 6-9 bits. These particular lengths have been selected because it has been found in [4] that the data frames of about 3- bits is likely to provide the highest average throughput in multi-path fading environments. These are compared with that of a selective repeat ARQ protocol realized using the same 6-bit CRC code for error detection in similarly sized data frames.

3 2. robability of Having to Transmit arity Frames Once a data frame of length L is received at the receiver, a NAck_ is generated in case it is found to contain errors by using CRC error detection. The probability of this event,, can be expressed by ( p) L () where p is the channel bit error probability. If this event occurs, a parity frame is sent to the receiver. 2.2 robability of Having to Retransmit Data Frames If the number of errors in both the data frame and the parity frame exceeds the error correction capability, t, of the BCH code, a copy of the data frame will be transmitted. The probability of this event,, can be expressed by [r ob( N () e > t)] (2) F+ where N F+ (e) is the number of bit errors in both data and parity frames. Therefore, t x { ( C [ p ( p) ] ( L CRC) x ( L CRC x) x t x ( ) [ y ( ) C y y p p ] y } ) 2.3 Long Term Average Throughput The throughput of BCH H-ARQ protocol is dependant on the lengths of data and control fields as well as on the average number of data and parity frames that has to be transmitted for successful transmission of one error-free data frame. Therefore, the error free average throughput, γ H-ARQ, can be found from (3) where D γ H ARQ (4) [( L+ S)( + m ) + ( L + Sm ) ] n p n m n the average number of data-frames retransmitted, except the original. m n the average number of parity frames transmitted. 2.4 Average Number of Data-Frame Retransmissions, m n As shown in the state diagram in Fig., it can be seen that the end state can be reached in two ways, via path or 2 with probabilities of (- ) and 2 (- ). Before that, depending on the condition of the channel, the events may have looped from states F to (F+), n- times with a probability of Loop (. ) n. Therefore, the probability of successful frame transmission after n- loops, after retransmitting n-data frames, can be expressed as S( n) Loop+ Loop2 (5) n n ( )( ) + ( ) ( ) where n, 2, 3, Therefore, the average number of retransmitted dataframes can be expressed by m n n n ( n) S (6) 2.5 Average Number of arity Frame Transmissions, m n Say, (n-) data frame and parity retransmissions have taken place, (n-)-loops in the state diagram with a probability of (. ) (n-). However, the probability that the data-frame is transmitted successfully only after one retransmission of a parity-frame or a data-frame is [(- ) + (- )]. Therefore, the probability of success after n-parity frame retransmissions, (n), can be expressed as

4 n ( ) ( ) [( ) ( )]( ) n + (7) where n, 2, 3,.. 23,883,4 23,848,8 23,88,22 23,768,26 23,728,3 23,78,34 Then, the average number of parity-frame transmissions can be found by m n n n ( n) For comparison, a normal selective repeat ARQ scheme with C field for multiple acknowledgements is used. The error free throughput of this scheme, γ ARQ, is given by γ ARQ D( FER) ( L+ S) (8) (9) Average normalised error-free throughpu Log (channel bit error probability) Fig. 2: Normalized Average Throughput of Various BCH H-ARQ Schemes/Random Bit Errors where the frame error rate, FER - (-p) (L-CRC). BCH H-ARQ CRC/ARQ The throughput can be further improved by using passive frame-error estimation methods described in [5] and [6]. These estimation techniques will not require the CRC parity overhead in reasonably good channels and therefore may improve the average throughput. 3. eormance of the New BCH H-ARQ rotocol The major peormance indicators of link protocols are the average error-free throughput and the average time delay associated with the successful frame transmission. The Fig. 2 and 3 show the throughput of the new H-ARQ scheme realized using the different BCH codes,[7], graphed against the channel bit error probability. It was assumed that the channel noise is Gaussian and introduces random bit errors to transmitted data or parity frames. With these BCH codes, the sizes of data frames, D, are 85, 86, 776, 736, 696 and 676 bits and the sizes of parity frames,, are 4, 75, 25, 255, 295 and 35 bits respectively. Average normalised error-free throughput Fig. 3: Comparison of Throughput with CRC/ARQ, for D85; 4; L899; L Conclusions -Log (channel bit error probability) It can be seen that the throughput of the new H- ARQ scheme is much higher compared to that of a normal CRC/ARQ-scheme implemented using the same data frame sizes. This is emphasized particularly at high error rates when the H-ARQ scheme is about 7 times better and provides a useable throughput. The normalized

5 throughput shoots up to.5 with the new H-ARQ while that with CRC/ARQ is near zero. The H-ARQ scheme, in this region, needs about 3-dB less power if the channel modulation is of type BSK. References: [] Shu Lin, hilips S Yu, A Hybrid ARQ Scheme with arity Retransmission for Error Control in Satellite Channels, IEEE Transactions on Communications, Vol. COM-3, No. 7, July 982 [2] Samir Kallel, David Haccoun, Generalized Type 2 Hybrid ARQ Scheme Using unctured Convolutional Coding, IEEE Transactions on Communications, Vol. 38, No., November 99 [3] Samir Kallel, Analysis of Memory and Incremental Redundancy ARQ Schemes Over a Nonstationary Channel, IEEE Transactions on Communications, Vol. 4, No. 9, September 992 [4] K. D. R. Jagath-Kumara, S.C.Cook, An Investigation of ARQ Frame Sizes for an HF TCM arallel-tone Modem, Second International Symposium on DS for Communication Systems, Adelaide, April 994 [5] K. D. R. Jagath-Kumara Automatic Generation of Retransmission Requests in ARQ/HARQ Schemes Using a New Decoder Metric, Third Asia acific Communications Conference, Sydney, 7- December 997 [6] K. D. R. Jagath-Kumara A New Frame Error Estimation Criterion for ARQ/HARQ Schemes, IEEE GLOBECOM98, Sydney, 8-2 November 998 [7] T. R. N. Rao, E. Fujiwara, Error control coding for computer systems, rentice Hall, New Jersey, 989

TSG-RAN Working Group 2 (Radio layer 2 and Radio layer 3) TSGR2#2(99)085 Stockholm 8th to 11th March 1999

TSG-RAN Working Group 2 (Radio layer 2 and Radio layer 3) TSGR2#2(99)085 Stockholm 8th to 11th March 1999 Agenda Item: 8.3.2 Source: Title: Document for: Siemens AG ARQ error control techniques Decision